‎Let $R$ be a noncommutative prime ring of‎ ‎characteristic different from $2$‎, ‎$U$ the Utumi quotient ring of $R$‎, ‎$C$ $(=Z(U))$ the extended centroid‎ ‎of $R$‎. ‎Let $0neq ain R$ and $f(x_1,ldots,x_n)$ a multilinear‎ ‎polynomial over $C$ which is noncentral valued on $R$‎. ‎Suppose‎ ‎that $G$ and $H$ are two nonzero generalized derivations of $R$‎ ‎such that $a(H(f(x))f(x)-f(x)G(f(x)))in ...

Given a symmetric Sobolev inner product of order N , the corresponding sequence of monic orthogonal polynomials {Qn} satisfies that Q2n(x) = Pn(x), Q2n+1(x) = xRn(x) for certain sequences of monic polynomials {Pn} and {Rn}. In this paper, we deduce the integral representation of the inner products such that {Pn} and {Rn} are the corresponding sequences of orthogonal polynomials. Moreover, we st...

Under mild conditions on n, p, we give a lower bound on the number of n-variable balanced symmetric polynomials over finite fields GF (p), where p is a prime number. The existence of nonlinear balanced symmetric polynomials is an immediate corollary of this bound. Furthermore, we prove that X(2, 2`− 1) are balanced and conjecture that these are the only balanced symmetric polynomials over GF (2...

A Kuga fiber variety is a family of abelian varieties parametrized by a locally symmetric space and is constructed by using an equivariant holomorphic map of Hermitian symmetric domains. We construct a complex torus bundle T over a Kuga fiber variety Y parametrized by X and express its cohomology H∗(T ,C) in terms of the cohomology of Y as well as in terms of the cohomology of the locally symme...

A graph is symmetric or arc-transitive if its automorphism group acts transitively on vertices, edges and arcs. Let p, q be odd primes with p, q ≥ 5 and X a q-valent symmetric graph of order 4p. In this paper, we proved that X K4p with 4p-1=q, X K2p,2p-2pK2 with 2p-1=q, the quotient graph of X is isomorphic to Kp,p and p=q, or K2p and 2p-1=q.

Symmetricity of an optimal solution of Semi-Definite Program (SDP) with certain symmetricity is discussed based on symmetry property of the central path that is traced by a primal-dual interior-point method. A symmetric SDP is defined by operators for rearranging elements of matrices and vectors, and the solution on the central path is proved to be symmetric. Therefore, it is theoretically guar...

We present a model for the structure, temporal behavior, and evolutionary status of the bipolar nebula M2−9. According to this model the system consists of an AGB or post-AGB star and a hot white dwarf companion, with an orbital period of about 120 years. The white dwarf has undergone a symbiotic nova eruption about 1200 years ago, followed by a supersoft x-ray source phase. The positional shif...