Let P : F × F → F be a polynomial of bounded degree over a finite field F of large characteristic. In this paper we establish the following dichotomy: either P is a moderate asymmetric expander in the sense that |P (A,B)| |F| whenever A,B ⊂ F are such that |A||B| ≥ C|F|2−1/8 for a sufficiently large C, or else P takes the form P (x, y) = Q(F (x) + G(y)) or P (x, y) = Q(F (x)G(y)) for some polyn...

We prove the topological invariance of the combinatorial Euler characteristic of ominimal sets with the help of a canonical, topologically defined stratification of o-minimal sets by locally compact ones. Introduction. Let Bn be the collection of semi-algebraic subsets of R, i.e. sets definable by a finite boolean combination of polynomial equalities and inequalities. The Bn, n ∈ N, satisfy (i)...

We determine the nature of the fixed point sets of groups of order p, acting on complexes of distinguished p-subgroups (those p-subgroups containing pcentral elements in their centers). The case when G has parabolic characteristic p is analyzed in detail.

A method based on the determination of maximum common substructures is applied for the generation of substructures which are characteristic for a given set of molecular structures. The molecular structures are from hitlists obtained by spectral library searches; the hitlists contain those reference compounds, which have infrared spectra most similar to that from the query compound. The influenc...

Modelling and forecasting Stock market is a challenging task for economists and engineers since it has a dynamic structure and nonlinear characteristic. This nonlinearity affects the efficiency of the price characteristics. Using an Artificial Neural Network (ANN) is a proper way to model this nonlinearity and it has been used successfully in one-step-ahead and multi-step-ahead prediction of di...

Recently, the interest in semifields has increased due to the discovery of several new families and progress in the classification problem. Commutative semifields play an important role since they are equivalent to certain planar functions (in the case of odd characteristic) and to modified planar functions in even characteristic. Similarly, commutative semifields are equivalent to relative dif...

Brouwerian ordered sets generalize Brouwerian lattices. The aim of this paper is to characterize α-complete Brouwerian ordered sets in a manner similar to that used previously for pseudocomplemented, Stone, Boolean and distributive ordered sets. The sublattice G(P ) in the Dedekind-Mac Neille completion DM(P ) of an ordered set P generated by P is said to be the characteristic lattice of P . We...

We introduce a new class of “random” subsets of natural numbers, WM sets. This class contains normal sets (sets whose characteristic function is a normal binary sequence). We provide necessary and sufficient conditions of solvability of systems of linear equations within every WM subset of N. We also provide a proof of solvability of partition-regular systems (Rado’s systems) within every WM su...

People usually try to show themselves attractively, since attractive looks are generally preferred. We propose a new method for modifying facial data in order to improve facial beauty while retaining the original features as much as possible. Based on investigations into related work of facial attractiveness, the targets for modification in our method are small and/or unbalanced eyes, and a pro...