In this article, we introduce the notion of cyclic generalized iterated function system (GIFS), which is a family of functions , where each is a cyclic generalized -contraction (contractive) map on a collection of subsets of a complete metric space respectively, and are natural numbers. When
This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.
The security of a broad family of coding-based cryptographic techniques relies on the hardness of the Syndrome Decoding Problem (SDP). In this problem, the aim is to find a word with a given syndrome and of Hamming weight smaller than a prefixed bound. If this last condition is replaced by “of minimum weight,” then we have the Coset Leader Problem (CLP), being Finding Low Weight Codewords (FLWC) a particular case (when the zero syndrome is considered). An algorithm that has been proposed in order to obtain approximate solutions of problems of these kind (NP-complete) is the Quantum Approximate Optimization Algorithm (QAOA), a variational hybrid quantum-classical algorithm. In this paper, we apply the QAOA to the CLP for binary linear codes. We model the problem, make the theoretical analysis the case of the first level, and introduce some experiments to test its performance. The experiments have been carried out on quantum computer simulators with codes of different lengths and QAOA of different depth.
The objective of the article is to present a qualitative analysis of a mathematical model for the spread of a sexually transmitted infection caused by Mycoplasma genitalium. Recent investigations revealed that this pathogen is becoming resistant to the use of macrolides and can turn into a superbug in the next few years. We present an epidemiological model to describe the spread of the disease. The equilibrium points are computed, and their local and global stability are studied. In order to make the mathematical problem more realistic, we propose two different optimal control problems that establish a balance between the number of infected individuals and the use of macrolides. Several numerical illustrations regarding the solutions of the proposed problems will be provided.
In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.
It is well known that one of the most relevant applications of the reverse Bessel polynomials is filter design. In particular, the poles of the transfer function of a Bessel filter are basically the zeros of . In this article we discuss an algorithm to compute the zeros of reverse generalized Bessel polynomials . A key ingredient in the algorithm will be a method to compute the polynomials. For this purpose, we analyze the use of recurrence relations and asymptotic expansions in terms of elementary functions to obtain accurate approximations to the polynomials. The performance of all the numerical approximations will be illustrated with examples.
We investigate a mathematical model in crop pest controlling, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pests and infected pests. We assume that the growth rate of self-aware people is proportional to the density of susceptible pests existing in the crop arena. Impacts of awareness are modeled through the usual mass action term and a saturated term. It is further assumed that self-aware people will adopt chemical and biological control methods, namely, integrated pest management. Bio-pesticides are costly and require a long-term process, expensive to impose. However, if chemical pesticides are introduced in the farming system along with bio-pesticides, the process will be faster as well as cost-effective. Also, farming knowledge is equally important. In this article, a mathematical model is derived for controlling crop pests through an awareness-based integrated approach. In order to reduce the negative effects of pesticides, we apply optimal control theory.
A dynamical system is studied. This system belongs to the class of contour networks introduced by A.P. Buslaev. The system is a version of the system called an open chain of contours. Continuous and discrete versions of the system were considered earlier. The system contains N contours. There is one adjacent contour for the utmost left and the utmost right contour, and there are two adjacent contours for any other contour. There is a common point of any two adjacent contours. This point is called a node. There is a cluster in each contour. For the continuous version, the cluster is a segment, moving with constant velocity if there is no delay. For the discrete version, the cluster is a group of adjacent particles. Delays are due to that two clusters may not move through the same node simultaneously. The main system characteristic, studied earlier, is the average velocity of clusters. In this paper, the continious and discrete version of the open chain of contours are considered. The following version of the system is also considered. Each cluster is a segment, and the cluster is shifted onto the distance α at any discrete moment if no delay occurs. We have obtained the limit distribution of the system states. We have also obtained the limit state distribution (invariant measure) for the open chain of contours with continuous state space and continuos time and for the open chain of contours with discrete state space and discrete time.
In this work, we focus on the non-linear fourth order class of singular boundary value problem which contains the parameter . We convert this non-linear differential equation into third order non-linear differential equation. The third order problem is singular, non self adjoint, and nonlinear. Moreover, depending upon , it admits multiple solutions. Hence, it is too difficult to capture these solutions by any discrete method such as finite difference and so forth. Here we develop an iterative technique with the help of homotopy perturbation method and variational iteration method in a suitable way. Convergence of this series solution is studied in a novel way. We compute these solutions numerically. For small positive values of , singular BVP has two solutions while solutions can not be found for large positive values of . Furthermore, we also find dual solutions for .
The article discusses derivative-free algorithms with and without memory for solving numerically nonlinear systems. We proposed a family of fifth- and sixth-order schemes and extended them to algorithms with memory. We further discuss the convergence and computational efficiency of these algorithms. Numerical examples of mixed Hammerstein integral equation, discrete nonlinear ordinary differential equation, and Fisher's partial differential equation with Neumann's boundary conditions are discussed to demonstrate the convergence and efficiency of these schemes. Finally, some numerical results are included to examine the performance of the developed methods.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：