We study the growth of polynomials on semialgebraic sets. For this purpose we associate a graded algebra to the set, and address all kinds of questions about finite generation. We show that for a certain class of sets, the algebra is finitely generated. This implies that the total degree of a polynomial determines its growth on the set, at least modulo bounded polynomials. We however also provi...

We recently described the isolation of mutant KB cells (Cyt 1 cells) resistant to the cytotoxic effect of cytochalasin B (CB). This mutant carried an altered beta-actin; i.e., beta'-actin (Toyama, S., and S. Toyama. 1984. Cell. 37:609-614). In the present study, we have examined the functional properties of actin in Cyt 1 cells. Our results showed that increased resistance of Cyt 1 cells to CB ...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

Let V be a finitely generated variety of algebras. We show that there is a finite bound on the size of the 〈R,S〉-irreducible sets of finite algebras in V iff V is congruence 3-permutable and has a near unanimity term operation of some arity.

The notion of a semi-commutativity set for word mappings was defined in [3] as an abstraction of a problem in cryptography. The notion is of special interest in case the mappings are morphisms. Then rather surprising constructions become possible. We investigate such constructions, paying special attention to exceptional values of inverse mappings. Some of our results bear a close relation to c...

We describe the extremal positive harmonic functions for finitely supported measures on discrete Heisenberg group: they are proportional either to characters or translates of induced from characters.

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

Gromov’s Polynomial Growth Theorem [Gro81] states that the property of having polynomial growth characterizes virtually nilpotent groups among all finitely generated groups. Gromov’s theorem inspired the more general problem (see, e.g. [GdlH91]) of understanding to what extent the asymptotic geometry of a finitelygenerated solvable group determines its algebraic structure—in short, are solvable...

The supercapacitive behavior of polyaniline/MnO2-carbon black (PANI/MnO2-CB), MnO2-CB nanocompositesand CB was studied. MnO2-CB made by the in situ direct coating method to deposit MnO2 onto CB; then PANI coating was coated on it. Morphology of the nanocomposite was studied by X-ray diffraction (XRD), Fourier transform...

We study finitely repeated two-person zero-sum games in which Player 1 is restricted to mixing over a fixed number of pure strategies while Player 2 is unrestricted. We describe an optimal set of pure strategies for Player 1 along with an optimal mixed strategy. We show that the entropy of this mixed strategy appears as a factor in an exact formula for the value of the game and thus is seen to ...