Let rex(n,F) denote the maximum number of edges in an n-vertex graph that is regular and does not contain F as a subgraph. We give lower bounds on rex(n,F), are best possible up to constant factor, when one C4, K2,t, K3,3 or Ks,t for t>s!.

For a filter over a regular cardinal, least functions and the consequent notion of weak normality are described. The following two results, which make a basic connection between the existence of least functions and irregularity of ultrafilters, are then proved: Let U be a uniform ultrafilter over a regular cardinal k. (a) If k = \+, then U is not (\, \ )-regular iff V has a least function / suc...

Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let F =

Recently a generalization of simple convex polytopes to combinatorial entit ies known as abstract polytopes has been proposed. The graph of an abstract polytope o f d imension d is a regular connected graph of degree d. Given a connected regular graph F o f degree d, it is interesting to find out whether it is the graph of some abstract polytope P. We obtain necessary and sufficient condit ions...

We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F + g is not metrically regular is equa...

Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p. Let F be a Frobenius endomorphism on G and write G := G F for the corresponding finite group of Lie type. We consider projective characters of G in characteristic p of the form St ·β, where β is an irreducible Brauer character and St the Steinberg character of G. Let M be a rational G...

This article concerns the problem of stable recovering of any function in a shiftinvariant space from irregular samples of some filtered versions of the function itself. These samples arise as a perturbation of regular samples. The starting point is the generalized regular sampling theory which allows to recover any function f in a shiftinvariant space from the samples at {rn}n∈Z of s filtered ...

In this paper we study 3-dimensional visibility representations of complete graphs. The vertices are represented by equal regular polygons lying in planes parallel to the xy-plane. Two vertices are adjacent if and only if the two corresponding polygons see each other i.e. it is possible to construct an abscissa perpendicular to the xy-plane connecting the two polygons and avoiding all the other...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 → R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular triangular and ...

The classical Eilenberg correspondence, based on the concept of the syntactic monoid, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence appeared, with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. For example, classes of languages need not be clos...