A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P if and only if its underlying term rewriting system Θ(R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sort.

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam–Liu–Sharifi–Wake–Wang. prove that the completion right-angled Artin group associated to chordal simplicial graph is and moreover it satisfies strong version Massey vanishing property. Also, we Demushkin are free product — and, under certain conditions, direct two type satisfying property, again Consequently, th...

A family F ⊆ 2[n] saturates the monotone decreasing property P if F satisfies P and one cannot add any set to F such that property P is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets.

Given a universe (a set) U and a property P, (closed under inclusions, for subsets of U). Results of the type “if every subset of cardinality μ of a finite family F ⊂ U has property P, then the entire family F has property P”are called Helly type theorems. The minimum number μ for which the result is true is called the Helly number of the Helly-type theorem (U ,P , μ). In the case of Helly’s cl...

Let X be a reduced closed scheme in P and let IX be its saturated defining ideal. As a generalization of property Np due to Green-Larzarsfeld, we say that X satisfies property N2,p if IX has only the simplest linear syzygies up to p-th step. When p = 1, then IX is generated by quadrics. Recently, many interesting geometric results have been proved for projective varieties with property N2,p (se...

For a graphical property P and a graph G, a subset S of vertices of G is a P-set if the subgraph induced by S has the property P . The domination number with respect to the property P , is the minimum cardinality of a dominating P-set. In this paper we present results on changing and unchanging of the domination number with respect to the nondegenerate and hereditary properties when a graph is ...

Motivated by the Q-property of nonsingular M-matrices, Lyapunov and Stein transformations (corresponding to positive stable and Schur stable matrices, respectively) and their products [A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994; M.S. Gowda, Y. Song, Math. Prog. 88 (2000) 575–587; M.S. Gowda, T. Parthasarathy, Linear Algebra Appl. 320 (2...

where g:(0, 1)-»X is an essentially bounded strongly measurable function. In this paper we examine analogues of the Radon-Nikodym Property for quasiBanach spaces. If 0 < p < 1, there are several possible ways of defining "differentiable" operators on Lp, but they inevitably lead to the conclusion that the only differentiable operator is zero. For example, a differentiable operator on L\ has the...

A graph G is said to have property P(k) if for any two sets A and B of vertices of G with A n B = $J and /A u BI = k , there is a vertex u P A u B which is joined to every vertex of A and not joined to any vertex of B . Note that if a graph G has property P(k) , then the complement GC of G also has property P(k) . If we specify the sizes of A and B as x and y respectively (x + y = k) then we de...

This gives complete freedom to answer if the input is close to having property P but does not exactly have this property. It is natural to think of property testing algorithms for which the input queries might have a very small probability of error. In this case it would be good to be able to separate inputs that are ε-far from having property P from those that are ε′-close to having property P...