a kernel $j$ of a digraph $d$ is an independent set of vertices of $d$ such that for every vertex $w,in,v(d),setminus,j$ there exists an arc from $w$ to a vertex in $j.$in this paper, among other results, a characterization of $2$-regular circulant digraph having a kernel is obtained. this characterization is a partial solution to the following problem: characterize circulant digraphs which hav...

Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...

We consider the problem of inferring an ancestral state from observations at leaves a tree, assuming evolves along tree according to two-state symmetric Markov process. establish general branching rate condition under which maximum parsimony, common reconstruction method requiring only knowledge topology (but not substitution rates or other parameters), succeeds better than random guessing unif...

let be a set and let be the set of subsets of . the pair in which is a collection of elements of (blocks) is called a design if every element of appears in , times. is called a symmetric design if . in a symmetric design, each element of appears times in blocks of . a mapping between two designs and is an isomorphism if is a one-to-one correspondence and . every isomorphism of a design, , to it...

A constellation of $N=d-1$ Majorana stars represents an arbitrary pure quantum state dimension $d$ or a permutation-symmetric system consisting $n$ qubits. We generalize the latter construction to represent in similar way symmetric $k$ subsystems with levels each. For $d\geq 3$, such states are equivalent, as far rotations concerned, collection various spin states, definite relative complex wei...

The present investigation deals with the propagation of waves in the layer of an anisotropic fibre reinforced thermoelastic solid. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitude of displacements and temperature distribution were also obtained. Finally, the numerical solution was carried out for Cobalt material...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj−2Fij . When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting ...

For a nonsymm etri c threshold network equippe d with an asynchronous dynamics, we show that if the product of weights in any cycle of units is nonnegative, then each tr ajectory converges to a stable state with probability one. We also show that such networks have a natural feed-forward layer struc ture and stabilit y is achieved in a hierarchical order due to this struct ure. It follows then ...