I show that in an o-minimal structure on the real field, satisfying certain conditions, every closed definable set is the zero set of a smooth definable function. The conditions are shown to hold in the Pfaffian closure of a polynomially bounded o-minimal structure having smooth cell decomposition.

We discuss the problem of transforming representations of number elds by generating polynomials and by Q-basis into each other. We prove that for a number eld or an order of discriminant one can determine in polynomial time a representation whose size is polynomially bounded in log jj.

We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0, 1] by a series ∑ cnxn with 0 ≤ αn → ∞ and ∑ |cn|rαn < ∞ for some r > 1 is definable. This expansion is polynomially bounded.

We prove an analog of Parikh’s theorem for weighted context-free grammars over commutative, idempotent semirings, and exhibit a stochastic context-free grammar with behavior that cannot be realized by any stochastic right-linear context-free grammar. Finally, we show that every unary stochastic context-free grammar with polynomially-bounded ambiguity has an equivalent stochastic right-linear co...

Abstract The paper investigates the algebraic properties of weakly inverse-closed complex Banach function algebras generated by functions bounded variation on a finite interval. It is proved that such have Bass stable rank 1 and are projective-free if they do not contain nontrivial idempotents. These derived from new result vanishing second Čech cohomology group polynomially convex hull continu...

Let $T$ be a polynomially bounded o-minimal theory extending the of real closed ordered fields. $K$ model equipped with $T$-convex valuation ring and $T$-derivation. If this derivation is continuous respect to topology, then we call $T$-differential field. We show that every field has an immediate strict extension which spherically complete. In some important cases, assumption polynomial bounde...

This paper studies envy-free allocations for economies with indivisible objects, quasilinear utility functions, and an amount of money. We give a polynomially bounded algorithm for finding envy-free allocations. Connectedness of envy-graphs, which are used in the algorithm, characterizes the extreme points of the polytopes of sidepayments corresponding with envy-free allocations. Classification...

We study the neighborhood polynomial and complexity of its computation for chordal graphs. The a graph is generating function subsets vertices that have common neighbor. introduce parameter graphs called anchor width an algorithm to compute which runs in time if polynomially bounded. maximal number different sub-cliques clique appear as neighborhood. Furthermore we some subclasses such comparab...

We describe a (1+ε) approximation algorithm for finding the minimum distortion embedding of an n-point metric space, (X, dX), into a tree with vertex set X. The running time of our algorithm is n · (∆/ε)opt 2λ+1 parameterized with respect to the spread of X, denoted by ∆, the minimum possible distortion for embedding X into any tree, denoted by δopt, and the doubling dimension of X, denoted by ...

In this paper using a transform defined by the translation operator we introduce concept of spectrum sequences that are bounded given polynomial. We apply spectral theory to study asymptotic behavior solutions fractional linear difference equations. One obtained results is an extension famous Katznelson-Tzafriri Theorem, saying ?-resolvent associated with equation, satisfies estimate type, prov...