Ural Mathematical Journal (UMJ)
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SET MEMBERSHIP ESTIMATION WITH A SEPARATE RESTRICTION ON INITIAL STATE AND DISTURBANCES
Get PDFWe consider a set membership estimation problem for linear non-stationary systems for which initial states belong to a compact set and uncertain disturbances in an observation equation are integrally restricted. We provethat the exact information set of the system can be approximated by a set of external ellipsoids in the absence of disturbances in the dynamic equation.There are three examples of linear systems. Two examples illustrate the main theorem of the paper, the latter one shows the possibility of generalizing the theorem to the case with disturbances in the dynamic equation
LINEARIZATION OF POISSON–LIE STRUCTURES ON THE 2D EUCLIDEAN AND (1 + 1) POINCARÉ GROUPS
Get PDFThe paper deals with linearization problem of Poisson-Lie structures on the Poincaré and Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebra structures on their Lie algebras which we first determine
ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS
Get PDFLet be a chromatic polynomial of a graph . Two graphs and are called chromatically equivalent iff . A graph is called chromatically unique if for every chromatically equivalent to . In this paper, the chromatic uniqueness of complete tripartite graphs is proved for and
ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES
Get PDFA subset of a graph is a hop dominating set (HDS) if for every there is at least one vertex such that . The minimum cardinality of a hop dominating set of is called the hop domination number of and is denoted by . In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs
PRODUCTS OF ULTRAFILTERS AND MAXIMAL LINKED SYSTEMS ON WIDELY UNDERSTOOD MEASURABLE SPACES
Get PDFConstructions related to products of maximal linked systems (MLSs) and MLSs on the product of widely understood measurable spaces are considered (these measurable spaces are defined as sets equipped with -systems of their subsets; a -system is a family closed with respect to finite intersections). We compare families of MLSs on initial spaces and MLSs on the product. Separately, we consider the case of ultrafilters. Equipping set-products with topologies, we use the box-topology and the Tychonoff product of Stone-type topologies. The properties of compaction and homeomorphism hold, respectively
NOTE ON SUPER ––ANTIMAGIC TOTAL LABELING OF STAR
Get PDFLet be a simple graph and be a subgraph of . Then admits an -covering, if every edge in belongs to at least one subgraph of that is isomorphic to . An -antimagic total labeling of is bijection such that for all subgraphs of isomorphic to , the weights constitute an arithmetic progression , where and are positive integers and is the number of subgraphs of isomorphic to . The labeling is called a super -antimagic total labeling if In [5], David Laurence and Kathiresan posed a problem that characterizes the super -antimagic total labeling of Star where In this paper, we completely solved this problem
OPTIMAL CONTROL FOR A CONTROLLED ILL-POSED WAVE EQUATION WITHOUT REQUIRING THE SLATER HYPOTHESIS
Get PDFIn this paper, we investigate the problem of optimal control for an ill-posed wave equation without using the extra hypothesis of Slater i.e. the set of admissible controls has a non-empty interior. Firstly, by a controllability approach, we make the ill-posed wave equation a well-posed equation with some incomplete data initial condition. The missing data requires us to use the no-regret control notion introduced by Lions to control distributed systems with ncomplete data. After approximating the no-regret control by a low-regret control sequence, we characterize the optimal control by a singular optimality system
THE VARIETY GENERATED BY AN AI-SEMIRING OF ORDER THREE
Get PDFUp to isomorphism, there are 61 ai-semirings of order three. The finite basis problem for these semirings is investigated. This problem for 45 semirings of them is answered by some results in the literature. The remaining semirings are studied using equational logic. It is shown that with the possible exception of the semiring , all ai-semirings of order three are finitely based
ASYMPTOTIC ALMOST AUTOMORPHY OF FUNCTIONS AND DISTRIBUTIONS
Get PDFThis work aims to introduce and to study asymptotic almost automorphy in the context of Sobolev–Schwartz distributions. Applications to linear ordinary differential equation and neutral difference differential equations are also given
SOME NOTES ABOUT THE MARTINGALE REPRESENTATION THEOREM AND THEIR APPLICATIONS
Get PDFAn important theorem in stochastic finance field is the martingale representation theorem. It is useful in the stage of making hedging strategies (such as cross hedging and replicating hedge) in the presence of different assets with different stochastic dynamics models. In the current paper, some new theoretical results about this theorem including derivation of serial correlation function of a martingale process and its conditional expectations approximation are proposed. Applications in optimal hedge ratio and financial derivative pricing are presented and sensitivity analyses are studied. Throughout theoretical results, simulation-based results are also proposed. Two real data sets are analyzed and concluding remarks are given. Finally, a conclusion section is given