Let S = (s1, s2, . . . , sm, . . .) be a linear recurring sequence with terms in GF (q) and T be a linear transformation of GF (q) over GF (q). Denote T (S) = (T (s1), T (s2), . . . , T (sm), . . .). In this paper, we first present counter examples to show the main result in [A.M. Youssef and G. Gong, On linear complexity of sequences over GF (2), Theoretical Computer Science, 352(2006), 288-29...

In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework. In spite of its generality, this probl...

Let I be a homogeneous ideal in polynomial ring over field. $$I^{(n)}$$ the n-th symbolic power of I. Motivated by results about ordinary powers I, we study asymptotic behavior regularity function $${{\,\mathrm{reg}\,}}(I^{(n)})$$ and maximal generating degree $$\omega (I^{(n)})$$ , when is monomial ideal. It known that both functions are eventually quasi-linear. We show that, addition, sequenc...

Three different kinds of condition numbers: normwise, mixed and componentwise, are discussed for the canonical generalized polar decomposition (CGPD) of real matrices. The technique used herein is different from the ones in previous literatures of the polar decomposition. With some modifications of the definition of the componentwise condition number, its application scope is extended. Explicit...

In this paper we study path-by-path uniqueness for multidimensional stochastic differential equations driven by the Brownian sheet. We assume that drift coefficient is unbounded, verifies a spatial linear growth condition and componentwise nondeacreasing. Our approach consists of showing result bounded nondecreasing using both local time-space representation law iterated logarithm sheets. The d...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

Let G be a finite simple graph and J(G) denote its vertex cover ideal in polynomial ring over field. The k-th symbolic power of is denoted by \(J(G)^{(k)}\). In this paper, we give criterion for ideals decomposable graphs to have the property that all their powers are not componentwise linear. Also, necessary sufficient condition on so \(J(G)^{(k)}\) linear some (equivalently, all) \(k \ge 2\) ...