Ural Mathematical Journal (UMJ)
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-STATISTICAL CONVERGENCE OF COMPLEX UNCERTAIN SEQUENCES IN MEASURE
No full textThe main aim of this paper is to present and explore some of properties of the concept of -statistical convergence in measure of complex uncertain sequences. Furthermore, we introduce the concept of -statistical Cauchy sequence in measure and study the relationships between different types of convergencies. We observe that, in complex uncertain space, every -statistically convergent sequence in measure is -statistically Cauchy sequence in measure, but the converse is not necessarily true
ON THE MODULAR SEQUENCE SPACES GENERATED BY THE CESÀRO MEAN
Get PDFIn this paper, the seminormed Ces\`aro difference sequence space is defined by using the generalized Orlicz function. Some algebraic and topological properties of the space are investigated. Various inclusion relations for this sequence space are also studied
STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES IN NEUTROSOPHIC 2-NORMED SPACES
Get PDFIn this paper, we have studied the notion of statistical convergence for double sequences in neutrosophic 2-normed spaces. Also, we have defined statistically Cauchy double sequences and statistically completeness for double sequences and investigated some interesting results in connection with neutrosophic 2-normed space
TRAJECTORIES OF DYNAMIC EQUILIBRIUM AND REPLICATOR DYNAMICS IN COORDINATION GAMES
Get PDFThe paper analyzes average integral payoff indices for trajectories of the dynamic equilibrium and replicator dynamics in bimatrix coordination games. In such games, players receive large payoffs when choosing the same type of behavior. A special feature of a coordination game is the presence of three static Nash equilibria. In the dynamic formulation, the trajectories of coordination games are estimated by the average integral payoffs for a wide range of models arising in economics and biology. In optimal control problems and dynamic games, average integral payoffs are used to synthesize guaranteed strategies, which are involved, among other things, in the constructions of the dynamic Nash equilibrium. In addition, average integral payoffs are a natural tool for assessing the quality of trajectories of replicator dynamics. In the paper, we compare values of average integral indices for trajectories of replicator dynamics and trajectories generated by guaranteed strategies in constructing the dynamic Nash equilibrium. An analysis is provided for trajectories of mixed dynamics when the first player plays a guaranteed strategy, and the behavior of replicator dynamics guides the second player
TAUBERIAN THEOREM FOR GENERAL MATRIX SUMMABILITY METHOD
Get PDFIn this paper, we prove certain Littlewood–Tauberian theorems for general matrix summability method by imposing the Tauberian conditions such as slow oscillation of usual as well as matrix generated sequence, and the De la Vallée Poussin means of real sequences. Moreover, we demonstrate and – summability methods as the generalizations of our proposed general matrix method and establish an equivalence relation connecting them. Finally, we draw several remarks in view of the generalizations of some existing well-known results based on our results
CONVEXITY OF REACHABLE SETS OF QUASILINEAR SYSTEMS
Get PDFThis paper investigates convexity of reachable sets for quasilinear systems under integral quadratic constraints. Drawing inspiration from B.T. Polyak's work on small Hilbert ball image under nonlinear mappings, the study extends the analysis to scenarios where a small nonlinearity exists on the system's right-hand side. At zero value of a small parameter, the quasilinear system turns into a linear system and its reachable set is convex. The investigation reveals that to maintain convexity of reachable sets of these systems, the nonlinear mapping's derivative must be Lipschitz continuous. The proof methodology follows a Polyak's scheme. The paper's structure encompasses problem formulation, exploration of parameter linear mapping and image transformation, application to quasilinear control systems, and concludes with illustrative examples
LATTICE UNIVERSALITY OF LOCALLY FINITE -GROUPS
Get PDFFor an arbitrary prime , we prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite -group. In particular, every lattice is embeddable in the subgroup lattice of a locally finite -group
SOME TRIGONOMETRIC SIMILARITY MEASURES OF COMPLEX FUZZY SETS WITH APPLICATION
Get PDFSimilarity measures of fuzzy sets are applied to compare the closeness among fuzzy sets. These measures have numerous applications in pattern recognition, image processing, texture synthesis, medical diagnosis, etc. However, in many cases of pattern recognition, digital image processing, signal processing, and so forth, the similarity measures of the fuzzy sets are not appropriate due to the presence of dual information of an object, such as amplitude term and phase term. In these cases, similarity measures of complex fuzzy sets are the most suitable for measuring proximity between objects with two-dimensional information. In the present paper, we propose some trigonometric similarity measures of the complex fuzzy sets involving similarity measures based on the sine, tangent, cosine, and cotangent functions. Furthermore, in many situations in real life, the weight of an attribute plays an important role in making the right decisions using similarity measures. So in this paper, we also consider the weighted trigonometric similarity measures of the complex fuzzy sets, namely, the weighted similarity measures based on the sine, tangent, cosine, and cotangent functions. Some properties of the similarity measures and the weighted similarity measures are discussed. We also apply our proposed methods to the pattern recognition problem and compare them with existing methods to show the validity and effectiveness of our proposed methods
FIXED RATIO POLYNOMIAL TIME APPROXIMATION ALGORITHM FOR THE PRIZE-COLLECTING ASYMMETRIC TRAVELING SALESMAN PROBLEM
Get PDFWe develop the first fixed-ratio approximation algorithm for the well-known Prize-Collecting Asymmetric Traveling Salesman Problem, which has numerous valuable applications in operations research. An instance of this problem is given by a complete node- and edge-weighted digraph . Each node of the graph can either be visited by the resulting route or skipped, for some penalty, while the arcs of are weighted by non-negative transportation costs that fulfill the triangle inequality constraint. The goal is to find a closed walk that minimizes the total transportation costs augmented by the accumulated penalties. We show that an arbitrary -approximation algorithm for the Asymmetric Traveling Salesman Problem induces an -approximation for the problem in question. In particular, using the recent -approximation algorithm of V. Traub and J. Vygen that improves the seminal result of O. Svensson, J. Tarnavski, and L. Végh, we obtain -approximate solutions for the problem
TERNARY ∗-BANDS ARE GLOBALLY DETERMINED
Get PDFA non-empty set together with the ternary operation denoted by juxtaposition is said to be ternary semigroup if it satisfies the associativity property for all . The global set of a ternary semigroup is the set of all non empty subsets of and it is denoted by . If is a ternary semigroup then is also a ternary semigroup with a naturally defined ternary multiplication. A natural question arises: "Do all properties of remain the same in ?" The global determinism problem is a part of this question. A class of ternary semigroups is said to be globally determined if for any two ternary semigroups and of , implies that . So it is interesting to find the class of ternary semigroups which are globally determined. Here we will study the global determinism of ternary -band