In a Cayley digraph on a group G, if a distinct colour is assigned to each arc-orbit under the left-regular action of G, it is not hard to show that the elements of the left-regular action of G are the only digraph automorphisms that preserve this colouring. In this paper, we show that the equivalent statement is not true in the most straightforward generalisation to G-vertex-transitive digraph...

For an (n− 1)-Auslander algebra Λ with global dimension n, we give some necessary conditions for Λ admitting a maximal (n − 1)-orthogonal subcategory in terms of the properties of simple Λ-modules with projective dimension n − 1 or n. For an almost hereditary algebra Λ with global dimension 2, we prove that Λ admits a maximal 1orthogonal subcategory if and only if for any non-projective indecom...

In this paper, we investigate the undetected error probabilities for bounded-distance decoding of binary primitive BCH codes when they are used for both error correction and detection on a binary symmetric channel. We show that the undetected error probability of binary linear codes can be quite simplified and quantified if weight distribution of the code is binomial-like. We obtain bounds on t...

We investigate the application of a cell vertex nite volume discretization to multi-symplectic PDEs. The investigated discretization reduces to the Preissmann box scheme when used on a rectangular grid. Concerning arbitrary quadrilateral grids, we show that only methods with parallelogram-like nite volume cells lead to a multi-symplectic discretization, i.e., to a method that preserves a discre...

game theory models decision makers' behaviors in strategic situations. since the structures of games are different, behavior and preferences of the players are different in various types of game. this paper reviews various situations of games. here, characteristics of some common games are discussed and compared. specifically, we focus on a group of games called symmetric games including p...

in this research, numerical simulation of a symmetric impact of a 2-d wedge, considering dynamic equations in two-phase flow is taken into account. the two-phase flow around the wedge is solved based on finite volume method and volume of fluid (vof) scheme. the dynamic mesh model is used to simulate dynamic motion of the wedge, thereby the effects of different dynamic meshes in both structured ...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

We study the question whether multistep methods or general multi-value methods can be symplectic. Already a precise understanding of symplecticity of such methods is a nontrivial task, because they advance the numerical solution in a higher dimensional space (in contrast to one-step methods). The essential ingredient for the present study is the formal existence of an invariant manifold, on whi...

When numerically integrating canonical Hamiltonian systems, the long-term conservation of some of its invariants, for example the Hamiltonian function itself, assumes a central role. The classical approach to this problem has led to the definition of symplectic methods, among which we mention Gauss–Legendre collocation formulae. Indeed, in the continuous setting, energy conservation is derived ...

Let a, b and c be positive integers, and consider a hexagon with side lengths a, b, c, a, b, c whose angles are 120◦ (see Figure 1.a). The subject of enumerating rhombus tilings of this hexagon (cf. Figure 1.b; here, and in the sequel, by a rhombus we always mean a rhombus with side lengths 1 and angles of 60◦ and 120◦) gained a lot of interest recently. This interest comes from two facts. Firs...