Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper, we study limit cycle bifurcations near homoclinic and heteroclinic loops in piecewise smooth systems with three zones separated by two parallel straight lines. By introducing suitable Poincaré map near a homoclinic loop, we derive some stability criteria and establish bifurcation theory of limit cycles via stability-changing method near homoclinic and heteroclinic loops, respectively. As applications, we give two examples, which consider a class of Liénard piecewise linear differential systems. PubDate: 2024-06-10

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this work, we proposed some generalized Darbo type fixed point theorem by employing the concept of generalized operators and measure of non-compactness within the framework of partial order Banach spaces. Some fixed point theorems and their consequences are presented as part of our exploration. These theorems encompass the presentation of various fixed point theorems and the subsequent implications they entail. Further, we demonstrate the practical application of our findings by establishing the existence of solutions for delay differential equations. To substantiate our conclusions, we provide numerical estimations based on a real-world example. This research contributes to the advancement of fixed point theory in the context of partial order Banach spaces and showcases its practical relevance through a concrete application and empirical support. PubDate: 2024-06-08

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract As a nonlinear circuit component, memristor can be utilized to simulate neural discharging activities in biological neural networks with synapses and neurons. In this paper, a polynomial memristor model is presented, with subcomponents acting on Fitzhugh–Nagumo (FN) and Hindmarsh–Rose (HR) neurons respectively to form new artificial neurons. One new memristor-based HR neuron simulates the electromagnetic induction environment of a 3D HR neuron, where the formation mechanism of firing activities is analyzed by fast-and-slow subsystems analysis method and nonlinear theory; the other is activated to couple the above memristor-based HR neuron with the FN neuron. The complex dynamics and the peak synchronous firing of the two different neurons are then further explored, and their synchronous firing is tested and verified based on their interspike intervals bifurcation diagrams, phase differences, and firing synchronization errors. This work provides necessary support for further exploring the complex dynamic mechanisms of biomimetic neurons. PubDate: 2024-06-07

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The Sombor index is a novel vertex-degree-based topological index which was proposed by Gutman in 2021. This index has been shown to be helpful in predicting the enthalpy of vaporization and entropy of octane isomers. In 2022, Gutman put forward a new variant of the Sombor index and gave its geometric interpretation. This invariant which we call the geometric Sombor index can be considered as a practical tool for measuring irregularity in graphs. Our aim is to study some basic mathematical properties of this new Sombor-type invariant. Especially, we prove that for any tree (resp. unicyclic graph) with a fixed order and maximum degree \(\Delta \) , the geometric Sombor index is bounded below by \(\frac{\Delta ^3-\Delta }{2}\) (resp. \(\frac{\Delta ^3-\Delta -6}{2}\) ). Also the extremal trees and unicyclic graphs that achieve the lower bound are characterized. PubDate: 2024-06-05

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This study revisits the problem of identifying the unknown interior Robin boundary of a connected domain using Cauchy data from the exterior region of a harmonic function. It investigates two shape optimization reformulations employing least-squares boundary-data-tracking cost functionals. Firstly, it rigorously addresses the existence of optimal shape solutions, thus filling a gap in the literature. The argumentation utilized in the proof strategy is contingent upon the specific formulation under consideration. Secondly, it demonstrates the ill-posed nature of the two shape optimization formulations by establishing the compactness of the Riesz operator associated with the quadratic shape Hessian corresponding to each cost functional. Lastly, the study employs multiple sets of Cauchy data to address the difficulty of detecting concavities in the unknown boundary. Numerical experiments in two and three dimensions illustrate the numerical procedure relying on Sobolev gradients proposed herein. PubDate: 2024-06-04

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Let p be a prime number and \(q=p^m\) for some positive integer m. In this paper, we find the possible Hermitian hull dimensions of \(\lambda \) -constacyclic codes over \(R_e={\mathbb {F}}_{q^2}+u{\mathbb {F}}_{q^2} +u^2{\mathbb {F}}_{q^2}+\cdots +u^{e-1}{\mathbb {F}}_{q^2}\) , \(u^e=1\) where \({\mathbb {F}}_{q^2}\) is the finite field of \(q^2\) elements, \(e (q+1)\) and \(\lambda =\eta _1\alpha _1+\eta _2\alpha _2+\cdots +\eta _e\alpha _e\) for \(\alpha _l \in {\mathbb {F}}_{q^2}^{*}\) of order \(r_l\) such that \(r_l\mid q+1\) (for each \(1\le l \le e\) ). Further, we obtain some conditions for these codes to be Hermitian LCD. Also, under certain conditions, we establish a strong result that converts every constacyclic code to a Hermitian LCD code (Corollaries 2 and 3). We also study the structure of generator polynomials for Hermitian dual-containing constacyclic codes (Theorems 8 and 9), and obtain parameters of quantum codes using the Hermitian construction. The approach we used to derive Hermitian dual-containing conditions via the hull has not been used earlier. As an application, we obtain several optimal and near-to-optimal LCD codes, constacyclic codes having small hull dimensions, and quantum codes. PubDate: 2024-06-04

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This research delves into the comprehensive study of the mathematical model governing the propagation of tsunami waves along ocean coastlines in imprecise or uncertain environment. The model is based on the widely used shallow-water assumption, which can be represented by a system of non-linear fuzzy partial differential equations. Utilizing fuzzy numbers to represent the problem’s uncertainty may have distinct advantages from a certain perspective. As such, this work employs the homotopy perturbation method (HPM) to obtain fuzzy approximate analytical solutions for the governing model under various coastal slopes and ocean depths. The addition of uncertainty to the model may add complexity to the methodology. Therefore, a double parametric approach has been integrated into the HPM procedure. This approach allows us to analyze the impact of coastal slope and sea depth on tsunami wave characteristics, specifically wave velocity and run-up height, in uncertain environments. Furthermore, the numerical results obtained for fuzzy tsunami wave velocity and wave height resemble the real behavior of tsunamis. These can be seen through the given fuzzy plots, both in 2D and 3D forms. Finally, to validate the obtained solutions, a comparison has been made between the special case of the present fuzzy solutions and the existing precise (crisp) solutions. PubDate: 2024-06-03

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract We consider a local non-Frobenius ring \(R_p={\mathbb {F}}_p[u,v]/\langle u^2, v^2, uv,vu \rangle \) defined for each prime number p and study the ideal representation of the ring \(R_p[x]/\langle x^n+1\rangle \) , which is well-known to be related to negacyclic codes over \(R_p\) of length \(n=p^s\) with \(s \ge 1\) . We assume that n is a power of p, and under this setting, we show that a specific class of ideals can be represented uniquely in terms of degrees related to its generators. We also give a lower bound of the minimum Hamming distances of negacyclic codes over \(R_p\) , and show that the lower bound is sharp for several codes whose corresponding ideals of \(R_p[x]/\langle x^n+1\rangle \) belong to the aforementioned class. PubDate: 2024-06-03

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The popular fully-connected tensor network (FCTN) decomposition has achieved successful applications in many fields. A standard method to this decomposition is the alternating least squares. However, it often converges slowly and suffers from issues of numerical stability. In this work, we investigate the SVD-based algorithms for FCTN decomposition to tackle the aforementioned deficiencies. On the basis of a result about FCTN-ranks, a deterministic algorithm, namely FCTN-SVD, is first proposed, which can approximate the FCTN decomposition under a fixed accuracy. Then, we present the randomized version of the algorithm. Both synthetic and real data are used to test our algorithms. Numerical results show that they perform much better than the existing methods, and the randomized algorithm can indeed yield acceleration on FCTN-SVD. Moreover, we also apply our algorithms to tensor-on-vector regression and achieve quite decent performance. PubDate: 2024-06-03

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The work reported here is our first attempt to investigate the equilibria of independent distributions (ID) on unbalanced game trees, after a long series of studies on balanced AND-OR trees, e.g., Liu and Tanaka (Inform Process Lett 104(2):73–77, 2007; Liu and Tanaka (The computational complexity of game trees by eigen-distribution. In: Proceeding 436 of the 1st International Conference on COCOA, pp. 323–334, 2007; Suzuki and Niida (Ann Pure Appl Log 166(11):1150–1164, 2015; Peng et al. (Inform Process Lett 125:41–45, 2017; Suzuki (Ann Jpn Assoc Philos Sci 25:79–88, 2017; Inform Process Lett 139:13–17, 2018); Peng et al. (Methodol Comput Appl Probab 24:277–287, 2022). To handle an unbalanced tree, we decompose the tree into subtrees with different weights (= costs). The present research not only generalizes our previous results on balanced trees to unbalanced weighted trees, but also gives simpler inductive proofs and new perspectives for some old results. Our primary objective is to characterize the “eigen-distribution" \(d \in \) ID(r) for a weighted game tree (with a fixed probability for the root having value 0 as \(0<r<1\) ), which achieves the distributional complexity. In this paper, we introduce two new concepts on independent distributions: “proportional" ID (PID for short) and “decent" ID. For \(0<r<1\) , a PID (r) on a weighted tree is uniquely constructed by a technique “Super-RAT" which is inspired by the reverse assigning technique (RAT) for the CD case in Liu and Tanaka (Inform Process Lett 104(2):73–77, 2007). As a main theorem, we show that if the eigen-distribution \(d \in \) ID(r) is decent then it is a PID, from which we can deduce our previous theorem in Peng et al. (Inform Process Lett 125:41–45, 2017) that for a balanced AND-OR tree (without weights), the eigen-distribution \(d \in \) ID(r) is an IID. PubDate: 2024-06-03

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this article, we consider a two-player zero-sum stochastic differential game with regime-switching. Different from the results in existing literature on stochastic differential games with regime-switching, we consider a game between a Markov chain and a state process which are two fully coupled stochastic processes. The payoff function is given by an integral with random terminal horizon. We first study the continuity of the lower and upper value functions under some additional conditions, based on which we establish the dynamic programming principle. We further prove that the lower and upper value functions are unique viscosity solutions of the associated lower and upper Hamilton–Jacobi–Bellman–Isaacs equations with regime-switching, respectively. These two value functions coincide under the Isaacs condition, which implies that the game admits a value. We finally apply our results to an example. PubDate: 2024-05-31

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The Hopf bifurcation, Turing instability and steady state bifurcation to a fresh-water tussock sedge model with nonlocal interaction under Neumman boundary condition are investigated in this paper. First, we analyze the existence of constant steady states and the effect of the nonlocal term on the its stability and the existence of Hopf bifurcation. Furthermore, the occurrence conditions of Turing instability to such system are studied. Second, we focus on steady state bifurcation to the reaction–diffusion system with nonlocal interaction via Lyapunov–Schmidt reduced method. Finally, numerical simulations have been illustrated to verify our theoretical analysis. PubDate: 2024-05-30

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract The transmission of a vertex in a connected graph is the sum of its distances to all the other vertices. A graph is transmission irregular, or TI for short, when all of its vertices have mutually distinct transmissions. In an earlier paper, Al-Yakoob and Stevanović (Appl. Math. Comput. 380:125257, 2020) gave the full characterization of TI starlike trees with three branches. Here, we improve these results by using a different approach to provide the complete characterization of all TI starlike trees. Moreover, we find the precise conditions under which a double starlike tree is TI. Finally, we implement the aforementioned conditions in order to find several infinite families of TI starlike trees and TI double starlike trees. PubDate: 2024-05-30

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract In this paper we study the periodic orbits of a class of 2n-dimensional control dynamical systems with a perturbation of continuous piecewise smooth quadratic polynomial and a perturbation of discontinuous piecewise smooth polynomial of an arbitrarily given degree, respectively. By applying the averaging theory for continuous and discontinuous piecewise smooth systems, the number of isolated zeros of the averaging function can be determined, which provides a lower bound of the maximum number of isolated periodic orbits. At last, we give examples to show that the lower bound of the maximum number is accessible by the properties of algebraic closure and transcendental extension. PubDate: 2024-05-29

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper investigates a technique that uses Riemann-Liouville fractional integrals to study several Euler-Maclaurin-type inequalities for various function classes. Afterwards, we provide our results by using special cases of obtained theorems and This paper is to derive examples. Moreover, we give some Euler-Maclaurin-type inequalities for bounded functions by fractional integrals. Furthermore, we construct some fractional Euler-Maclaurin-type inequalities for Lipschitzian functions. Finally, we offer some Euler-Maclaurin-type inequalities by fractional integrals of bounded variation. PubDate: 2024-05-29

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper aims to propose a double inertial Mann-type extragradient algorithm using non-monotonic step size and establish a weak convergence result to find a common solution to the variational inequality problem involving pseudo-monotone mapping and fixed point problem for quasi-nonexpansive mapping. Moreover, we establish a strong convergence for the variational inequality involving strongly pseudo-monotone mapping. To illustrate our algorithm’s potential, we present several numerical experiments, including the Nash–Cournot oligopolistic market equilibrium model and fractional programming problem. We also employ performance profiles to discuss the efficiency of our algorithm over earlier established algorithms based on two performance metrics. PubDate: 2024-05-29

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: In this paper, we study the pseudo almost periodic solutions for a class of nonlinear Duffing equations with \(S^p\) -pseudo almost periodic coefficients and delays on time scales. For this purpose, we establish a result of the existence and uniqueness of pseudo almost periodic solution for an abstract linear equation with \(S^p\) -almost periodic coefficients and \(S^p\) -pseudo almost periodic forcing term. Meanwhile, to deal with the delay, we extend some concepts of functions from \(\mathbb {T}\rightarrow \mathbb {R}\) to \(\mathbb {T}\rightarrow \Pi \) , where \(\mathbb {T}\) is a time scale with translation set \(\Pi \) , and give some basic properties for these concepts. Then, applying these results, we obtain some results on the existence and uniqueness of pseudo almost periodic solutions for the Duffing equation. Moreover, some examples are given to illustrate our main results. PubDate: 2024-05-28

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper presents a novel approach for predicting electricity prices in fuzzy and stochastic environments. First, we analyze historical data on daily PJM Western Hub Real-Time Peak electricity prices and extract relevant features for modeling. Then, we introduce a comprehensive model for predicting the price of electricity within the PJM market. To adapt the model to the electricity price data, we implement algorithms based on the least squares algorithm to calibrate the model’s parameters. However, considering the model’s purpose in forecasting future electricity prices, we apply the parameters as fuzzy numbers. After that, acknowledging the significant losses that severe electricity fluctuations can incur for producers, consumers, and industrial owners, we develop a formula to assess the probability of such fluctuations occurring in both random and fuzzy spaces. Finally, because electricity transactions are conducted through contracts, we calculate the price of these contracts across various time frames and use the fuzzy numbers to obtain a margin for the price of the contracts. PubDate: 2024-05-28

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient low-rank formulation, which is a variant of the Cholesky decomposition in the Lyapunov GADI method, saving storage space and making it computationally effective. When solving the continuous-time algebraic Riccati matrix equation, the Riccati equation is first simplified to a Lyapunov equation using the Newton method, and then the R-GADI method is employed for computation. Additionally, we analyze the convergence of the R-GADI method and prove its consistency with the convergence of the GADI method. Finally, the effectiveness of the new algorithm is demonstrated through corresponding numerical experiments. PubDate: 2024-05-27

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Abstract: Abstract Data envelopment analysis (DEA) has come to be recognized as an important technique for evaluating the efficiency of decision-making units (DMUs) in recent years. In conventional DEA, it is often assumed that each DMU being assessed for efficiency utilizes the same number of inputs and produces the same number of outputs. In recent years, some academicians have attempted to address the non-homogeneity of the data in DEA; nevertheless, there is a lack of models that take into consideration the non-homogeneity of negative data. To address the issue of data heterogeneity in the presence of negative data, the research suggests a DEA model based on the range directional measure (RDM). More precisely, we are concerned in this study with the heterogeneity of output data generated by a homogeneous set of input data collections. Our objective is to determine the inefficiency of each subunit associated with an output that utilizes the optimal proportion of inputs instead of merely categorizing DMUs according to their output structure, as was the case in previous research. For empirical analysis of the proposed model first, we made a comparison between the proposed model and a representative set of data from earlier studies. We next used synthesized negative data generated uniformly using Matlab software version R2021b to provide an empirical illustration of the proposed model. In addition, we carried out an analysis to assess the research efficiency of 20 institutions. PubDate: 2024-05-25