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- Mathematics, Vol. 5, Pages 19: A Generalization of b-Metric Space and Some
Fixed Point Theorems
Authors: Tayyab Kamran, Maria Samreen, Qurat UL Ain
First page: 19
Abstract: In this paper, inspired by the concept of b-metric space, we introduce the concept of extended b-metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our results extend/generalize many pre-existing results in literature.
PubDate: 2017-03-23
DOI: 10.3390/math5020019
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 20: F-Harmonic Maps between Doubly Warped
Product Manifolds
Authors: Seyed Torbaghan, Morteza Rezaii
First page: 20
Abstract: In this paper, some properties of F -harmonic and conformal F -harmonic maps between doubly warped product manifolds are studied and new examples of non-harmonic F -harmonic maps are constructed.
PubDate: 2017-03-23
DOI: 10.3390/math5020020
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 21: On Some Extended Block Krylov Based Methods
for Large Scale Nonsymmetric Stein Matrix Equations
Authors: Abdeslem Bentbib, Khalide Jbilou, EL Sadek
First page: 21
Abstract: In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA) or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments.
PubDate: 2017-03-27
DOI: 10.3390/math5020021
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 22: On Optimal Fuzzy Best Proximity Coincidence
Points of Proximal Contractions Involving Cyclic Mappings in
Non-Archimedean Fuzzy Metric Spaces
Authors: Manuel Sen, Mujahid Abbas, Naeem Saleem
First page: 22
Abstract: The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair ( g , T ) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p -cyclic proximal contraction. Two types of such contractions (so called of type I and of type II) are dealt with. In particular, the existence, uniqueness and limit properties for sequences to optimal fuzzy best proximity coincidence points are investigated for such pairs of mappings.
PubDate: 2017-04-01
DOI: 10.3390/math5020022
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 23: Best Proximity Point Results in
Non-Archimedean Modular Metric Space
Authors: Mohadeshe Paknazar, Manuel Sen
First page: 23
Abstract: In this paper, we introduce the new notion of Suzuki-type ( α , β , θ , γ ) -contractive mapping and investigate the existence and uniqueness of the best proximity point for such mappings in non-Archimedean modular metric space using the weak P λ -property. Meanwhile, we present an illustrative example to emphasize the realized improvements. These obtained results extend and improve certain well-known results in the literature.
PubDate: 2017-04-05
DOI: 10.3390/math5020023
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 24: Fixed Points of Set Valued Mappings in
Terms of Start Point on a Metric Space Endowed with a Directed Graph
Authors: Murchana Neog, Pradip Debnath
First page: 24
Abstract: In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and establish its relation with start point in the setting of a metric space endowed with a directed graph. Further, some fixed point theorems for set valued maps have been proven in this context. A version of the Knaster–Tarski theorem has also been established using our results.
PubDate: 2017-04-19
DOI: 10.3390/math5020024
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 25: Discrete-Time Fractional Optimal Control
Authors: Tirumalasetty Chiranjeevi, Raj Biswas
First page: 25
Abstract: A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples are taken up and their solution technique is presented. Results are produced for different values of α .
PubDate: 2017-04-19
DOI: 10.3390/math5020025
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 26: A New Variational Iteration Method for a
Class of Fractional Convection-Diffusion Equations in Large Domains
Authors: Mohammad Abolhasani, Saeid Abbasbandy, Tofigh Allahviranloo
First page: 26
Abstract: In this paper, we introduced a new generalization method to solve fractional convection–diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in controlling the convergence region of the approximate solution. By solving some fractional convection–diffusion equations with a propounded method and comparing it with standard VIM, it was concluded that complete reliability, efficiency, and accuracy of this method are guaranteed. Additionally, we studied and investigated the convergence of the proposed method, namely the VIM with an auxiliary parameter. We also offered the optimal choice of the auxiliary parameter in the proposed method. It was noticed that the approach could be applied to other models of physics.
PubDate: 2017-05-11
DOI: 10.3390/math5020026
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 27: Analysis of Magneto-hydrodynamics Flow and
Heat Transfer of a Viscoelastic Fluid through Porous Medium in Wire
Coating Analysis
Authors: Zeeshan Khan, Muhammad Khan, Saeed Islam, Bilal Jan, Fawad Hussain, Haroon Ur Rasheed, Waris Khan
First page: 27
Abstract: Wire coating process is a continuous extrusion process for primary insulation of conducting wires with molten polymers for mechanical strength and protection in aggressive environments. Nylon, polysulfide, low/high density polyethylene (LDPE/HDPE) and plastic polyvinyl chloride (PVC) are the common and important plastic resin used for wire coating. In the current study, wire coating is performed using viscoelastic third grade fluid in the presence of applied magnetic field and porous medium. The governing equations are first modeled and then solved analytically by utilizing the homotopy analysis method (HAM). The convergence of the series solution is established. A numerical technique called ND-solve method is used for comparison and found good agreement. The effect of pertinent parameters on the velocity field and temperature profile is shown with the help of graphs. It is observed that the velocity profiles increase as the value of viscoelastic third grade parameter β increase and decrease as the magnetic parameter M and permeability parameter K increase. It is also observed that the temperature profiles increases as the Brinkman number B r , permeability parameter K , magnetic parameter M and viscoelastic third grade parameter (non-Newtonian parameter) β increase.
PubDate: 2017-05-16
DOI: 10.3390/math5020027
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 28: A Two-Stage Method for Piecewise-Constant
Solution for Fredholm Integral Equations of the First Kind
Authors: Fu-Rong Lin, Shi-Wei Yang
First page: 28
Abstract: A numerical method is proposed for estimating piecewise-constant solutions for Fredholm integral equations of the first kind. Two functionals, namely the weighted total variation (WTV) functional and the simplified Modica-Mortola (MM) functional, are introduced. The solution procedure consists of two stages. In the first stage, the WTV functional is minimized to obtain an approximate solution f TV * . In the second stage, the simplified MM functional is minimized to obtain the final result by using the damped Newton (DN) method with f TV * as the initial guess. The numerical implementation is given in detail, and numerical results of two examples are presented to illustrate the efficiency of the proposed approach.
PubDate: 2017-05-22
DOI: 10.3390/math5020028
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 29: Emergence of an Aperiodic Dirichlet Space
from the Tetrahedral Units of an Icosahedral Internal Space
Authors: Amrik Sen, Raymond Aschheim, Klee Irwin
First page: 29
Abstract: We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford’s geometric algebra. Consequently, we establish a connection between a three-dimensional icosahedral seed, a six-dimensional (6D) Dirichlet quantized host and a higher dimensional lattice structure. The 20G, owing to its icosahedral symmetry, bears the signature of a 6D lattice that manifests in the Dirichlet integer representation. We present an interpretation whereby the three-dimensional 20G can be regarded as the core substratum from which the higher dimensional lattices emerge. This emergent geometry is based on an induction principle supported by the Clifford multi-vector formalism of three-dimensional (3D) Euclidean space. This lays a geometric framework for understanding several physics theories related to S U ( 5 ) , E 6 , E 8 Lie algebras and their composition with the algebra associated with the even unimodular lattice in R 3 , 1 . The construction presented here is inspired by Penrose’s three world mode.
PubDate: 2017-05-26
DOI: 10.3390/math5020029
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 30: Coincidence Points of a Sequence of
Multivalued Mappings in Metric Space with a Graph
Authors: Muhammad Khan, Akbar Azam, Nayyar Mehmood
First page: 30
Abstract: In this article the coincidence points of a self map and a sequence of multivalued maps are found in the settings of complete metric space endowed with a graph. A novel result of Asrifa and Vetrivel is generalized and as an application we obtain an existence theorem for a special type of fractional integral equation. Moreover, we establish a result on the convergence of successive approximation of a system of Bernstein operators on a Banach space.
PubDate: 2017-05-26
DOI: 10.3390/math5020030
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 31: Nonlinear Gronwall–Bellman Type
Inequalities and Their Applications
Authors: Weimin Wang, Yuqiang Feng, Yuanyuan Wang
First page: 31
Abstract: In this paper, some nonlinear Gronwall–Bellman type inequalities are established. Then, the obtained results are applied to study the Hyers–Ulam stability of a fractional differential equation and the boundedness of solutions to an integral equation, respectively.
PubDate: 2017-05-31
DOI: 10.3390/math5020031
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 32: Metrization Theorem for Uniform Loops with
the Invertibility Property
Authors: Dagmar Markechová, Peter Vrábel, Beáta Stehlíková
First page: 32
Abstract: In this paper, we have proved a metrization theorem that gives the sufficient conditions for a uniform IP-loop X to be metrizable by a left-invariant metric. It is shown that by consideration of topological IP-loop dual to X we obtain an analogical theorem for the case of the right-invariant metric.
PubDate: 2017-06-02
DOI: 10.3390/math5020032
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 33: An Analysis on the Fractional Asset Flow
Differential Equations
Authors: Din Prathumwan, Wannika Sawangtong, Panumart Sawangtong
First page: 33
Abstract: The asset flow differential equation (AFDE) is the mathematical model that plays an essential role for planning to predict the financial behavior in the market. In this paper, we introduce the fractional asset flow differential equations (FAFDEs) based on the Liouville-Caputo derivative. We prove the existence and uniqueness of a solution for the FAFDEs. Furthermore, the stability analysis of the model is investigated and the numerical simulation is accordingly performed to support the proposed model.
PubDate: 2017-06-16
DOI: 10.3390/math5020033
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 34: Lie Symmetries, Optimal System and
Invariant Reductions to a Nonlinear Timoshenko System
Authors: Shadi Al-Omari, Fiazuddin Zaman, Hassan Azad
First page: 34
Abstract: Lie symmetries and their Lie group transformations for a class of Timoshenko systems are presented. The class considered is the class of nonlinear Timoshenko systems of partial differential equations (PDEs). An optimal system of one-dimensional sub-algebras of the corresponding Lie algebra is derived. All possible invariant variables of the optimal system are obtained. The corresponding reduced systems of ordinary differential equations (ODEs) are also provided. All possible non-similar invariant conditions prescribed on invariant surfaces under symmetry transformations are given. As an application, explicit solutions of the system are given where the beam is hinged at one end and free at the other end.
PubDate: 2017-06-17
DOI: 10.3390/math5020034
Issue No: Vol. 5, No. 2 (2017)
- Mathematics, Vol. 5, Pages 2: On Autonomy Imposition in Zero Interval
Limit Perturbation Expansion for the Spectral Entities of
Hilbert–Schmidt Integral Operators
Authors: Süha Tuna, Metin Demiralp
First page: 2
Abstract: In this work, we deal with the autonomy issue in the perturbation expansion for the eigenfunctions of a compact Hilbert–Schmidt integral operator. Here, the autonomy points to the perturbation expansion coefficients of the relevant eigenfunction not depending on the perturbation parameter explicitly, but the dependence on this parameter arises from the coordinate change at the zero interval limit. Moreover, the related half interval length is utilized as the perturbation parameter in the perturbative analyses. Thus, the zero interval limit perturbation for solving the eigenproblem under consideration is developed. The aim of this work is to show that the autonomy imposition brings an important restriction on the kernel of the corresponding integral operator, and the constructed perturbation series is not capable of expressing the exact solution approximately unless a specific type of kernel is considered. The general structure for the encountered constraints is revealed, and the specific class of kernels is identified to this end. Error analysis of the developed method is given. These analyses are also supported by certain illustrative implementations involving the kernels, which are and are not in the specific class addressed above. Thus, the efficiency of the developed method is shown, and the relevant analyses are confirmed.
PubDate: 2017-01-06
DOI: 10.3390/math5010002
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 3: From the Underdamped Generalized Elastic
Model to the Single Particle Langevin Description
Authors: Alessandro Taloni
First page: 3
Abstract: The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a probe particle and we show that this equation reduces to the usual Langevin equation for Brownian motion, and to the fractional Langevin equation on the long-time limit.
PubDate: 2017-01-06
DOI: 10.3390/math5010003
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 4: Logical Entropy of Dynamical Systems—A
General Model
Authors: Abolfazl Ebrahimzadeh, Zahra Giski, Dagmar Markechová
First page: 4
Abstract: In the paper by Riečan and Markechová (Fuzzy Sets Syst. 96, 1998), some fuzzy modifications of Shannon’s and Kolmogorov-Sinai’s entropy were studied and the general scheme involving the presented models was introduced. Our aim in this contribution is to provide analogies of these results for the case of the logical entropy. We define the logical entropy and logical mutual information of finite partitions on the appropriate algebraic structure and prove basic properties of these measures. It is shown that, as a special case, we obtain the logical entropy of fuzzy partitions studied by Markechová and Riečan (Entropy 18, 2016). Finally, using the suggested concept of entropy of partitions we define the logical entropy of a dynamical system and prove that it is the same for two dynamical systems that are isomorphic.
PubDate: 2017-01-06
DOI: 10.3390/math5010004
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 5: Data Clustering with Quantum Mechanics
Authors: Tony Scott, Madhusudan Therani, Xing Wang
First page: 5
Abstract: Data clustering is a vital tool for data analysis. This work shows that some existing useful methods in data clustering are actually based on quantum mechanics and can be assembled into a powerful and accurate data clustering method where the efficiency of computational quantum chemistry eigenvalue methods is therefore applicable. These methods can be applied to scientific data, engineering data and even text.
PubDate: 2017-01-06
DOI: 10.3390/math5010005
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 6: Zoology of Atlas-Groups: Dessins
D’enfants, Finite Geometries and Quantum Commutation
Authors: Michel Planat, Hishamuddin Zainuddin
First page: 6
Abstract: Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P . It is unusual, but significant to recognize that a P is a Grothendieck’s “dessin d’enfant” D and that a wealth of standard graphs and finite geometries G —such as near polygons and their generalizations—are stabilized by a D . In our paper, tripods P − D − G of rank larger than two, corresponding to simple groups, are organized into classes, e.g., symplectic, unitary, sporadic, etc. (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All of the defined geometries G ′ s have a contextuality parameter close to its maximal value of one.
PubDate: 2017-01-14
DOI: 10.3390/math5010006
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 7: Deterministic Seirs Epidemic Model for
Modeling Vital Dynamics, Vaccinations, and Temporary Immunity
Authors: Marek Trawicki
First page: 7
Abstract: In this paper, the author proposes a new SEIRS model that generalizes several classical deterministic epidemic models (e.g., SIR and SIS and SEIR and SEIRS) involving the relationships between the susceptible S, exposed E, infected I, and recovered R individuals for understanding the proliferation of infectious diseases. As a way to incorporate the most important features of the previous models under the assumption of homogeneous mixing (mass-action principle) of the individuals in the population N, the SEIRS model utilizes vital dynamics with unequal birth and death rates, vaccinations for newborns and non-newborns, and temporary immunity. In order to determine the equilibrium points, namely the disease-free and endemic equilibrium points, and study their local stability behaviors, the SEIRS model is rescaled with the total time-varying population and analyzed according to its epidemic condition R0 for two cases of no epidemic (R0 ≤ 1) and epidemic (R0 > 1) using the time-series and phase portraits of the susceptible s, exposed e, infected i, and recovered r individuals. Based on the experimental results using a set of arbitrarily-defined parameters for horizontal transmission of the infectious diseases, the proportional population of the SEIRS model consisted primarily of the recovered r (0.7–0.9) individuals and susceptible s (0.0–0.1) individuals (epidemic) and recovered r (0.9) individuals with only a small proportional population for the susceptible s (0.1) individuals (no epidemic). Overall, the initial conditions for the susceptible s, exposed e, infected i, and recovered r individuals reached the corresponding equilibrium point for local stability: no epidemic (DFE X ¯ D F E ) and epidemic (EE X ¯ E E ).
PubDate: 2017-01-17
DOI: 10.3390/math5010007
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 8: An Analysis of the Influence of Graph Theory
When Preparing for Programming Contests
Authors: Cristina Jordán, Jon Gómez, J. Conejero
First page: 8
Abstract: The subject known as Programming Contests in the Bachelor’s Degree in Computer Engineering course focuses on solving programming problems frequently met within contests such as the Southwest Europe Regional Contest (SWERC). In order to solve these problems one first needs to model the problem correctly, find the ideal solution, and then be able to program it without making any mistakes in a very short period of time. Leading multinationals such as Google, Apple, IBM, Facebook and Microsoft place a very high value on these abilities when selecting candidates for posts in their companies. In this communication we present some preliminary results of an analysis of the interaction between two optional subjects in the Computer Science Degree course: Programming Contests (PC) and Graphs, Models and Applications (GMA). The results of this analysis enabled us to make changes to some of the contents in GMA in order to better prepare the students to deal with the challenges they have to face in programming contests.
PubDate: 2017-01-20
DOI: 10.3390/math5010008
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 9: Existence of Mild Solutions for Impulsive
Fractional Integro-Differential Inclusions with State-Dependent Delay
Authors: Selvaraj Suganya, Mani Mallika Arjunan
First page: 9
Abstract: In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI) with state-dependent delay (SDD) in Banach spaces. An example is provided to illustrate the obtained abstract results.
PubDate: 2017-01-25
DOI: 10.3390/math5010009
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 10: Approximation in Müntz Spaces MΛ,p of Lp
Functions for 1 < p < ∞ and Bases
Authors: Sergey Ludkowski
First page: 10
Abstract: Müntz spaces satisfying the Müntz and gap conditions are considered. A Fourier approximation of functions in the Müntz spaces MΛ,p of Lp functions is studied, where 1 < p < ∞. It is proven that up to an isomorphism and a change of variables, these spaces are contained in Weil–Nagy’s class. Moreover, the existence of Schauder bases in the Müntz spaces MΛ,p is investigated.
PubDate: 2017-01-25
DOI: 10.3390/math5010010
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 11: The Split Common Fixed Point Problem for a
Family of Multivalued Quasinonexpansive Mappings and Totally
Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces
Authors: Ali Abkar, Elahe Shahrosvand, Azizollah Azizi
First page: 11
Abstract: In this paper, we introduce an iterative algorithm for solving the split common fixed point problem for a family of multi-valued quasinonexpansive mappings and totally asymptotically strictly pseudocontractive mappings, as well as for a family of totally quasi-ϕ-asymptotically nonexpansive mappings and k-quasi-strictly pseudocontractive mappings in the setting of Banach spaces. Our results improve and extend the results of Tang et al., Takahashi, Moudafi, Censor et al., and Byrne et al.
PubDate: 2017-02-11
DOI: 10.3390/math5010011
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 12: Fractional Fokker-Planck Equation
Authors: Gerd Baumann, Frank Stenger
First page: 12
Abstract: We shall discuss the numerical solution of the Cauchy problem for the fully fractional Fokker-Planck (fFP) equation in connection with Sinc convolution methods. The numerical approximation is based on Caputo and Riesz-Feller fractional derivatives. The use of the transfer function in Laplace and Fourier spaces in connection with Sinc convolutions allow to find exponentially converging computing schemes. Examples using different initial conditions demonstrate the effective computations with a small number of grid points on an infinite spatial domain.
PubDate: 2017-02-11
DOI: 10.3390/math5010012
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 13: A Few Finite Trigonometric Sums
Authors: Chandan Datta, Pankaj Agrawal
First page: 13
Abstract: Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products of trigonometric functions can become complicated, and may not have a simple expression in a number of cases. Some of these sums have interesting properties, and can have amazingly simple values. However, only some of them are available in the literature. We obtain a number of such sums using the method of residues.
PubDate: 2017-02-18
DOI: 10.3390/math5010013
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 14: A Novel Iterative Algorithm Applied to
Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces
Authors: Ali Abkar, Mohsen Shekarbaigi
First page: 14
Abstract: In this paper we introduce a new iterative algorithm for approximating fixed points of totally asymptotically quasi-nonexpansive mappings on CAT(0) spaces. We prove a strong convergence theorem under suitable conditions. The result we obtain improves and extends several recent results stated by many others; they also complement many known recent results in the literature. We then provide some numerical examples to illustrate our main result and to display the efficiency of the proposed algorithm.
PubDate: 2017-02-22
DOI: 10.3390/math5010014
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 15: Dialectical Multivalued Logic and
Probabilistic Theory
Authors: José Usó Doménech, Josué Nescolarde-Selva, Lorena Segura-Abad
First page: 15
Abstract: There are two probabilistic algebras: one for classical probability and the other for quantum mechanics. Naturally, it is the relation to the object that decides, as in the case of logic, which algebra is to be used. From a paraconsistent multivalued logic therefore, one can derive a probability theory, adding the correspondence between truth value and fortuity.
PubDate: 2017-02-23
DOI: 10.3390/math5010015
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 16: On the Additively Weighted Harary Index of
Some Composite Graphs
Authors: Behrooz Khosravi, Elnaz Ramezani
First page: 16
Abstract: The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. The additively weighted Harary index H A ( G ) is a modification of the Harary index in which the contributions of vertex pairs are weighted by the sum of their degrees. This new invariant was introduced in (Alizadeh, Iranmanesh and Došlić. Additively weighted Harary index of some composite graphs, Discrete Math, 2013) and they posed the following question: What is the behavior of H A ( G ) when G is a composite graph resulting for example by: splice, link, corona and rooted product? We investigate the additively weighted Harary index for these standard graph products. Then we obtain lower and upper bounds for some of them.
PubDate: 2017-03-07
DOI: 10.3390/math5010016
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 17: Certain Concepts of Bipolar Fuzzy Directed
Hypergraphs
Authors: Muhammad Akram, Anam Luqman
First page: 17
Abstract: A hypergraph is the most developed tool for modeling various practical problems in different fields, including computer sciences, biological sciences, social networks and psychology. Sometimes, given data in a network model are based on bipolar information rather than one sided. To deal with such types of problems, we use mathematical models that are based on bipolar fuzzy (BF) sets. In this research paper, we introduce the concept of BF directed hypergraphs. We describe certain operations on BF directed hypergraphs, including addition, multiplication, vertex-wise multiplication and structural subtraction. We introduce the concept of B = ( m + , m − ) -tempered BF directed hypergraphs and investigate some of their properties. We also present an algorithm to compute the minimum arc length of a BF directed hyperpath.
PubDate: 2017-03-04
DOI: 10.3390/math5010017
Issue No: Vol. 5, No. 1 (2017)
- Mathematics, Vol. 5, Pages 18: Characterization of the Minimizing Graph of
the Connected Graphs Whose Complements Are Bicyclic
Authors: Muhammad Javaid
First page: 18
Abstract: In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. Let G 1 , n c and G 2 , n c be the classes of the connected graphs of order n whose complements are bicyclic with exactly two and three cycles, respectively. In this paper, we characterize the unique minimizing graph among all the graphs which belong to G n c = G 1 , n c ∪ G 2 , n c , a class of the connected graphs of order n whose complements are bicyclic.
PubDate: 2017-03-11
DOI: 10.3390/math5010018
Issue No: Vol. 5, No. 1 (2017)