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Axioms
Number of Followers: 1  Open Access journalISSN (Online) 2075-1680 Published by MDPI  [84 journals]
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- Axioms, Vol. 11, Pages 300: Smooth Versions of the
Mann–Whitney–Wilcoxon Statistics
Authors: Netti Herawati, Ibrahim A. Ahmad
First page: 300
Abstract: The well-known Mann–Whitney–Wilcoxon (MWW) statistic is based on empirical distribution estimates. However, the data are often drawn from smooth populations. Therefore, the smoothness characteristic is not preserved. In addition, several authors have pointed out that empirical distribution is often an inadmissible estimate. Thus, in this work, we develop smooth versions of the MWW statistic based on smooth distribution function estimates. This approach preserves the data characteristics and allows the efficiency of the procedure to improve. In addition, our procedure is shown to be robust against a large class of dependent observations. Hence, by choosing a rectangular array of known distribution functions, our procedure allows the test to be a lot more reflective of the real data.
Citation: Axioms
PubDate: 2022-06-21
DOI: 10.3390/axioms11070300
Issue No: Vol. 11, No. 7 (2022)
- Axioms, Vol. 11, Pages 301: New Theorems in Solving Families of Improper
Integrals
Authors: Mohammad Abu Ghuwaleh, Rania Saadeh, Aliaa Burqan
First page: 301
Abstract: Many improper integrals appear in the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik. It is a challenge for some researchers to determine the method in which these integrations are formed or solved. In this article, we present some new theorems to solve different families of improper integrals. In addition, we establish new formulas of integrations that cannot be solved by mathematical software such as Mathematica or Maple. In this article, we present three main theorems that are essential in generating new formulas for solving improper integrals. To show the efficiency and the simplicity of the presented techniques, we present some applications and examples on integrations that cannot be solved by regular methods. Furthermore, we acquire new results for integrations and compare them to that obtained in the classical table of integrations. Some previous results, become special cases of our outcomes or generalizations to acquire new integrals.
Citation: Axioms
PubDate: 2022-06-21
DOI: 10.3390/axioms11070301
Issue No: Vol. 11, No. 7 (2022)
- Axioms, Vol. 11, Pages 302: Information Measures Based on T-Spherical
Fuzzy Sets and Their Applications in Decision Making and Pattern
Recognition
Authors: Xiaomin Shen, Sidra Sakhi, Kifayat Ullah, Muhammad Nabeel Abid, Yun Jin
First page: 302
Abstract: The T-spherical fuzzy set (TSFS) is a modification of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), q-rung orthopair fuzzy set (q-ROFS), and picture fuzzy set (PFS), with three characteristic functions: the membership degree (MD) denoted by , the nonmembership degree (NMD) denoted by , and the abstinence degree (AD) denoted by . It can be used to solve problems of uncertain information with no restrictions. The distance measure (DM) is a tool that sums up the difference between points, while the similarity measure (SM) is a method applied to calculate the similarity between objects within an interval of . The current work aims to introduce novel DMs and SMs in the environment of TSFSs to show the limitations of the previously defined DMs and SMs. The suggested DMs and SMs provide more room for all three degrees to be selected without restriction. We investigated the effectiveness of the proposed DMs and SMs by applying a pattern-recognition technique, and we determined their applicability for multicriteria decision making (MCDM) using numerical examples. The newly proposed DMs and SMs are briefly compared to existing DMs and SMs, and appropriate conclusions are drawn.
Citation: Axioms
PubDate: 2022-06-21
DOI: 10.3390/axioms11070302
Issue No: Vol. 11, No. 7 (2022)
- Axioms, Vol. 11, Pages 303: A Simultaneous Estimation of the Baseline
Intensity and Parameters for Modulated Renewal Processes
Authors: Jiancang Zhuang, Hai-Yen Siew
First page: 303
Abstract: This paper proposes a semiparametric solution to estimate the intensity (hazard) function of modulated renewal processes: a nonparametric estimate for the baseline intensity function together with a parametric estimate of the model parameters of the covariate processes. Based on the martingale property associated with the conditional intensity, we construct a statistic from a residual analysis to estimate the baseline renewal intensity function, when the model parameters of the covariate processes are known. In addition, when the baseline intensity is obtained, the model parameters can be estimated using the usual maximum likelihood estimation. In practice, both the baseline intensity and model parameters are suggested to be estimated simultaneously via an expectation–maximization (E–M)-type iterative algorithm. A more important feature of the newly proposed algorithm is that, given n events in the observation dataset, its computation time is of order O(n2), while the Nelson–Aalen–Breslow estimator takes a computation time of order O(n3). For illustration, we apply the proposed estimation procedure to a set of data simulated from a modulated gamma renewal process and the aftershock sequence following the Ms8 Wenchuan earthquake, which occurred in Sichuan Province, China on 12 May 2008.
Citation: Axioms
PubDate: 2022-06-23
DOI: 10.3390/axioms11070303
Issue No: Vol. 11, No. 7 (2022)
- Axioms, Vol. 11, Pages 304: Several Double Inequalities for Integer Powers
of the Sinc and Sinhc Functions with Applications to the
Neuman–Sándor Mean and the First Seiffert Mean
Authors: Wen-Hui Li, Qi-Xia Shen, Bai-Ni Guo
First page: 304
Abstract: In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the first Seiffert mean.
Citation: Axioms
PubDate: 2022-06-23
DOI: 10.3390/axioms11070304
Issue No: Vol. 11, No. 7 (2022)
- Axioms, Vol. 11, Pages 305: Software Defects Prediction Based on Hybrid
Beetle Antennae Search Algorithm and Artificial Bee Colony Algorithm with
Comparison
Authors: Ya Zhang, Tong Li, Zhen Li, Yu-Mei Wu, Hong Miao
First page: 305
Abstract: Software defects are problems in software that destroy normal operation ability and reflect the quality of the software. Software fault can be predicted by the software reliability model. In this paper, the hybrid algorithm is applied to parameter estimation in software defect prediction. As a biological heuristic algorithm, BAS (Beetle Antennae Search Algorithm) has fast convergence speed and is easy to implement. ABC (Artificial Bee Colony Algorithm) is better in optimization and has strong robustness. In this paper, the BAS-ABC hybrid algorithm is proposed by mixing the two algorithms and the goal of the proposed method is to improve the convergence and stability of the algorithm. Five datasets were used to carry out the experiments, and the data results showed that the hybrid algorithm was more accurate than the single algorithm, with stronger convergence and stability, so it was more suitable for parameter estimation of the software reliability model. Meanwhile, this paper implemented the comparison between hybrid BAS + ABC and hybrid PSO + SSA, and the result shows that BAS + ABC has better performance both in convergence and stability. The comparison result shows the strong ability in estimation and prediction of software defects hybrid BAS and ABC.
Citation: Axioms
PubDate: 2022-06-24
DOI: 10.3390/axioms11070305
Issue No: Vol. 11, No. 7 (2022)
- Axioms, Vol. 11, Pages 244: A Spatially Bounded Airspace Axiom
Authors: Peter Szabó, Miroslava Ferencová, Monika Blišťanová
First page: 244
Abstract: Free Route Airspace (FRA), a new concept implemented across European airspace, is designed to eliminate the adverse effects of air traffic, reduce fuel consumption, simplify and expand flight planning. In our research, we model FRA system by using graph theory and we use networks and convex analysis to study it. We work with 2-dimensional space defined by latitude a longitude. We know that the basic mathematical properties of a scientific discipline can be expressed using mathematical axioms. Therefore, in our work, we sought to answer the question, what are the basic mathematical properties of airspace' We found a mathematical object that can describe airspace in general. Using this object, we uttered an axiom describing airspace. Our axiom is given by means of practical, significant entry and entry-exit points in the airspace.
Citation: Axioms
PubDate: 2022-05-24
DOI: 10.3390/axioms11060244
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 245: Macdonald Formula, Ricci Curvature, and
Concentration Locus for Classical Compact Lie Groups
Authors: Sergio Cacciatori, Pietro Ursino
First page: 245
Abstract: We consider the phenomenon of concentration of measures, which is restricted to the case of families of compact connected Lie groups. While in the literature, powerful general results regarding the existence of concentration and its relations to extremal amenability of infinite dimensional groups have been determined, there are few explicit examples, specially regarding the determination of the region where the measure concentrates. Since they can be relevant for concrete applications, both in mathematics and in physics, in the present paper, we provide a number of such examples, using compact Lie groups as basic ingredients. In particular, our strategy is to employ the Macdonald’s formula, giving the volume of compact simple Lie groups, and Ricci curvature of the bi-invariant metric for analyzing a “concentration locus”, which is a tool to detect where a sequence of metric, Borel measurable spaces concentrates its measure.
Citation: Axioms
PubDate: 2022-05-24
DOI: 10.3390/axioms11060245
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 246: Adaptive Enhancement for Coal-Rock Cutting
Sound Based on Parameter Self-Tuning Bistable Stochastic Resonance Model
Authors: Jie Xu, Jing Xu, Chaofan Ren, Yanxin Liu, Ning Sun
First page: 246
Abstract: The traditional bistable stochastic resonance model has always had the drawback of being difficult when choosing accurate system parameters when a weak signal is enhanced. This paper proposes a parameter self-tuning adaptive optimization method based on the bat optimization algorithm to address this issue. The cubic mapping strategy of chaos optimization is introduced in the initial process of the individual position of the bat algorithm. Chaos is characterized by randomness, sensitivity, fractal dimension, and universality. The initial problem of the algorithm falling into local extremums is overcome. The global search capability of the basic bat optimization algorithm has been improved. The improved bat optimization algorithm’s objective function is the signal-to-noise ratio (SNR) of the target weak signal output by the bistable stochastic resonance model. An adaptive signal enhancement algorithm based on the improved bat optimization algorithm and bistable stochastic resonance (IBA-BSR) model is constructed to increase the proportion of weak signals in the mixed signal. Simulation signals are created to validate the proposed algorithm’s feasibility. The engineering application effect of this algorithm is further demonstrated by enhancing the sound signal of coal and rock cutting by a shearer in a coal face. Engineering test results demonstrate that this algorithm can significantly increase the SNR of coal and rock cutting sound signals by 42.4537 dB, and the effect is remarkable.
Citation: Axioms
PubDate: 2022-05-25
DOI: 10.3390/axioms11060246
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 247: Exact Solutions of Nonlinear Partial
Differential Equations via the New Double Integral Transform Combined with
Iterative Method
Authors: Shams A. Ahmed, Ahmad Qazza, Rania Saadeh
First page: 247
Abstract: This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs.
Citation: Axioms
PubDate: 2022-05-25
DOI: 10.3390/axioms11060247
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 248: Edge Neighbor Toughness of Graphs
Authors: Xin Feng, Zongtian Wei, Yucheng Yang
First page: 248
Abstract: A new graph parameter, edge neighbor toughness is introduced to measure how difficult it is for a graph to be broken into many components through the deletion of the closed neighborhoods of a few edges. Let G=(V,E) be a graph. An edge e is said to be subverted when its neighborhood and the two endvertices are deleted from G. An edge set S⊆E(G) is called an edge cut-strategy if all the edges in S has been subverted from G and the survival subgraph, denoted by G/S, is disconnected, or is a single vertex, or is. The edge neighbor toughness of a graph G is defined to be tEN(G)=minS⊆E(G){ S c(G/S)}, where S is any edge cut strategy of G, c(G/S) is the number of the components of G/S. In this paper, the properties of this parameter are investigated, and the proof of the computation problem of edge neighbor toughness is NP-complete; finally, a polynomial algorithm for computing the edge neighbor toughness of trees is given.
Citation: Axioms
PubDate: 2022-05-25
DOI: 10.3390/axioms11060248
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 249: An Earthquake-Clustering Model in North Aegean
Area (Greece)
Authors: Ourania Mangira, Rodolfo Console, Eleftheria Papadimitriou, Maura Murru, Vasileios Karakostas
First page: 249
Abstract: The investigation of short-term earthquake-clustering features is made feasible through the application of a purely stochastic Epidemic-Type Aftershock Sequence (ETAS) model. The learning period that is used for the estimation of the parameters is composed by earthquakes with M ≥ 2.6 that occurred between January 2008 and May 2017. The model predictability is retrospectively examined for the 12 June 2017 Lesvos earthquake (Mw6.4) and the subsequent events. The construction of time-dependent seismicity maps and comparison between the observed and expected earthquake number are performed in order to temporally and spatially test the evolution of the sequence, respectively. The generation of 127 target events with M ≥ 3.0 in the period June–July 2017, just before the main shock occurrence, is examined in a quantitative evaluation. The statistical criteria used for assessing the model performance are the Relative Operating Characteristic Diagram, the R-score, and the probability gain. Reliable forecasts are provided through the epidemic model testifying its superiority towards a time-invariant Poisson model.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060249
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 250: Further Study on C-Eigenvalue Inclusion
Intervals for Piezoelectric Tensors
Authors: Gang Wang, Xiaoxuan Yang, Wei Shao, Qiuling Hou
First page: 250
Abstract: The C-eigenpair of piezoelectric tensors finds applications in the area of the piezoelectric effect and converse piezoelectric effect. In this paper, we provide some characterizations of C-eigenvectors by exploring the structure of piezoelectric tensors, and establish sharp C-eigenvalue inclusion intervals via Cauchy–Schwartz inequality. Further, we propose the lower and upper bounds of the largest C-eigenvalue and evaluate the efficiency of the best rank-one approximation of piezoelectric tensors. Numerical examples are proposed to verify the efficiency of the obtained results.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060250
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 251: Interval Type-3 Fuzzy Aggregation of Neural
Networks for Multiple Time Series Prediction: The Case of Financial
Forecasting
Authors: Oscar Castillo, Juan R. Castro, Patricia Melin
First page: 251
Abstract: In this work, we present an approach for fuzzy aggregation of neural networks for forecasting. The interval type-3 aggregator is used to combine the outputs of the networks to improve the quality of the prediction. This is carried out in such a way that the final output is better than the outputs of the individual modules. In our approach, a fuzzy system is used to estimate the prediction increments that will be assigned to the output in the process of combining them with a set of fuzzy rules. The uncertainty in the process of aggregation is modeled with an interval type-3 fuzzy system, which, in theory, can outperform type-2 and type-1 fuzzy systems. Publicly available data sets of COVID-19 cases and the Dow Jones index were utilized to test the proposed approach, as it has been stated that a pandemic wave can have an effect on the economies of countries. The simulation results show that the COVID-19 data does have, in fact, an influence on the Dow Jones time series and its use in the proposed model improves the forecast of the Dow Jones future values.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060251
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 252: General Opial Type Inequality and New Green
Functions
Authors: Ana Gudelj, Kristina Krulić Himmelreich, Josip Pečarić
First page: 252
Abstract: In this paper we provide many new results involving Opial type inequalities. We consider two functions—one is convex and the other is concave—and prove a new general inequality on a measure space (Ω,Σ,μ). We give an new result involving four new Green functions. Our results include Grüss and Ostrowski type inequalities related to the generalized Opial type inequality. The obtained inequalities are of Opial type because the integrals contain the function and its integral representation. They are not a direct generalization of the Opial inequality.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060252
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 253: Development of Patent Technology Prediction
Model Based on Machine Learning
Authors: Chih-Wei Lee, Feng Tao, Yu-Yu Ma, Hung-Lung Lin
First page: 253
Abstract: Intellectual property rights have a great impact on the development of the automobile industry. Issues related to the timeliness of patent applications often arise, such as the inability of firms to predict new technologies and patents developed by peers. To find the proper direction of product development, the R&D departments of enterprises need to accurately predict the technology trends. Machine learning adopts calculation through a large amount of data through mathematical models and methods and finds the best solution at the fastest speed through repeated simulation and experiments, to provide decision makers with a reference basis. Therefore, this paper provides accurate forecasts through established models. In terms of the significance of management, the planning of future enterprise strategy can be divided into three stages as a short-term plan of 1–3 years, a medium-term plan of 3–5 years, and a long-term plan of 5–10 years. This study will give appropriate suggestions for the development of automobile industry technology.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060253
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 254: Total Rainbow Connection Number of Some Graph
Operations
Authors: Hengzhe Li, Yingbin Ma, Yan Zhao
First page: 254
Abstract: In a graph H with a total coloring, a path Q is a total rainbow if all elements in V(Q)∪E(Q), except for its end vertices, are assigned different colors. The total coloring of a graph H is a total rainbow connected coloring if, for any x,y∈V(H), there is a total rainbow path joining them. The total rainbow connection number trc(H) of H is the minimum integer r such that there is a total rainbow-connected coloring of H using r colors. In this paper, we study the total rainbow connection number of several graph operations (specifically, adding an edge, deleting an edge, and the Cartesian product) for which the total rainbow connection number is upper-bounded by a linear function of its radius.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060254
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 255: On the Generalized Gaussian Fibonacci Numbers
and Horadam Hybrid Numbers: A Unified Approach
Authors: Fatih Yılmaz, Mustafa Özkan
First page: 255
Abstract: In this paper, we consider an approach based on the elementary matrix theory. In other words, we take into account the generalized Gaussian Fibonacci numbers. In this context, we consider a general tridiagonal matrix family. Then, we obtain determinants of the matrix family via the Chebyshev polynomials. Moreover, we consider one type of tridiagonal matrix, whose determinants are Horadam hybrid polynomials, i.e., the most general form of hybrid numbers. Then, we obtain its determinants by means of the Chebyshev polynomials of the second kind. We provided several illustrative examples, as well.
Citation: Axioms
PubDate: 2022-05-26
DOI: 10.3390/axioms11060255
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 256: Dynamical Analysis of a Modified Epidemic
Model with Saturated Incidence Rate and Incomplete Treatment
Authors: Lazarus Kalvein Beay, Nursanti Anggriani
First page: 256
Abstract: This paper addresses a modified epidemic model with saturated incidence and incomplete treatment. The existence of all equilibrium points is analyzed. A reproduction number R0 is determined. Next, it is found that the non-endemic point P0 is stable in case R0<1, but unstable in case R0>1. The special conditions to analyze the local and global stability of the non-endemic and endemic points are investigated. Globally, the sensitivity analysis of the system is studied by combining the Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods. By using the Pontryagins maximum principle, the optimal control problem is studied. Various numerical results are given to support our analysis.
Citation: Axioms
PubDate: 2022-05-27
DOI: 10.3390/axioms11060256
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 257: Recursive Aggregation and Its Fusion Process
for Intuitionistic Fuzzy Numbers Based on Non-Additive Measure
Authors: Yongfu Shi, Zengtai Gong
First page: 257
Abstract: In this paper, the recursive aggregation of OWA operators for intuitionistic fuzzy numbers (IFN) based on a non-additive measure (NAM) with σ−λ rules is constructed and investigated in light of the σ−λ rules of a non-additive measure (NAM). Additionally, an integrator is designed by drawing on the genetic algorithm and the process of calculation is elaborated by an example.
Citation: Axioms
PubDate: 2022-05-28
DOI: 10.3390/axioms11060257
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 258: Analysis of Interval-Valued Intuitionistic
Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their
Application to Multiple Attribute Decision-Making
Authors: Tapan Senapati, Radko Mesiar, Vladimir Simic, Aiyared Iampan, Ronnason Chinram, Rifaqat Ali
First page: 258
Abstract: When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to solving the multiple attribute decision making (MADM) difficulties, where all of the evidence provided by the decision-makers is demonstrated as interval-valued intuitionistic fuzzy (IVIF) decision matrices, in which all of the components are distinguished by an IVIF number (IVIFN), is based on Aczel–Alsina operational processes. We begin by introducing novel IVIFN operations including the Aczel–Alsina sum, product, scalar multiplication, and exponential. We may then create IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted geometric operator, the IVIF Aczel–Alsina ordered weighted geometric operator, and the IVIF Aczel–Alsina hybrid geometric operator, among others. We present a MADM approach that relies on the IVIF aggregation operators that have been developed. A case study is used to demonstrate the practical applicability of the strategies proposed in this paper. By contrasting the newly developed technique with existing techniques, the method is capable of demonstrating the advantages of the newly developed approach. A key result of this work is the discovery that some of the current IVIF aggregation operators are subsets of the operators reported in this article.
Citation: Axioms
PubDate: 2022-05-29
DOI: 10.3390/axioms11060258
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 259: Volatility Co-Movement between Bitcoin and
Authors: Kuo-Shing Chen, Shen-Ho Chang
First page: 259
Abstract: This paper aims to investigate and measure Bitcoin and the five largest stablecoin market volatilities by incorporating various range-based volatility estimators to the BEKK- GARCH and Copula-DCC-GARCH models. Specifically, we further measure Bitcoins’ volatility related to five major stablecoins and examine the connectedness between Bitcoin and the stablecoins. Our empirical findings document that the connectedness between Bitcoin and stablecoin market volatility behaviors exhibits the presence of stable interconnection. This study is of particular importance since it is crucial for market participation in the ongoing crypto assets to be informed about both the volatility patterns of major cryptocurrencies and the relative volatility of Bitcoin against the stablecoin markets. Eventually, we find that there is no systematic evidence for the various parity deviations of the stablecoins that are profoundly impacted by Bitcoin volatility. Thus, Bitcoin and the largest stablecoin Tether could stabilize together. However, Bitcoin shall not be generalized to other stablecoins in terms of stability results.
Citation: Axioms
PubDate: 2022-05-29
DOI: 10.3390/axioms11060259
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 260: Spectral Invariants and Their Application on
Spectral Characterization of Graphs
Authors: Jun Yin, Haixing Zhao, Sun Xie
First page: 260
Abstract: In this paper, we give a method to characterize graphs determined by their adjacency spectrum. At first, we give two parameters Π1(G) and Π2(G), which are related to coefficients of the characteristic polynomial of graph G. All connected graphs with Π1(G) ∈ {1,0,−1,−2,−3} and Π2(G) ∈ {0,−1,−2,−3} are characterized. Some interesting properties of Π1(G) and Π2(G) are also given. We then find the necessary and sufficient conditions for two classes of graphs to be determined by their adjacency spectrum.
Citation: Axioms
PubDate: 2022-05-29
DOI: 10.3390/axioms11060260
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 261: The Expected Value of Hosoya Index and
Merrifield–Simmons Index in a Random Cyclooctylene Chain
Authors: Yushuang Sun, Xianya Geng
First page: 261
Abstract: The Hosoya index m(G) and the Merrifield–Simmons index i(G) of a graph G are the number of matchings and the number of independent sets in G. In this paper, we establish exact formulas for the expected value of the Hosoya index and Merrifield–Simmons index of the random cyclooctylene chains, which are graphs of a chemical chain consisting of n octagons, each of which is connected to the end of the previous octagon by an edge. In addition, we obtain the expected values and the average values of the two indexes through the relevant chemical diagrams and a series of accurate formulas with respect to the set of all cyclooctylene chains with n octagons.
Citation: Axioms
PubDate: 2022-05-30
DOI: 10.3390/axioms11060261
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 262: Bounds for Quotients of Inverse Trigonometric
and Inverse Hyperbolic Functions
Authors: Sumedh B. Thool, Yogesh J. Bagul, Ramkrishna M. Dhaigude, Christophe Chesneau
First page: 262
Abstract: We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin−1xsinh−1x and tanh−1xtan−1x. The main results provide polynomial bounds using even quadratic functions and exponential bounds under the form eax2. Graph validation is also performed.
Citation: Axioms
PubDate: 2022-05-30
DOI: 10.3390/axioms11060262
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 263: A GIS-MCDM Method for Ranking Potential
Station Locations in the Expansion of Bike-Sharing Systems
Authors: Mohammad Sadegh Bahadori, Alexandre B. Gonçalves, Filipe Moura
First page: 263
Abstract: Bicycle-sharing systems (BSSs) are an effective solution to reduce private car usage in most cities and are an influential factor in encouraging citizens to shift to more sustainable transport modes. In this sense, the location of BSS stations has a critical impact on the system’s efficiency. This study proposed an integrated geographic information system–multi-criteria decision-making (GIS-MCDM) framework that includes the analytic hierarchy process (AHP), technique for order preference by similarity to the ideal solution (TOPSIS), and spatial data processing in GIS to determine a ranking of potential locations for BSS stations. The results of the proposed GIS-MCDM method can be used for both planning a new BSS or expanding one that is currently under operation. The framework was applied to a case study for expanding GIRA, the BSS of Lisbon, Portugal. In it, location criteria were selected in four categories, including criteria from the literature and extracted from available transaction data; in addition, we also suggested some criteria. The rebalancing operator’s staff were the decision makers in this study via their responses to the AHP questionnaire. The rebalancing staff believed that the main criterion of “city infrastructure” with the two sub-criteria of “population density” and “slope” were the most important. Furthermore, the proximity to the “bike network” with the sub-criterion of “proximity to the current bike stations” had less importance. Each criterion’s weight and inconsistency rate were obtained using the Expert Choice software. The geographic values of each criterion were created utilizing the ArcGIS software, and its network analyst module was employed for applying location techniques. Based on the created suitability map, the city’s center was the main suitable area for establishing new stations. Forty-five new bike stations were identified in those areas and ranked using the TOPSIS technique.
Citation: Axioms
PubDate: 2022-05-31
DOI: 10.3390/axioms11060263
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 264: Mathematical Modeling Research Output
Impacting New Technological Development: An Axiomatization to Build
Novelty
Authors: Mohd Razip Bajuri, Zailan Siri, Mohd Nor Syahrir Abdullah
First page: 264
Abstract: The mathematical modeling of research-based output impacting new technology development is crucial for a developing country. However, the complexity of modern mathematical modeling research output makes it unclear over how it can impact the development of new technology. Therefore, this study aims to explore, categorize and formulize the axioms of mathematical modeling research output that impacts the development of new technology. Seven participants were involved in this research. Interviews were conducted to explore their remarkable mathematical modeling output and how the output can impact the development of new technology. The categorization axioms are: i. mathematical modeling for theorizing, ii. mathematical modeling for simulations, iii. mathematical modeling for useable innovation and iv. patent and product commercialization. Finally, the categorization can be formulized as an axiom of mathematical modeling novelty, which is the desired research output. Moreover, patents and commercialization are the elements that mathematical modeling should possess for new technological development. The limited number of participants involved in this study makes this study formulation limited to only some types of mathematical modeling output. However, this substantive formulation could give some ideas in proposing the path and processes on how to enhance the effort for society to develop the culture of mathematical modeling in developing new technology.
Citation: Axioms
PubDate: 2022-05-31
DOI: 10.3390/axioms11060264
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 265: A Recommendation Model for Selling Rules in
the Telecom Retail Industry
Authors: Tsung-Ying Ou, Wen-Lung Tsai, Yi-Chen Lee, Tien-Hsiang Chang, Shih-Hsiung Lee, Fen-Fen Huang
First page: 265
Abstract: The recommendation of the optimal selling rules for any product or service is challenging, owing to the complexity of the customer’s behavior and the competitiveness existing in the telecom retail industry. This study proposes a recommendation model for selling rules that utilizes a hybrid decision-making approach based on K-means and the C5.0 decision tree to analyze the historical sales information of telecom retailers. To evaluate the efficacy of the proposed recommendation model, it was used to analyze original data from a case company. The results indicated that the proposed hybrid decision-making approach resulted in sales content with a high gross profit and high agreement rates. The experimental results show each cluster that can be used to identify rules for the combination of good tariff items in different tariff ranges. Rules for the recommendation of special tariffs are also established to assist salespeople.
Citation: Axioms
PubDate: 2022-06-01
DOI: 10.3390/axioms11060265
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 266: On Fractional Inequalities Using Generalized
Proportional Hadamard Fractional Integral Operator
Authors: Vaijanath L. Chinchane, Asha B. Nale, Satish K. Panchal, Christophe Chesneau, Amol D. Khandagale
First page: 266
Abstract: The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator to establish some new fractional integral inequalities for extended Chebyshev functionals. In addition, we investigate some fractional integral inequalities for positive continuous functions by employing a generalized proportional Hadamard fractional integral operator. The findings of this study are theoretical but have the potential to help solve additional practical problems in mathematical physics, statistics, and approximation theory.
Citation: Axioms
PubDate: 2022-06-01
DOI: 10.3390/axioms11060266
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 267: An Avant-Garde Construction for Subclasses of
Analytic Bi-Univalent Functions
Authors: Feras Yousef, Ala Amourah, Basem Aref Frasin, Teodor Bulboacă
First page: 267
Abstract: The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the zero-truncated Poisson distribution probabilities to construct a new subclass of analytic bi-univalent functions involving Gegenbauer polynomials. For functions in the constructed class, we explore estimates of Taylor–Maclaurin coefficients a2 and a3, and next, we solve the Fekete–Szegő functional problem. A number of new interesting results are presented to follow upon specializing the parameters involved in our main results.
Citation: Axioms
PubDate: 2022-06-01
DOI: 10.3390/axioms11060267
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 268: On r-Ideals and m-k-Ideals in BN-Algebras
Authors: Sri Gemawati, Musnis Musraini, Abdul Hadi, La Zakaria, Elsi Fitria
First page: 268
Abstract: A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the following axioms: (B1) x∗x=0, (B2) x∗0=x, and (BN) (x∗y)∗z=(0∗z)∗(y∗x) for all x, y, z ∈X. A non-empty subset I of X is called an ideal in BN-algebra X if it satisfies 0∈X and if y∈I and x∗y∈I, then x∈I for all x,y∈X. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.
Citation: Axioms
PubDate: 2022-06-02
DOI: 10.3390/axioms11060268
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 269: Robust Spectral Clustering Incorporating
Statistical Sub-Graph Affinity Model
Authors: Zhenxian Lin, Jiagang Wang, Chengmao Wu
First page: 269
Abstract: Hyperspectral image (HSI) clustering is a challenging work due to its high complexity. Subspace clustering has been proven to successfully excavate the intrinsic relationships between data points, while traditional subspace clustering methods ignore the inherent structural information between data points. This study uses graph convolutional subspace clustering (GCSC) for robust HSI clustering. The model remaps the self-expression of the data to non-Euclidean domains, which can generate a robust graph embedding dictionary. The EKGCSC model can achieve a globally optimal closed-form solution by using a subspace clustering model with the Frobenius norm and a Gaussian kernel function, making it easier to implement, train, and apply. However, the presence of noise can have a noteworthy negative impact on the segmentation performance. To diminish the impact of image noise, the concept of sub-graph affinity is introduced, where each node in the primary graph is modeled as a sub-graph describing the neighborhood around the node. A statistical sub-graph affinity matrix is then constructed based on the statistical relationships between sub-graphs of connected nodes in the primary graph, thus counteracting the uncertainty image noise by using more information. The model used in this work was named statistical sub-graph affinity kernel graph convolutional subspace clustering (SSAKGCSC). Experiment results on Salinas, Indian Pines, Pavia Center, and Pavia University data sets showed that the SSAKGCSC model can achieve improved segmentation performance and better noise resistance ability.
Citation: Axioms
PubDate: 2022-06-05
DOI: 10.3390/axioms11060269
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 270: k-Path-Connectivity of Completely Balanced
Tripartite Graphs
Authors: Pi Wang, Shasha Li, Xiaoxue Gao
First page: 270
Abstract: For a graph G=(V,E) and a set S⊆V(G) of a size at least 2, a path in G is said to be an S-path if it connects all vertices of S. Two S-paths P1 and P2 are said to be internally disjoint if E(P1)∩E(P2)=∅ and V(P1)∩V(P2)=S; that is, they share no vertices and edges apart from S. Let πG(S) denote the maximum number of internally disjoint S-paths in G. The k-path-connectivity πk(G) of G is then defined as the minimum πG(S), where S ranges over all k-subsets of V(G). In this paper, we study the k-path-connectivity of the complete balanced tripartite graph Kn,n,n and obtain πkKn,n,n=2nk−1 for 3≤k≤n.
Citation: Axioms
PubDate: 2022-06-05
DOI: 10.3390/axioms11060270
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 271: Solvability of Conformable Type Frictionless
Contact Problem via Hemivariational Inequalities
Authors: Jianwei Hao, Jinrong Wang, Jiangfeng Han
First page: 271
Abstract: In this paper, we study a class of conformable frictionless contact problems with the surface traction driven by the conformable impulsive differential equation. The existence of a mild solution for conformable impulsive hemivariational inequality is obtained by the Rothe method, subjectivity of multivalued pseudomonotone operators and the property of the conformable derivative. Notice that we imply some new fractional viscoelastic constitutive laws.
Citation: Axioms
PubDate: 2022-06-05
DOI: 10.3390/axioms11060271
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 272: On a Class of Positive Definite Operators and
Their Application in Fractional Calculus
Authors: Temirkhan Aleroev
First page: 272
Abstract: This paper is devoted to the spectral analysis of one class of integral operators, associated with the boundary value problems for differential equations of fractional order. Approximation matrices are also investigated. In particular, the positive definiteness of the studied operators is shown, which makes it possible to select areas in the complex plane where there are no eigenvalues of these operators.
Citation: Axioms
PubDate: 2022-06-05
DOI: 10.3390/axioms11060272
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 273: Topological and Geometrical Properties of
k-Symplectic Structures
Authors: Essabab Said, Fanich El Mokhtar, Awane Azzouz
First page: 273
Abstract: We study new geometrical and topological aspects of polarized k-symplectic manifolds. In addition, we study the De Rham cohomology groups of the k-symplectic group. In this work, we pay particular attention to the problem of the orientation of polarized k-symplectic manifolds in a way analogous to symplectic manifolds which are all orientable.
Citation: Axioms
PubDate: 2022-06-06
DOI: 10.3390/axioms11060273
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 274: Homogeneity of Complex Fuzzy Operations
Authors: Bo Hu, Wei Wu, Songsong Dai
First page: 274
Abstract: The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies the homogeneity of binary functions on the unit circle of the complex plane. The homogeneity is a generalization of both rotational invariance and ratio scale invariance for complex fuzzy operations. We show that a binary function is homogeneous if and only if it is both rotationally invariant and ratio scale invariant. Moreover, we consider the simplification of the homogeneity for complex fuzzy binary operators.
Citation: Axioms
PubDate: 2022-06-06
DOI: 10.3390/axioms11060274
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 275: A Novel Multi-Criteria Decision-Making Method
Based on Rough Sets and Fuzzy Measures
Authors: Jingqian Wang, Xiaohong Zhang
First page: 275
Abstract: Rough set theory provides a useful tool for data analysis, data mining and decision making. For multi-criteria decision making (MCDM), rough sets are used to obtain decision rules by reducing attributes and objects. However, different reduction methods correspond to different rules, which will influence the decision result. To solve this problem, we propose a novel method for MCDM based on rough sets and a fuzzy measure in this paper. Firstly, a type of non-additive measure of attributes is presented by the importance degree in rough sets, which is a fuzzy measure and called an attribute measure. Secondly, for a decision information system, the notion of the matching degree between two objects is presented under an attribute. Thirdly, based on the notions of the attribute measure and matching degree, a Choquet integral is constructed. Moreover, a novel MCDM method is presented by the Choquet integral. Finally, the presented method is compared with other methods through a numerical example, which is used to illustrate the feasibility and effectiveness of our method.
Citation: Axioms
PubDate: 2022-06-06
DOI: 10.3390/axioms11060275
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 276: Interval Type-3 Fuzzy Control for Automated
Tuning of Image Quality in Televisions
Authors: Oscar Castillo, Juan R. Castro, Patricia Melin
First page: 276
Abstract: In this article, an intelligent system utilizing type-3 fuzzy logic for automated image quality tuning in televisions is presented. The tuning problem can be formulated as controlling the television imaging system to achieve the requirements of production quality. Previously, the tuning process has been carried out by experts, by manually adjusting the television imaging system on production lines to meet the quality control standards. In this approach, interval type-3 fuzzy logic is utilized with the goal of automating the tuning of televisions manufactured on production lines. An interval type-3 fuzzy approach for image tuning is proposed, so that the best image quality is obtained and, in this way, meet quality requirements. A system based on type-3 fuzzy control is implemented with good simulation results. The validation of the type-3 fuzzy approach is made by comparing the results with human experts on the process of electrical tuning of televisions. The key contribution is the utilization of type-3 fuzzy in the image tuning application, which has not been reported previously in the literature.
Citation: Axioms
PubDate: 2022-06-09
DOI: 10.3390/axioms11060276
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 277: Super Connected Direct Product of Graphs and
Cycles
Authors: Jiaqiong Yin, Yingzhi Tian
First page: 277
Abstract: The topology of an interconnection network can be modeled by a graph G=(V(G),E(G)). The connectivity of graph G is a parameter used to measure the reliability of a corresponding network. The direct product is an important graph product. This paper mainly focuses on the super connectedness of the direct product of graphs and cycles. The connectivity of G, denoted by κ(G), is the size of a minimum vertex set S⊆V(G) such that G−S is not connected or has only one vertex. The graph G is said to be super connected, simply super-κ, if every minimum vertex cut is the neighborhood of a vertex with minimum degree. The direct product of two graphs G and H, denoted by G×H, is the graph with vertex set V(G×H)=V(G)×V(H) and edge set E(G×H)={(u1,v1)(u2,v2) u1u2∈E(G),v1v2∈E(H)}. In this paper, we give some sufficient conditions for the direct product G×Cn to be super connected, where Cn is the cycle on n vertices. Furthermore, those sufficient conditions are the best possible.
Citation: Axioms
PubDate: 2022-06-09
DOI: 10.3390/axioms11060277
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 278: On the Laplacian, the Kirchhoff Index, and the
Number of Spanning Trees of the Linear Pentagonal Derivation Chain
Authors: Yue Tu, Xiaoling Ma, Yuqing Zhang, Junyu Ren
First page: 278
Abstract: Let Pn be a pentagonal chain with 2n pentagons in which two pentagons with two edges in common can be regarded as adding one vertex and two edges to a hexagon. Thus, the linear pentagonal derivation chains QPn represent the graph obtained by attaching four-membered rings to every two pentagons of Pn. In this article, the Laplacian spectrum of QPn consisting of the eigenvalues of two symmetric matrices is determined. Next, the formulas for two graph invariants that can be represented by the Laplacian spectrum, namely, the Kirchhoff index and the number of spanning trees, are studied. Surprisingly, the Kirchhoff index is almost one half of the Wiener index of a linear pentagonal derivation chain QPn.
Citation: Axioms
PubDate: 2022-06-09
DOI: 10.3390/axioms11060278
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 279: New Inequalities and Generalizations for
Symmetric Means Induced by Majorization Theory
Authors: Huan-Nan Shi, Wei-Shih Du
First page: 279
Abstract: In this paper, the authors study new inequalities and generalizations for symmetric means and give new proofs for some known results by applying majorization theory.
Citation: Axioms
PubDate: 2022-06-09
DOI: 10.3390/axioms11060279
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 280: Application of Deep Learning and Neural
Network to Speeding Ticket and Insurance Claim Count Data
Authors: Jong-Min Kim, Jihun Kim, Il Do Ha
First page: 280
Abstract: With the popularity of big data analysis with insurance claim count data, diverse regression models for count response variable have been developed. However, there is a multicollinearlity issue with multivariate input variables to the count response regression models. Recently, deep learning and neural network models for count response have been proposed, and a Keras and Tensorflow-based deep learning model has been also proposed. To apply the deep learning and neural network models to non-normal insurance claim count data, we perform the root mean square error accuracy comparison of gradient boosting machines (a popular machine learning regression tree algorithm), principal component analysis (PCA)-based Poisson regression, PCA-based negative binomial regression, and PCA-based zero inflated poisson regression to avoid the multicollinearity of multivariate input variables with the simulated normal distribution data and the non-normal simulated data combined with normally distributed data, binary data, copula-based asymmetrical data, and two real data sets, which consist of speeding ticket and Singapore insurance claim count data.
Citation: Axioms
PubDate: 2022-06-10
DOI: 10.3390/axioms11060280
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 281: Nonoscillation and Oscillation Criteria for a
Class of Second-Order Nonlinear Neutral Delay Differential Equations with
Positive and Negative Coefficients
Authors: Rongrong Guo, Qingdao Huang, Haifeng Tian
First page: 281
Abstract: In this paper, we investigate some nonoscillatory and oscillatory solutions for a class of second-order nonlinear neutral delay differential equations with positive and negative coefficients. By means of the method of contraction mapping principle and some integral inequality techniques, we extend the recent results provided in the literature.
Citation: Axioms
PubDate: 2022-06-10
DOI: 10.3390/axioms11060281
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 282: The Existence of Radial Solutions to the
Schrödinger System Containing a Nonlinear Operator
Authors: Guotao Wang, Zhuobin Zhang, Zedong Yang
First page: 282
Abstract: In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ and ν are bounded, μ and ν are blow-up, and one of the components is bounded, while the other is blow-up. Finally, we present two examples to verify our results.
Citation: Axioms
PubDate: 2022-06-10
DOI: 10.3390/axioms11060282
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 283: Controllability of a Class of Impulsive
ψ-Caputo Fractional Evolution Equations of Sobolev Type
Authors: Qing Yang, Chuanzhi Bai, Dandan Yang
First page: 283
Abstract: In this paper, we investigate the controllability of a class of impulsive ψ-Caputo fractional evolution equations of Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, fractional calculus, and Schauder fixed point theorem. Our works are generalizations and continuations of the recent results about controllability of a class of impulsive ψ-Caputo fractional evolution equations. Finally, an example is given to illustrate the effectiveness of the main results.
Citation: Axioms
PubDate: 2022-06-10
DOI: 10.3390/axioms11060283
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 284: Evaluating the Digital Transformation
Performance of Retail by the DEA Approach
Authors: Ling-Jing Kao, Chih-Chou Chiu, Hung-Tse Lin, Yun-Wei Hung, Cheng-Chin Lu
First page: 284
Abstract: In recent years, under the impact of digitization, all industries around the world have undergone unprecedented changes. Such changes have not only altered people’s consumption behavior but have also forced enterprises to accelerate the pace of digitization and actively start digital transformation. In this study, a literature review and focus group interview (FGI) were used to develop the dimensions and criteria to assess enterprise digital transformation status. To illustrate the digital transformation criteria proposed in this research, the retail industry was used as an example to measure the overall digital transformation performance by data envelopment analysis (DEA). The results show that the poor technical efficiency demonstrated by a vendor was not only due to the gradually decreasing returns to scale of the market; a decline in pure technical efficiency was also a contributor. In addition to adjusting their production on the basis of market conditions, vendors should properly manage their internal operations and pay attention to their resource and scale allocations to prevent reductions in their pure technical efficiency.
Citation: Axioms
PubDate: 2022-06-13
DOI: 10.3390/axioms11060284
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 285: Some Generalized Euclidean Operator Radius
Inequalities
Authors: Mohammad W. Alomari, Khalid Shebrawi, Christophe Chesneau
First page: 285
Abstract: In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian decomposition of a given Hilbert space operator are proven.
Citation: Axioms
PubDate: 2022-06-13
DOI: 10.3390/axioms11060285
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 286: A Selection Principle and Products in
Topological Groups
Authors: Marion Scheepers
First page: 286
Abstract: We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of T0 topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded group is an o-bounded group—Corollary 1. (2) In the generic extension by a finite support iteration of ℵ1 Hechler reals the product of any o-bounded group with a ground model ℵ0 bounded group is an o-bounded group—Theorem 11. (3) In the generic extension by a countable support iteration of Mathias reals the product of any o-bounded group with a ground model ℵ0 bounded group is an o-bounded group—Theorem 12.
Citation: Axioms
PubDate: 2022-06-13
DOI: 10.3390/axioms11060286
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 287: A Story of Computational Science: Colonel
Titus’ Problem from the 17th Century
Authors: Trond Steihaug
First page: 287
Abstract: Experimentation and the evaluation of algorithms have a long history in algebra. In this paper we follow a single test example over more than 250 years. In 1685, John Wallis published A treatise of algebra, both historical and practical, containing a solution of Colonel Titus’ problem that was proposed to him around 1650. The Colonel Titus problem consists of three algebraic quadratic equations in three unknowns, which Wallis transformed into the problem of finding the roots of a fourth-order (quartic) polynomial. When Joseph Raphson published his method in 1690, he demonstrated the method on 32 algebraic equations and one of the examples was this quartic equation. Edmund Halley later used the same polynomial as an example for his new methods in 1694. Although Wallis used the method of Vietè, which is a digit–by–digit method, the more efficient methods of Halley and Raphson are clearly demonstrated in the works by Raphson and Halley. For more than 250 years the quartic equation has been used as an example in a wide range of solution methods for nonlinear equations. This paper provides an overview of the Colonel Titus problem and the equation first derived by Wallis. The quartic equation has four positive roots and the equation has been found to be very useful for analyzing the number of roots and finding intervals for the individual roots, in the Cardan–Ferrari direct approach for solving quartic equations, and in Sturm’s method of determining the number of real roots of an algebraic equation. The quartic equation, together with two other algebraic equations, have likely been the first set of test examples used to compare different iteration methods of solving algebraic equations.
Citation: Axioms
PubDate: 2022-06-14
DOI: 10.3390/axioms11060287
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 288: On Unique Factorization Modules: A Submodule
Approach
Authors: Sri Wahyuni, Hidetoshi Marubayashi, Iwan Ernanto, I Putu Yudi Prabhadika
First page: 288
Abstract: Let M be a torsion-free module over an integral domain D. We define a concept of a unique factorization module in terms of v-submodules of M. If M is a unique factorization module (UFM), then D is a unique factorization domain. However, the converse situation is not necessarily to be held, and we give four different characterizations of unique factorization modules. Further, it is shown that the concept of the UFM is equivalent to Nicolas’s UFM, which is defined in terms of irreducible elements of D and M.
Citation: Axioms
PubDate: 2022-06-14
DOI: 10.3390/axioms11060288
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 289: Pipeline Corrosion Prediction Using the Grey
Model and Artificial Bee Colony Algorithm
Authors: Shiguo Li, Hualong Du, Qiuyu Cui, Pengfei Liu, Xin Ma, He Wang
First page: 289
Abstract: Pipeline corrosion prediction (PCP) is an important technology for pipeline maintenance and management. How to accurately predict pipeline corrosion is a challenging task. To address the drawback of the poor prediction accuracy of the grey model (GM(1,1)), this paper proposes a method named ETGM(1,1)-RABC. The proposed method consists of two parts. First, the exponentially transformed grey model (ETGM(1,1)) is an improvement of the GM(1,1), in which exponential transformation (ET) is used to preprocess the raw data. Next, dynamic coefficients, instead of background fixed coefficients, are optimized by the reformative artificial bee colony (RABC) algorithm, which is a variation of the artificial bee colony (ABC) algorithm. Experiments are performed on actual pipe corrosion data, and four different methods are included in the comparative study, including GM(1,1), ETGM(1,1), and three ETGM(1,1)-ABC variants. The results show that the proposed method proves to be superior for the PCP in terms of Taylor diagram and absolute error.
Citation: Axioms
PubDate: 2022-06-14
DOI: 10.3390/axioms11060289
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 290: Some Cardinal and Geometric Properties of the
Space of Permutation Degree
Authors: Ljubiša D. R. Kočinac, Farkhod G. Mukhamadiev, Anvar K. Sadullaev
First page: 290
Abstract: This paper is devoted to the investigation of cardinal invariants such as the hereditary density, hereditary weak density, and hereditary Lindelöf number. The relation between the spread and the extent of the space SP2(R,τ(A)) of permutation degree of the Hattori space is discussed. In particular, it is shown that the space SP2(R,τS) contains a closed discrete subset of cardinality c. Moreover, it is shown that the functor SPGn preserves the homotopy and the retraction of topological spaces. In addition, we prove that if the spaces X and Y are homotopically equivalent, then the spaces SPGnX and SPGnY are also homotopically equivalent. As a result, it has been proved that the functor SPGn is a covariant homotopy functor.
Citation: Axioms
PubDate: 2022-06-14
DOI: 10.3390/axioms11060290
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 291: Characterizations of Matrix Equalities for
Generalized Inverses of Matrix Products
Authors: Yongge Tian
First page: 291
Abstract: This paper considers how to construct and describe matrix equalities that are composed of algebraic operations of matrices and their generalized inverses. We select a group of known and new reverse-order laws for generalized inverses of several matrix products and derive various necessary and sufficient conditions for them to hold using the matrix rank method and the block matrix method.
Citation: Axioms
PubDate: 2022-06-14
DOI: 10.3390/axioms11060291
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 292: Multitask Learning Based on Least Squares
Support Vector Regression for Stock Forecast
Authors: Heng-Chang Zhang, Qing Wu, Fei-Yan Li, Hong Li
First page: 292
Abstract: Various factors make stock market forecasting difficult and arduous. Single-task learning models fail to achieve good results because they ignore the correlation between multiple related tasks. Multitask learning methods can capture the cross-correlation among subtasks and achieve a satisfactory learning effect by training all tasks simultaneously. With this motivation, we assume that the related tasks are close enough to share a common model whereas having their own independent models. Based on this hypothesis, we propose a multitask learning least squares support vector regression (MTL-LS-SVR) algorithm, and an extension, EMTL-LS-SVR. Theoretical analysis shows that these models can be converted to linear systems. A Krylov-Cholesky algorithm is introduced to determine the optimal solutions of the models. We tested the proposed models by applying them to forecasts of the Chinese stock market index trend and the stock prices of five stated-owned banks. The experimental results demonstrate their validity.
Citation: Axioms
PubDate: 2022-06-15
DOI: 10.3390/axioms11060292
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 293: Parameter Estimation of the Exponentiated
Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling
Authors: Hossein Jabbari Khamnei, Ieva Meidute-Kavaliauskiene, Masood Fathi, Asta Valackienė, Shahryar Ghorbani
First page: 293
Abstract: In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.
Citation: Axioms
PubDate: 2022-06-15
DOI: 10.3390/axioms11060293
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 294: RbfDeSolver: A Software Tool to Approximate
Differential Equations Using Radial Basis Functions
Authors: Ioannis G. Tsoulos, Alexandros Tzallas, Evangelos Karvounis
First page: 294
Abstract: A new method for solving differential equations is presented in this work. The solution of the differential equations is done by adapting an artificial neural network, RBF, to the function under study. The adaptation of the parameters of the network is done with a hybrid genetic algorithm. In addition, this text presents in detail the software developed for the above method in ANSI C++. The user can code the underlying differential equation either in C++ or in Fortran format. The method was applied to a wide range of test functions of different types and the results are presented and analyzed in detail.
Citation: Axioms
PubDate: 2022-06-16
DOI: 10.3390/axioms11060294
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 295: Existence Results for a Multipoint Fractional
Boundary Value Problem in the Fractional Derivative Banach Space
Authors: Djalal Boucenna, Amar Chidouh, Delfim F. M. Torres
First page: 295
Abstract: We study a class of nonlinear implicit fractional differential equations subject to nonlocal boundary conditions expressed in terms of nonlinear integro-differential equations. Using the Krasnosel’skii fixed-point theorem we prove, via the Kolmogorov–Riesz criteria, the existence of solutions. The existence results are established in a specific fractional derivative Banach space and they are illustrated by two numerical examples.
Citation: Axioms
PubDate: 2022-06-16
DOI: 10.3390/axioms11060295
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 296: Public Opinion Spread and Guidance Strategy
under COVID-19: A SIS Model Analysis
Authors: Ge You, Shangqian Gan, Hao Guo, Abd Alwahed Dagestani
First page: 296
Abstract: Both the suddenness and seriousness of COVID-19 have caused a variety of public opinions on social media, which becomes the focus of social attention. This paper aims to analyze the strategies regarding the prevention and guidance of public opinion spread under COVID-19 in social networks from the perspective of the emotional characteristics of user texts. Firstly, a model is established to mine text-based emotional tendency based on the Susceptible-Infectious-Susceptible (SIS) model. In addition, a mathematical and simulation analysis of the model is presented. Finally, an empirical study based on the data of microblog contents regarding COVID-19 public opinion in the Sina Weibo platform from January to March 2020 is conducted to analyze the factors that boost and hinder COVID-19 public opinion. The results show that when positive emotion is higher than 0.8, the spread of negative public opinion can be blocked. When the negative emotion and neutral emotion are both below 0.2, the spread of COVID-19 public opinion would be weakened. To accurately guide public opinion on COVID-19, the government authorities should establish a public opinion risk evaluation and an early warning mechanism. Platforms should strengthen public opinion supervision and users should improve their media literacy. The media organizations should insist on positive reporting, improve social cohesion, and guide the trend of public opinion.
Citation: Axioms
PubDate: 2022-06-17
DOI: 10.3390/axioms11060296
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 297: Context-Free Grammars for Several Triangular
Arrays
Authors: Roberta Rui Zhou, Jean Yeh, Fuquan Ren
First page: 297
Abstract: In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials. Additionally, as an application, a criterion for real zeros of row-generating polynomials is also presented.
Citation: Axioms
PubDate: 2022-06-20
DOI: 10.3390/axioms11060297
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 298: Dynamic Behaviors of an Obligate Commensal
Symbiosis Model with Crowley–Martin Functional Responses
Authors: Lili Xu, Yalong Xue, Xiangdong Xie, Qifa Lin
First page: 298
Abstract: A two species obligate commensal symbiosis model with Crowley–Martin functional response was proposed and studied in this paper. For an autonomous case, local and global dynamic behaviors of the system were investigated, respectively. The conditions that ensure the existence of the positive equilibrium is coincidentla to the conditions of global stability of a positive equilibrium. For nonautonomous cases, persistent and extinction properties of the system are investigated.
Citation: Axioms
PubDate: 2022-06-20
DOI: 10.3390/axioms11060298
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 299: A New Survey of Measures of Noncompactness and
Their Applications
Authors: Moosa Gabeleh, Eberhard Malkowsky, Mohammad Mursaleen, Vladimir Rakočević
First page: 299
Abstract: We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo’s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite systems of integral equations in some sequence spaces. We also present some recent results related to the existence of best proximity points (pairs) for some classes of cyclic and noncyclic condensing operators in Banach spaces equipped with a suitable measure of noncompactness. Finally, we discuss the existence of an optimal solution for systems of integro–differentials.
Citation: Axioms
PubDate: 2022-06-20
DOI: 10.3390/axioms11060299
Issue No: Vol. 11, No. 6 (2022)
- Axioms, Vol. 11, Pages 206: A Cross-Country European Efficiency
Measurement of Maritime Transport: A Data Envelopment Analysis Approach
Authors: Phi-Hung Nguyen, Thi-Ly Nguyen, Thi-Giang Nguyen, Duc-Thinh Nguyen, Thi-Hoai Tran, Hong-Cham Le, Huong-Thuy Phung
First page: 206
Abstract: Maritime transport, which includes shipping and port operations, is the fundamental basis of international trade and globalization. In transportation management, efficiency is critical for verifying performance and proposing the best countermeasure to meet predetermined goals. Various efforts in this field have been made to solve this problem satisfactorily. However, the significant proportion of conventional approaches are based on long-term observations and professional expertise, with only a few exceptions based on practice-based historical data. Data Envelopment Analysis (DEA) is a non-parametric technique for analyzing various output and input variables parallelly. The efficiency of maritime transport in European countries is explored using a two-stage DEA approach based on Malmquist and Epsilon-Based Measure (EBM). First, the Malmquist model analyses countries’ total productivity growth rates and their breakdown into technical efficiency (catch-up) and technology change (frontier-shift). Second, the EBM model is used to determine the efficiency and inefficiency of the maritime transportation systems in each European country. Apart from identifying the best-performing countries in specific areas over the study period (2016–2019), the results highlight that the gap in applying the EBM method to maritime transport has been successfully closed and that the emerging paradigm, when combined with the Malmquist model, can be a sustainable and appropriate evaluation model for other research areas.
Citation: Axioms
PubDate: 2022-04-27
DOI: 10.3390/axioms11050206
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 207: The Boundary Value Problem with Stationary
Inhomogeneities for a Hyperbolic-Type Equation with a Fractional
Derivative
Authors: Ludmila Vladimirovna Kirianova
First page: 207
Abstract: The paper presents an analytical solution of a partial differential equation of hyperbolic-type, containing both second-order partial derivatives and fractional derivatives of order below the second. Examples of applying the solution of a boundary value problem with stationary inhomogeneities for a hyperbolic-type equation with a fractional derivative in modeling the behavior of polymer concrete under the action of loads are considered.
Citation: Axioms
PubDate: 2022-04-28
DOI: 10.3390/axioms11050207
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 208: The Classification of All Singular
Nonsymmetric Macdonald Polynomials
Authors: Charles F. Dunkl
First page: 208
Abstract: The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys–Murphy elements whose simultaneous eigenfunctions are the nonsymmetric Macdonald polynomials, and basis vectors of irreducible modules of the Hecke algebra, respectively. For certain parameter values, it is possible for special polynomials to be simultaneous eigenfunctions with equal corresponding eigenvalues of both sets of operators. These are called singular polynomials. The possible parameter values are of the form qm=t−n with 2≤n≤N. For a fixed parameter, the singular polynomials span an irreducible module of the Hecke algebra. Colmenarejo and the author (SIGMA 16 (2020), 010) showed that there exist singular polynomials for each of these parameter values, they coincide with specializations of nonsymmetric Macdonald polynomials, and the isotype (a partition of N) of the Hecke algebra module is dn−1,n−1,…,n−1,r for some d≥1. In the present paper, it is shown that there are no other singular polynomials.
Citation: Axioms
PubDate: 2022-04-29
DOI: 10.3390/axioms11050208
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 209: Applications of Confluent Hypergeometric
Function in Strong Superordination Theory
Authors: Georgia Irina Oros, Gheorghe Oros, Ancuța Maria Rus
First page: 209
Abstract: In the research presented in this paper, confluent hypergeometric function is embedded in the theory of strong differential superordinations. In order to proceed with the study, the form of the confluent hypergeometric function is adapted taking into consideration certain classes of analytic functions depending on an extra parameter previously introduced related to the theory of strong differential subordination and superordination. Operators previously defined using confluent hypergeometric function, namely Kummer–Bernardi and Kummer–Libera integral operators, are also adapted to those classes and strong differential superordinations are obtained for which they are the best subordinants. Similar results are obtained regarding the derivatives of the operators. The examples presented at the end of the study are proof of the applicability of the original results.
Citation: Axioms
PubDate: 2022-04-29
DOI: 10.3390/axioms11050209
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 210: Randić Index of a Line Graph
Authors: Jiangfu Zhang, Baoyindureng Wu
First page: 210
Abstract: The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) for all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this note, we show that R(L(T))>n4 for any tree T of order n≥3. A number of relevant conjectures are proposed.
Citation: Axioms
PubDate: 2022-04-29
DOI: 10.3390/axioms11050210
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 211: Extended Form of Robust Solutions for
Uncertain Continuous-Time Linear Programming Problems with Time-Dependent
Matrices
Authors: Hsien-Chung Wu
First page: 211
Abstract: An extended form of robust continuous-time linear programming problem with time-dependent matrices is formulated in this paper. This complicated problem is studied theoretically in this paper. We also design a computational procedure to solve this problem numerically. The desired data that appeared in the problem are considered to be uncertain quantities, which are treated according to the concept of robust optimization. A discretization problem of the robust counterpart is formulated and solved to obtain the ϵ-optimal solutions.
Citation: Axioms
PubDate: 2022-05-01
DOI: 10.3390/axioms11050211
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 212: Finite Time Blowup in a Fourth-Order
Dispersive Wave Equation with Nonlinear Damping and a Non-Local Source
Authors: Stella Vernier-Piro
First page: 212
Abstract: In this work, we consider a class of initial boundary value problems for fourth-order dispersive wave equations with superlinear damping and non-local source terms as well as time-dependent coefficients in Ω×(t>0), where Ω is a bounded domain in RN and N≥2. We prove that there exists a safe time interval of existence in the solution [0,T], with T being a lower bound of the blowup time t*. Moreover, we find an explicit lower bound of t*, assuming the coefficients are positive constants.
Citation: Axioms
PubDate: 2022-05-01
DOI: 10.3390/axioms11050212
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 213: Change-Point Detection in Homogeneous Segments
of COVID-19 Daily Infection
Authors: Segun Light Jegede, Krzysztof J. Szajowski
First page: 213
Abstract: Modeling the number of individuals in different states is a principal tool in the event of an epidemic. The natural transition of individuals between possible states often includes deliberate interference such as isolation or vaccination. Thus, the mathematical model may need to be re-calibrated due to various factors. The model considered in this paper is the SIRD epidemic model. An additional parameter is the moment of changing the description of the phenomenon when the parameters of the model change and the change is not pre-specified. Detecting and estimating the moment of change in real time is the subject of statistical research. A sequential (online) approach was applied using the Bayesian shift point detection algorithm and trimmed exact linear time. We show how methods of analysis behave in different instances. These methods are verified on simulated data and applied to pandemic data of a selected European country. The simulation is performed with a social network graph to obtain a practical representation ability. The epidemiological data used come from the territory of Poland and concern the COVID-19 epidemic in Poland. The results show satisfactory detection of the moments where the applied model needs to be verified and re-calibrated. These show the effectiveness of the proposed combination of methods.
Citation: Axioms
PubDate: 2022-05-04
DOI: 10.3390/axioms11050213
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 214: Cheap Control in a Non-Scalarizable
Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis
Authors: Vladimir Turetsky, Valery Y. Glizer
First page: 214
Abstract: In this work, a finite-horizon zero-sum linear-quadratic differential game, modeling a pursuit-evasion problem, was considered. In the game’s cost function, the cost of the control of the minimizing player (the minimizer/the pursuer) was much smaller than the cost of the control of the maximizing player (the maximizer/the evader) and the cost of the state variable. This smallness was expressed by a positive small multiplier (a small parameter) of the square of the L2-norm of the minimizer’s control in the cost function. Parameter-free sufficient conditions for the existence of the game’s solution (the players’ optimal state-feedback controls and the game value), valid for all sufficiently small values of the parameter, were presented. The boundedness (with respect to the small parameter) of the time realizations of the optimal state-feedback controls along the corresponding game’s trajectory was established. The best achievable game value from the minimizer’s viewpoint was derived. A relation between solutions of the original cheap control game and the game that was obtained from the original one by replacing the small minimizer’s control cost with zero, was established. An illustrative real-life example is presented.
Citation: Axioms
PubDate: 2022-05-05
DOI: 10.3390/axioms11050214
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 215: Countermeasures of Double Carbon Targets in
Beijing–Tianjin–Hebei Region by Using Grey Model
Authors: Zhenxiu Liu, Meng Wang, Lifeng Wu
First page: 215
Abstract: In this paper, by combining the development characteristics of the Beijing–Tianjin–Hebei region, the fractional accumulation GM (1,1) model was used to predict the peak time of the Beijing–Tianjin–Hebei region, and the carbon peak year was predicted to be 2044. Then, according to the urbanization level and the proportion of the added value of the secondary industry in different regions in 2018, regions were divided into four categories: the first to reach the peak, the peak on schedule (easy), the peak on schedule (general), and the peak may be delayed. The Beijing–Tianjin–Hebei region plans to achieve a carbon peak by 2044 and proposes specific suggestions to achieve carbon neutrality by 2060 to achieve coordinated development of Beijing–Tianjin–Hebei and high-quality development.
Citation: Axioms
PubDate: 2022-05-05
DOI: 10.3390/axioms11050215
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 216: Interval-Valued Pseudo Overlap Functions and
Application
Authors: Rong Liang, Xiaohong Zhang
First page: 216
Abstract: A class of interval-valued OWA operators can be constructed from interval-valued overlap functions with interval-valued weights, which plays an important role in solving multi-attribute decision making (MADM) problems considering interval numbers as attribute values. Among them, when the importance of multiple attributes is different, it can only be calculated by changing the interval-valued weights. In fact, we can directly abandon the commutativity and extend the interval-valued overlap functions (IO) to interval-valued pseudo overlap functions (IPO) so that function itself implies the weights of the attributes, thus there is no need to calculate the OWA operator, which is more flexible in applications. In addition, the similar generalization on interval-valued pseudo t-norms obtained from interval-valued t-norms further enhances the feasibility of our study. In this paper, we mainly present the notion of interval-valued pseudo overlap functions and a few their qualities, including migrativity and homogeneity, and give some construction theorems and specific examples. Then, we propose the definitions of residuated implications induced by interval-valued pseudo overlap functions, give their equivalent forms, and prove some properties satisfied by them. Finally, two application examples about IPO to interval-valued multi-attribute decision making (I-MADM) are described. The results show that interval-valued pseudo overlap functions can not only be used to obtain the same rankings, but also be more flexible, simple and widely used.
Citation: Axioms
PubDate: 2022-05-06
DOI: 10.3390/axioms11050216
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 217: A Symplectic Algorithm for Constrained
Hamiltonian Systems
Authors: Jingli Fu, Lijun Zhang, Shan Cao, Chun Xiang, Weijia Zao
First page: 217
Abstract: In this paper, a symplectic algorithm is utilized to investigate constrained Hamiltonian systems. However, the symplectic method cannot be applied directly to the constrained Hamiltonian equations due to the non-canonicity. We firstly discuss the canonicalization method of the constrained Hamiltonian systems. The symplectic method is used to constrain Hamiltonian systems on the basis of the canonicalization, and then the numerical simulation of the system is carried out. An example is presented to illustrate the application of the results. By using the symplectic method of constrained Hamiltonian systems, one can solve the singular dynamic problems of nonconservative constrained mechanical systems, nonholonomic constrained mechanical systems as well as physical problems in quantum dynamics, and also available in many electromechanical coupled systems.
Citation: Axioms
PubDate: 2022-05-07
DOI: 10.3390/axioms11050217
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 218: On the Group of Absolutely Summable Sequences
Authors: Lydia Außenhofer
First page: 218
Abstract: For an abelian topological group G, the sequence group ℓ1(G) of all absolutely summable sequences in G is studied. It is shown that ℓ1(G) is a Pontryagin reflexive group in case G is a reflexive metrizable group or an LCA group. Further, ℓ1(G) has the Schur property if and only if G has it and ℓ1(G) is a Schwartz group if and only if G is linearly topologized.
Citation: Axioms
PubDate: 2022-05-07
DOI: 10.3390/axioms11050218
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 219: Characterizing Forbidden Pairs for the
Edge-Connectivity of a Connected Graph to Be Its Minimum Degree
Authors: Junfeng Du, Ziwen Huang, Liming Xiong
First page: 219
Abstract: Let H be a class of given graphs. A graph G is said to be H-free if G contains no induced copies of H for any H∈H. In this article, we characterize all connected subgraph pairs {R,S} guranteeing the edge-connectivity of a connected {R,S}-free graph to have the same minimum degree. Our result is a supplement of Wang et al. Furthermore, we obtain a relationship of forbidden sets when those general parameters have the recurrence relation.
Citation: Axioms
PubDate: 2022-05-09
DOI: 10.3390/axioms11050219
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 220: New Fuzzy Extensions on Binomial Distribution
Authors: Gia Sirbiladze, Janusz Kacprzyk, Teimuraz Manjafarashvili, Bidzina Midodashvili, Bidzina Matsaberidze
First page: 220
Abstract: The use of discrete probabilistic distributions is relevant to many practical tasks, especially in present-day situations where the data on distribution are insufficient and expert knowledge and evaluations are the only instruments for the restoration of probability distributions. However, in such cases, uncertainty arises, and it becomes necessary to build suitable approaches to overcome it. In this direction, this paper discusses a new approach of fuzzy binomial distributions (BDs) and their extensions. Four cases are considered: (1) When the elementary events are fuzzy. Based on this information, the probabilistic distribution of the corresponding fuzzy-random binomial variable is calculated. The conditions of restrictions on this distribution are obtained, and it is shown that these conditions depend on the ratio of success and failure of membership levels. The formulas for the generating function (GF) of the constructed distribution and the first and second order moments are also obtained. The Poisson distribution is calculated as the limit case of a fuzzy-random binomial experiment. (2) When the number of successes is of a fuzzy nature and is represented as a fuzzy subset of the set of possible success numbers. The formula for calculating the probability of convolution of binomial dependent fuzzy events is obtained, and the corresponding GF is built. As a result, the scheme for calculating the mathematical expectation of the number of fuzzy successes is defined. (3) When the spectrum of the extended distribution is fuzzy. The discussion is based on the concepts of a fuzzy-random event and its probability, as well as the notion of fuzzy random events independence. The fuzzy binomial upper distribution is specifically considered. In this case the fuzziness is represented by the membership levels of the binomial and non-binomial events of the complete failure complex. The GF of the constructed distribution and the first-order moment of the distribution are also calculated. Sufficient conditions for the existence of a limit distribution and a Poisson distribution are also obtained. (4) As is known, based on the analysis of lexical material, the linguistic spectrum of the statistical process of word-formation becomes two-component when switching to vocabulary. For this, two variants of the hybrid fuzzy-probabilistic process are constructed, which can be used in the analysis of the linguistic spectrum of the statistical process of word-formation. A fuzzy extension of standard Fuchs distribution is also presented, where the fuzziness is reflected in the growing numbers of failures. For better representation of the results, the examples of fuzzy BD are illustrated in each section.
Citation: Axioms
PubDate: 2022-05-09
DOI: 10.3390/axioms11050220
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 221: Aspects of Differential Calculus Related to
Infinite-Dimensional Vector Bundles and Poisson Vector Spaces
Authors: Helge Glöckner
First page: 221
Abstract: We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E×E is a kR-space.
Citation: Axioms
PubDate: 2022-05-09
DOI: 10.3390/axioms11050221
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 222: Exact Criteria for the Existence of a Moving
Singular Point in a Complex Domain for a Nonlinear Differential
Third-Degree Equation with a Polynomial Seventh-Degree Right-Hand Side
Authors: Victor Orlov, Magomedyusuf Gasanov
First page: 222
Abstract: Earlier, the authors formulated and proved interval and point criteria for the existence of moving singular points of a third-degree nonlinear differential equation with a polynomial seventh-degree right-hand side for a real domain. For the complex domain, these criteria are associated with specificity of transition to phase spaces. Necessary as well as necessary and sufficient conditions for the existence of moving singular points are obtained. The results of these studies are the basis of the algorithm for obtaining moving singular points of nonlinear differential equations in the complex domain. The results of this paper allow us to expand the classes of the studied nonlinear differential equations with moving peculiarities.
Citation: Axioms
PubDate: 2022-05-10
DOI: 10.3390/axioms11050222
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 223: Co-Training Method Based on Semi-Decoupling
Features for MOOC Learner Behavior Prediction
Authors: Huanhuan Wang, Libo Xu, Zhenrui Huang, Jiagong Wang
First page: 223
Abstract: Facing the problem of massive unlabeled data and limited labeled samples, semi-supervised learning is favored, especially co-training. Standard co-training requires sufficiently redundant and conditionally independent dual views; however, in fact, few dual views exist that satisfy this condition. To solve this problem, we propose a co-training method based on semi-decoupling features, that is, semi-decoupling features based on a known single view and then constructing independent and redundant dual views: (1) take a small number of important features as shared features of the dual views according to the importance of the features; (2) separate the remaining features one by one or in small batches according to the correlation between the features to make “divergent” features of the dual views; (3) combine the shared features and the “divergent” features to construct dual views. In this paper, the experimental dataset was from the edX dataset jointly released by Harvard University and MIT; the evaluation metrics adopted F1, Precision, and Recall. The analysis methods included three experiments: multiple models, iterations, and hyperparameters. The experimental results show that the effect of this model on MOOC learner behavior prediction was better than the other models, and the best prediction result was obtained in iteration 2. These all verify the effectiveness and superiority of this algorithm and provide a scientific and feasible reference for the development of the future education industry.
Citation: Axioms
PubDate: 2022-05-11
DOI: 10.3390/axioms11050223
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 224: Krein’s Theorem in the Context of
Topological Abelian Groups
Authors: Tayomara Borsich, Xabier Domínguez, Elena Martín-Peinador
First page: 224
Abstract: A topological abelian group G is said to have the quasi-convex compactness property (briefly, qcp) if the quasi-convex hull of every compact subset of G is again compact. In this paper we prove that there exist locally quasi-convex metrizable complete groups G which endowed with the weak topology associated to their character groups G∧, do not have the qcp. Thus, Krein’s Theorem, a well known result in the framework of locally convex spaces, cannot be fully extended to locally quasi-convex groups. Some features of the qcp are also studied.
Citation: Axioms
PubDate: 2022-05-12
DOI: 10.3390/axioms11050224
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 225: Tensor Product of Operators Satisfying
Zariouh’s Property (gaz), and Stability under Perturbations
Authors: Elvis Aponte, Narayanapillai Jayanthi, Domingo Quiroz, Ponraj Vasanthakumar
First page: 225
Abstract: For bounded linear operators defined on complex infinite-dimensional Banach space, H. Zariouh, in an article (Property (gz) for bounded linear operators, (2013)) introduced and studied the property (gaz). In this study, through techniques using the local spectral theory of operators, we discover the sufficient conditions that allow the transfer of the property (gaz) from two tensor factors T and S to their tensor product T⊗S. The stability of the property (gaz) in the tensor product under perturbations is also investigated. The theory is exemplified by considering suitable classes of operators such as shift operators, convolution operators, and m-invertible contractions.
Citation: Axioms
PubDate: 2022-05-12
DOI: 10.3390/axioms11050225
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 226: A Note on the Reverse Order Law for g-Inverse
of Operator Product
Authors: Yingying Qin, Zhiping Xiong
First page: 226
Abstract: The generalized inverse has many important applications in aspects of the theoretical research of matrices and statistics. One of the core problems of the generalized inverse is finding the necessary and sufficient conditions of the reverse order laws for the generalized inverse of the operator product. In this paper, we study the reverse order law for the g-inverse of an operator product T1T2T3 using the technique of matrix form of bounded linear operators. In particular, some necessary and sufficient conditions for the inclusion T3{1}T2{1}T1{1} ⊆ (T1T2T3){1} is presented. Moreover, some finite dimensional results are extended to infinite dimensional settings.
Citation: Axioms
PubDate: 2022-05-12
DOI: 10.3390/axioms11050226
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 227: Some Generalizations of the Jensen-Type
Inequalities with Applications
Authors: Mirna Rodić
First page: 227
Abstract: Motivated by some results about reverses of the Jensen inequality for positive measure, in this paper we give generalizations of those results for real Stieltjes measure dλ which is not necessarily positive using several Green functions. Utilizing these results we define some new mean value theorems of Lagrange and Cauchy types, and derive some new Cauchy-type means.
Citation: Axioms
PubDate: 2022-05-13
DOI: 10.3390/axioms11050227
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 228: A Two-Stage Multi-Criteria Supplier Selection
Model for Sustainable Automotive Supply Chain under Uncertainty
Authors: Thanh-Tuan Dang, Ngoc-Ai-Thy Nguyen, Van-Thanh-Tien Nguyen, Le-Thanh-Hieu Dang
First page: 228
Abstract: Sustainable supplier selection (SSS) is gaining popularity as a practical method to supply chain sustainability among academics and practitioners. However, in addition to balancing economic, social, and environmental factors, the emergence of the COVID-19 pandemic has affected the selection of long-term suppliers to ensure sustainable supply chains, recover better from the pandemic and effectively respond to any future unprecedented crises. The purpose of this study is to assess and choose a possible supplier based on their capability to adapt to the COVID-19 epidemic in a sustainable manner. For this assessment, a framework based on multi-criteria decision making (MCDM) is provided that integrates spherical fuzzy Analytical Hierarchical Process (SF-AHP) and grey Complex Proportional Assessment (G-COPRAS), in which spherical fuzzy sets and grey numbers are used to express the ambiguous linguistic evaluation statements of experts. In the first stage, the evaluation criteria system is identified through a literature review and experts’ opinions. The SF-AHP is then used to determine the criteria weights. Finally, the G-COPRAS method is utilized to select sustainable suppliers. A case study in the automotive industry in Vietnam is presented to demonstrate the proposed approach’s effectiveness. From the SF-AHP findings, “quality”, “use of personal protective equipment”, “cost/price”, “safety and health practices and wellbeing of suppliers”, and “economic recovery programs” have been ranked as the five most important criteria. From G-COPRAS analysis, THACO Parts (Supplier 02) is the best supplier. A sensitivity study was also conducted to verify the robustness of the proposed model, in which the priority rankings of the best suppliers are very similar. For long-term development and increased competitiveness, industrial businesses must stress the integration of response mechanisms during SSS implementation in the COVID-19 epidemic, according to the findings. This will result in significant cost and resource savings, as well as reduced environmental consequences and a long-term supply chain, independent of the crisis.
Citation: Axioms
PubDate: 2022-05-13
DOI: 10.3390/axioms11050228
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 229: The Possibility of Combining and Implementing
Deep Neural Network Compression Methods
Authors: Bratislav Predić, Uroš Vukić, Muzafer Saračević, Darjan Karabašević, Dragiša Stanujkić
First page: 229
Abstract: In the paper, the possibility of combining deep neural network (DNN) model compression methods to achieve better compression results was considered. To compare the advantages and disadvantages of each method, all methods were applied to the ResNet18 model for pretraining to the NCT-CRC-HE-100K dataset while using CRC-VAL-HE-7K as the validation dataset. In the proposed method, quantization, pruning, weight clustering, QAT (quantization-aware training), preserve cluster QAT (hereinafter PCQAT), and distillation were performed for the compression of ResNet18. The final evaluation of the obtained models was carried out on a Raspberry Pi 4 device using the validation dataset. The greatest model compression result on the disk was achieved by applying the PCQAT method, whose application led to a reduction in size of the initial model by as much as 45 times, whereas the greatest model acceleration result was achieved via distillation on the MobileNetV2 model. All methods led to the compression of the initial size of the model, with a slight loss in the model accuracy or an increase in the model accuracy in the case of QAT and weight clustering. INT8 quantization and knowledge distillation also led to a significant decrease in the model execution time.
Citation: Axioms
PubDate: 2022-05-13
DOI: 10.3390/axioms11050229
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 230: Evaluation of Digital Marketing Technologies
with Fuzzy Linguistic MCDM Methods
Authors: Ngo Quang Trung, Nguyen Van Thanh
First page: 230
Abstract: Technology is becoming the tool that changes how people live every day, and the marketing strategies of businesses are also gradually shifting to the industry 4.0 mindset of constant growth and development. Digital marketing has changed human habits of information accessibility, determined their interactions, and witnessed the birth of a variety of new marketing technologies. Marketers are creating digital marketing products and services that enhance the experience for consumers, products, and services that are also delivered through high digital marketing networks. As a result, data sources become more abundant and allow consumers to have more choices. All products, services, technologies, and data are increasingly meeting the needs of consumers, thereby confirming the effectiveness of digital marketing in today’s market. However, the evaluation and selection of digital marketing technology is very complex since it has many conflicting criteria and goals. The multi-criteria decision-making model (MCDM) is a powerful technique widely used for solving this type of problem. Thus, the author proposed a fuzzy linguistic MCDM method for evaluation of digital marketing technologies. After determining the evaluation criteria and alternatives, two MCDM methods, including Spherical Fuzzy Analytic Hierarchy Process (SF-AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), are used in the evaluation and selection of digital marketing technologies procedure. Finally, an application is present to demonstrate the potential use of the proposed methodology. The main contribution of this study is to propose a Spherical fuzzy MCDM model to support planners and decision makers in the digital marketing technology evaluation and selection processes. A case study is also performed to showcase the feasibility of the proposed approach.
Citation: Axioms
PubDate: 2022-05-13
DOI: 10.3390/axioms11050230
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 231: Taylor’s Formula for Generalized
Weighted Fractional Derivatives with Nonsingular Kernels
Authors: Houssine Zine, El Mehdi Lotfi, Delfim F. M. Torres, Noura Yousfi
First page: 231
Abstract: We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean value theorems for generalized weighted fractional operators are obtained. Direct corollaries allow one to obtain the recent Taylor’s and mean value theorems for Caputo–Fabrizio, Atangana–Baleanu–Caputo (ABC) and weighted ABC derivatives.
Citation: Axioms
PubDate: 2022-05-15
DOI: 10.3390/axioms11050231
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 232: Modeling Preferences through Personality and
Satisfaction to Guide the Decision Making of a Virtual Agent
Authors: Jorge Castro-Rivera, María Lucila Morales-Rodríguez, Nelson Rangel-Valdez, Claudia Gómez-Santillán, Luciano Aguilera-Vázquez
First page: 232
Abstract: Satisfaction is relevant for decision makers (DM, Decision Makers). Satisfaction is the feeling produced in individuals by executing actions to satisfy their needs, for example, the payment of debts, jobs, or academic achievements, and the acquisition of goods or services. In the satisfaction literature, some theories model the satisfaction of individuals from job and customer approaches. However, considering personality elements to influence satisfaction and define preferences in strategies that optimize decision making provides the unique characteristics of a DM. These characteristics favor the scope of solutions closer to the satisfaction expectation. Satisfaction theories do not include specific elements of personality and preferences, so integrating these elements will offer more efficient decisions in computable models. In this work, a model of satisfaction with personality characteristics that influence the preferences of a DM is proposed. The proposed model is integrated into a preference-based optimizer that improves the decision-making process of a Virtual Decision Maker (VDM) in an optimization context. The optimization context addressed in this work is the product selection process within a food product shopping problem. An experimental design is proposed that compares two configurations that represent the cognitive part of an agent’s decision process to validate the operation of the proposed model in the context of optimization: (1) satisfaction, personality, and preferences, and (2) personality and preferences. The results show that considering satisfaction and personality in combination with preferences provides solutions closer to the interests of an individual, reflecting a more realistic behavior. Furthermore, this work demonstrates that it is possible to create a configurable model that allows adapting to different aptitudes and reflecting them in a computable model.
Citation: Axioms
PubDate: 2022-05-17
DOI: 10.3390/axioms11050232
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 233: Some Upper Bounds for RKHS Approximation by
Bessel Functions
Authors: Mingdang Tian, Baohuai Sheng, Shuhua Wang
First page: 233
Abstract: A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel transforms, respectively. Their equivalent relation is shown, with which the upper bound estimate for the best RKHS approximation is provided. The convergence rate is bounded with the defined modulus of smoothness, which shows that the RKHS approximation can attain the same approximation ability as that of the Fourier–Bessel series and Fourier–Bessel transform. In particular, it is shown that for a RKHS produced by the Bessel operator, the convergence rate sums up to the bound of a corresponding convolution operator approximation. The investigations show some new applications of Bessel functions. The results obtained can be used to bound the approximation error in learning theory.
Citation: Axioms
PubDate: 2022-05-17
DOI: 10.3390/axioms11050233
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 234: Investigation into the Explicit Solutions of
the Integrable (2+1)-Dimensional Maccari System via the Variational
Approach
Authors: Kang-Jia Wang, Jing Si
First page: 234
Abstract: In this paper, the integrable (2+1)-dimensional Maccari system (MS), which can model many complex phenomena in hydrodynamics, plasma physics and nonlinear optics, is investigated by the variational approach (VA). This proposed approach that based on the variational theory and Ritz-like method can construct the explicit solutions via the stationary conditions only taking two steps. Finally, the dynamic behaviors of the solutions are exhibited by choosing the appropriate parameters through the 3-D and density plots. It can be seen that the proposed method is concise and straightforward, and can be adopted to study the travelling wave theory in physics.
Citation: Axioms
PubDate: 2022-05-18
DOI: 10.3390/axioms11050234
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 235: Projective Integration for Hyperbolic Shallow
Water Moment Equations
Authors: Amrita Amrita, Julian Koellermeier
First page: 235
Abstract: In free surface flows, shallow water models simplify the flow conditions by assuming a constant velocity profile over the water depth. Recently developed Shallow Water Moment Equations allow for variations of the velocity profile at the expense of a more complex PDE system. The resulting equations can become stiff depending on the friction parameters, which leads to severe time step constraints of standard numerical schemes. In this paper, we apply Projective Integration schemes to stiff Shallow Water Moment Equations to overcome the time step constraints in the stiff regime and accelerate the numerical computations while still achieving high accuracy. In different dam break and smooth wave test cases, we obtain a speedup of up to 55 with respect to standard schemes.
Citation: Axioms
PubDate: 2022-05-18
DOI: 10.3390/axioms11050235
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 236: Bounds for the Neuman–Sándor Mean
in Terms of the Arithmetic and Contra-Harmonic Means
Authors: Wen-Hui Li, Peng Miao, Bai-Ni Guo
First page: 236
Abstract: In this paper, the authors provide several sharp upper and lower bounds for the Neuman–Sándor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyperbolic cosine function.
Citation: Axioms
PubDate: 2022-05-19
DOI: 10.3390/axioms11050236
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 237: Certain Subclasses of Bi-Starlike Function of
Authors: Alhanouf Alburaikan, Gangadharan Murugusundaramoorthy, Sheza M. El-Deeb
First page: 237
Abstract: In the present paper, we introduce new subclasses of bi-starlike and bi-convex functions of complex order associated with Erdély–Kober-type integral operator in the open unit disc and find the estimates of initial coefficients in these classes. Moreover, we obtain Fekete-Szegő inequalities for functions in these classes. Some of the significances of our results are pointed out as corollaries.
Citation: Axioms
PubDate: 2022-05-20
DOI: 10.3390/axioms11050237
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 238: An Application of the Super-SBM MAX and
LTS(A,A,A) Models to Analyze the Business Performance of Hydropower
Suppliers in Vietnam
Authors: Thi Kim Lien Nguyen, Huu Ngoan Nguyen, Van Dan Dinh, Quoc Ngu Nguyen, Van Hung Le
First page: 238
Abstract: As Vietnam continues to industrialize and modernize, such economic development and high-tech will require a major electrical energy source to operate the electrical equipment; hence, the hydropower plants are established and growing up to demand. Therefore, the purpose of this study is to evaluate the business performance of Vietnamese hydropower suppliers by integrating the LTS(A,A,A) model of the Additive Holt-winters method in Tableau and a super-slacks-based measure (super-SBM) max model in data envelopment analysis (DEA). The LTS(A,A,A) model is applied to forecast future valuation from 2022 to 2025 based on historical time series from 2012 to 2021. Next, with the actual and predicted data, the researcher uses the super-SBM max model to calculate the business performance of these hydropower suppliers from past to future. The empirical result reveals efficient and inefficient cases to explore which hydropower suppliers can achieve the business performance in their operational process. The position of hydropower suppliers in Vietnam from past to future time is determined particularly based on their scores every year. Further, the empirical result recommends a solution to deal with inefficient cases by deducting the input excesses and raising the output shortages based on the principle of the super-SBM Max model in DEA. The finding results create an overview of the operational process with the continuing variations in each period to equip hydropower suppliers in Vietnam which will determine their future and operational orientation.
Citation: Axioms
PubDate: 2022-05-20
DOI: 10.3390/axioms11050238
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 239: Two Invariants for Geometric Mappings
Authors: Nenad O. Vesić, Vladislava M. Milenković, Mića S. Stanković
First page: 239
Abstract: Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection.
Citation: Axioms
PubDate: 2022-05-20
DOI: 10.3390/axioms11050239
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 240: Fuzzy Caratheodory’s Theorem and Outer
∗-Fuzzy Measure
Authors: Radko Mesiar, Chenkuan Li, Abbas Ghaffari, Reza Saadati
First page: 240
Abstract: The goal of this paper is to introduce two new concepts ∗-fuzzy premeasure and outer ∗-fuzzy measure, and to further prove some properties, such as Caratheodory’s Theorem, as well as the unique extension of ∗-fuzzy premeasure. This theorem is remarkable for it allows one to construct a ∗-fuzzy measure by first defining it on a small algebra of sets, where its ∗-additivity could be easy to verify, and then this theorem guarantees its extension to a sigma-algebra.
Citation: Axioms
PubDate: 2022-05-20
DOI: 10.3390/axioms11050240
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 241: Retrial Queuing-Inventory Systems with Delayed
Feedback and Instantaneous Damaging of Items
Authors: Agassi Melikov, Sevinj Aliyeva, Sajeev S. Nair, B. Krishna Kumar
First page: 241
Abstract: This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal to zero upon arrival of a primary customer, then this customer, according to the Bernoulli scheme, either leaves the system or goes into an infinite buffer to repeat their request in the future. The rate of retrial customers is constant, and if the inventory level is zero upon arrival of a retrial customer, then this customer, according to the Bernoulli scheme, either leaves orbit or remains in orbit to repeat its request in the future. According to the Bernoulli scheme, each served primary or retrial customer either leaves the system or feedbacks into orbit to repeat their request. Destructive customers that form a Poisson flow cause damage to items. Unlike primary, retrial, and feedback customers, destructive customers do not require items, since, upon arrival of such customers, the inventory level instantly decreases by one. The system adopted one of two replenishment policies: (s, Q) or (s, S). In both policies, the lead time is a random variable that has an exponential distribution. It is shown that the mathematical model of the system under study was a two-dimensional Markov chain with an infinite state space. Algorithms for calculating the elements of the generating matrices of the constructed chains were developed, and the ergodicity conditions for both policies were found. To calculate the steady-state probabilities, a matrix-geometric method was used. Formulas were found for calculating the main performance measures of the system. The results of the numerical experiments, including the minimization of the total cost, are demonstrated.
Citation: Axioms
PubDate: 2022-05-20
DOI: 10.3390/axioms11050241
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 242: The State of the Art of Data Mining Algorithms
for Predicting the COVID-19 Pandemic
Authors: Keila Vasthi Cortés-Martínez, Hugo Estrada-Esquivel, Alicia Martínez-Rebollar, Yasmín Hernández-Pérez, Javier Ortiz-Hernández
First page: 242
Abstract: Current computer systems are accumulating huge amounts of information in several application domains. The outbreak of COVID-19 has increased rekindled interest in the use of data mining techniques for the analysis of factors that are related to the emergence of an epidemic. Data mining techniques are being used in the analysis and interpretation of information, which helps in the discovery of patterns, planning of isolation policies, and even predicting the speed of proliferation of contagion in a viral disease such as COVID-19. This research provides a comprehensive study of various data mining algorithms that are used in conjunction with epidemiological prediction models. The document considers that there is an opportunity to improve or develop tools that offer an accurate prognosis in the management of viral diseases through the use of data mining tools, based on a comparative study of 35 research papers.
Citation: Axioms
PubDate: 2022-05-23
DOI: 10.3390/axioms11050242
Issue No: Vol. 11, No. 5 (2022)
- Axioms, Vol. 11, Pages 243: Some New Bounds for the Inverse Sum Indeg
Energy of Graphs
Authors: Fengwei Li, Qingfang Ye, Hajo Broersma
First page: 243
Abstract: Let G be a (molecular) graph with n vertices, and di be the degree of its i-th vertex. Then, the inverse sum indeg matrix of G is the n×n matrix C(G) with entries cij=didjdi+dj, if the i-th and the j-th vertices are adjacent and 0 otherwise. Let μ1≥μ2≥…≥μn be the eigenvalues of C arranged in order. The inverse sum indeg energy of G, εisi(G) can be represented as ∑j=1n μi . In this paper, we establish several novel upper and lower sharp bounds on μ1 and εisi(G) via some other graph parameters, and describe the structures of the extremal graphs.
Citation: Axioms
PubDate: 2022-05-23
DOI: 10.3390/axioms11050243
Issue No: Vol. 11, No. 5 (2022)
