Ural Mathematical Journal (UMJ)
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IMPROVED FIRST PLAYER STRATEGY FOR THE ZERO-SUM SEQUENTIAL UNCROSSING GAME
Get PDFThis paper deals with the known uncrossing zero-sum two-player sequential game, which is employed to obtain upper running time bound for the transformation of an arbitrary subset family of some finite set to an appropriate laminar one. In this game, the first player performs such a transformation, while the second one tries to slow down this process as much as possible. It is known that for any game instance specified by the ground set and initial subset family of size and respectively, the first player has a winning strategy of steps. In this paper, we show that the first player has a more efficient strategy, which helps him (her) to win in steps
ARTINIAN -COMPLETE, -REDUCED, AND MINIMALLY -COMPLETE ASSOCIATIVE RINGS
No full textIn 1996, the first author defined analogs of the concepts of complete (divisible), reduced, and periodic abelian groups, well-known in the theory of abelian groups, for arbitrary varieties of algebras. In 2021, the first author proposed a modification of the concepts of completeness and reducibility, which is more natural in the case of associative rings. The paper studies the modification of these concepts for associative rings. Artinian -complete, -reduced rings, and minimally -complete associative nilpotent rings, simple rings with unity, and finite rings are characterized
AN EXPLICIT ESTIMATE FOR APPROXIMATE SOLUTIONS OF ODES BASED ON THE TAYLOR FORMULA
Get PDFIn this paper, we consider a third-order explicit scheme based on Taylor's formula to obtain an approximate solution for the Cauchy problem of systems of ODEs. We prove an estimate for the accuracy of the approximate solution with an explicit constant that depends only on the right-hand side of the equation and the domain of the solution
A CHARACTERIZATION OF MEIXNER ORTHOGONAL POLYNOMIALS VIA A CERTAIN TRANSFERT OPERATOR
Get PDFHere we consider a certain transfert operator and we prove the following statement: up to an affine transformation, the only orthogonal sequence that remains orthogonal after application of this transfert operator is the Meixner polynomials of the first kind
COMPLETELY REACHABLE ALMOST GROUP AUTOMATA
Get PDFWe consider finite deterministic automata such that their alphabets consist of exactly one letter of defect 1 and a set of permutations of the state set. We study under which conditions such an automaton is completely reachable. We focus our attention on the case when the set of permutations generates a transitive imprimitive group
ALPHA LABELINGS OF DISJOINT UNION OF HAIRY CYCLES
Get PDFIn this paper, we prove the following results: 1) the disjoint union of isomorphic copies of the graph which is obtained by adding a pendent edge to each vertices of the cycle of order 4 admits -valuation; 2) the disjoint union of two isomorphic copies of the graph which is obtained by adding pendent edge to each vertices of the cycle of order 4 is admits -valuation; 3) the disjoint union of two isomorphic copies of the graph obtained by adding a pendent edge to each vertex of the cycle of order admits -valuation; 4) the disjoint union of two non-isomorphic copies of the graph obtained by adding a pendent edge to each vertices of the cycle of order and admits -valuation; 5) the disjoint union of two isomorphic copies of the graph which is obtained by adding a pendant edge to each vertex of the cycle of order is admitted graceful (-valuation)
ON -VERTEX-TRANSITIVE COVERS OF COMPLETE GRAPHS HAVING AT MOST TWO -ORBITS ON THE ARC SET
Get PDFWe investigate abelian (in the sense of Godsil and Hensel) distance-regular covers of complete graphs with the following property: there is a vertex-transitive group of automorphisms of the cover which possesses at most two orbits in the induced action on its arc set. We focus on covers whose parameters belong to some known infinite series of feasible parameters. We also complete the classification of arc-transitive covers with a non-solvable automorphism group and show that the automorphism group of any unknown edge-transitive cover induces a one-dimensional affine permutation group on the set of its antipodal classes
STATISTICAL CONVERGENCE IN TOPOLOGICAL SPACE CONTROLLED BY MODULUS FUNCTION
Get PDFThe notion of -statistical convergence in topological space, which is actually a statistical convergence's generalization under the influence of unbounded modulus function is presented and explored in this paper. This provides as an intermediate between statistical and typical convergence. We also present many counterexamples to highlight the distinctions among several related topological features. Lastly, this paper is concerned with the notions of -limit point and -cluster point for a unbounded modulus function
ON WIDTHS OF SOME CLASSES OF ANALYTIC FUNCTIONS IN A CIRCLE
Get PDFWe calculate exact values of some -widths of the class in the Banach spaces and with a weight . These classes consist of functions analytic in the unit circle, their th order derivatives belong to the Hardy space and the averaged moduli of smoothness of boundary values of are bounded by a given majorant at the system of points ; more precisely,for all , \(k>r.\
PRICING POWERED -POWER QUANTO OPTIONS WITH AND WITHOUT POISSON JUMPS
No full textThis paper deals with the problem of Black-Scholes pricing for the Quanto option pricing with power type powered and powered payoff underlying foreign currency is driven by Brownian motion and Poisson jumps, via risk-neutral probability measure. Our approach in this work is probabilistic, based on Feynman–Kac formula