Institute of Mathematics AS CR, v. v. i.
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The new iteration methods for solving absolute value equations
No full textsummary:Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations , where is an -matrix or strictly diagonally dominant matrix, and is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness of our methods
Faber polynomial coefficient estimates of bi-univalent functions connected with the -convolution
Get PDFsummary:We introduce a new class of bi-univalent functions defined in the open unit disc and connected with a -convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions and we obtain an estimation for the Fekete-Szegö problem for this class
On relative pure cyclic fields with power integral bases
Get PDFsummary:Let be an extension of a number field , where satisfies the monic irreducible polynomial of prime degree belonging to ( is the ring of integers of ). The purpose of this paper is to study the monogenity of over by a simple and practical version of Dedekind's criterion characterizing the existence of power integral bases over an arbitrary Dedekind ring by using the Gauss valuation and the index ideal. As an illustration, we determine an integral basis of a pure nonic field with a pure cubic subfield, which is not necessarily a composite extension of two cubic subfields. We obtain a slightly simpler computation of the discriminant
Robust optimality analysis for linear programming problems with uncertain objective function coefficients: an outer approximation approach
Get PDFsummary:Linear programming (LP) problems with uncertain objective function coefficients (OFCs) are treated in this paper. In such problems, the decision-maker would be interested in an optimal solution that has robustness against uncertainty. A solution optimal for all conceivable OFCs can be considered a robust optimal solution. Then we investigate an efficient method for checking whether a given non-degenerate basic feasible (NBF) solution is optimal for all OFC vectors in a specified range. When the specified range of the OFC vectors is a hyper-box, i. e., the marginal range of each OFC is given by an interval, it has been shown that the tolerance approach can efficiently solve the robust optimality test problem of an NBF solution. However, the hyper-box case is a particular case where the marginal ranges of some OFCs are the same no matter what values the remaining OFCs take. In real life, we come across cases where some OFCs' marginal ranges depend on the remaining OFCs' values. For example, the prices of products rise together in tandem with raw materials, the gross profit of exported products increases while that of imported products decreases because they depend on the currency exchange rates, and so on. Considering those dependencies, we consider a case where the range of the OFC vector is specified by a convex polytope. In this case, the tolerance approach to the robust optimality test problem of an NBF solution becomes in vain. To treat the problem, we propose an algorithm based on the outer approximation approach. By numerical experiments, we demonstrate how the proposed algorithm efficiently solves the robust optimality test problems of NBF solutions compared to a conventional vertex-listing method
Solving intuitionistic fuzzy multi-objective linear programming problem and its application in supply chain management
No full textsummary:The aim of this paper is solving an intuitionistic fuzzy multi-objective linear programming problem containing intuitionistic fuzzy parameters, intuitionistic fuzzy maximization/minimization, and intuitionistic fuzzy constraints. To do this, a linear ranking function is used to convert the intuitionistic fuzzy parameters to crisp ones first. Then, linear membership and non-membership functions are used to manipulate intuitionistic fuzzy maximization/minimization and intuitionistic fuzzy constraints. Then, a multi-objective optimization problem is formulated containing maximization of membership functions and minimization of non-membership functions. To solve this problem, the minimax and weighted sum methods are used. Then, the described procedure is summarized as an algorithm to solve the problem, and a numerical example is solved by the proposed method. Finally, to investigate the capability and performance of the model, a supplier selection problem, which is one of the important applications in supply chain management, is solved by the proposed algorithm
Fixed point theorems for hybrid pair of weak compatible mappings in partial metric spaces
Get PDFsummary:The notions of compatible mappings play a crucial role in metrical fixed point theory. Partial metric spaces are a generalization of the notion of a metric space in the sense that distance of a point from itself is not necessarily zero. In this paper, we prove coincidence and fixed point theorems for a pair of single-valued and multi-valued weak compatible mappings on a complete partial metric space. Our main results generalize, in particular, the results of Kaneko and Sessa (1989), Pathak (1995) and Kessy, Kumar and Kakiko (2017). Examples that illustrate the generality of our results are also provided
Bifurcation analysis of macroscopic traffic flow model based on the influence of road conditions
No full textsummary:A macroscopic traffic flow model considering the effects of curves, ramps, and adverse weather is proposed, and nonlinear bifurcation theory is used to describe and predict nonlinear traffic phenomena on highways from the perspective of global stability of the traffic system. Firstly, the stability conditions of the model shock wave were investigated using the linear stability analysis method. Then, the long-wave mode at the coarse-grained scale is considered, and the model is analyzed using the reduced perturbation method to obtain the Korteweg-de Vries (KdV) equation of the model in the sub-stable region. In addition, the type of equilibrium points and their stability are discussed by using bifurcation analysis, and a theoretical derivation proves the existence of Hopf bifurcation and saddle-knot bifurcation in the model. Finally, the simulation density spatio-temporal and phase plane diagrams verify that the model can describe traffic phenomena such as traffic congestion and stop-and-go traffic in real traffic, providing a theoretical basis for the prevention of traffic congestion
Pictures and mathematics
No full textsummary:Autor se v příspěvku zamýšlí nad úlohou obrázku v matematice. Vizuálním reprezentacím pojmů a postupů ve vyučování je nutno věnovat náležitou péči. Může to přispívat k porozumění matematice
Invitation to the national conference How to Teach Mathematics Pupils Aged 10–16
No full textsummary:Pozvánka na celostátní konferenci učitelů matematiky zaměřená na žáky 2. stupně základní školy, přechod mezi 1. a 2. stupněm a přechod mezi základní a střední školou