Acta Mathematica Hungarica最新文献

We study the boundary behavior of spatial mappings that distort themodulus of families of paths in the same way as the inverse Poletskyinequality. Under certain conditions on the boundaries of thecorresponding domains, we have shown that such mappings have acontinuous boundary extension. Separately, we study the problem ofdiscreteness of the indicated extension. It is shown that undersome requirements, it is light, and under some more strongconditions, it is discrete in the closure of a domain.

We obtain a small ultrafilter number at (aleph_{omega_1}). Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal (kappa) inaccessible. We apply this forcing to construct a model where (kappa) is the least inaccessible and ( V_kappa ) is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small.

Let ({(R_k,D_k)}_{k=1}^infty) be a sequence of pairs, where

is an integer vector set and (R_k) is an integer diagonal matrix or upper triangular matrix, i.e.,(R_k={begin{pmatrix} s_k & 0 0 & t_k end{pmatrix}})or(R_k={begin{pmatrix} u_k & 1 0 & v_k end{pmatrix}}).Associated with the sequence ({(R_k,D_k)}_{k=1}^infty) , Moran measure (mu_{{R_k},{D_k}}) is defined by

In this paper, we consider the spectrality of (mu_{{R_k},{D_k}}). We prove that (mu_{{R_k},{D_k}}) is a spectral measure under certain conditions in terms of ((R_k,D_k)), i.e., there exists a Fourier basis for (L^2(mu_{{R_k},{D_k}})).

Let G be a subgraph of the complete bipartite graph (K_{l,m},{l leq m}), with (e=qm+p>0), (0 leq p <m), edges. The maximal value of the sum of the squares of the degrees of the vertices of G is (qm^2+p^2+ p (q+1)^2+(m-p) q^2). We classify all graphs that attain this bound using the diagonal sequence of a partition.

A subgroup H of a finite group G is called c-normal if there exists a normal subgroup N in G such that G = HN and (Hcap N leq core_G (H)), the largest normal subgroup of G contained in H. c-Normality is a weaker formof normality, introduced by Y.M. Wang, that has led to interesting results andstructural criteria of finite groups. In this paper we study c-normality in thecoprime action setting so as to obtain several solvability and p-nilpotency criteriain terms of certain subsets of maximal invariant subgroups of a group or of itsSylow subgroups.

We study divisibility properties of p-ary partitions colored with k(p − 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of (k=p^{alpha}) and (k=p^{alpha}-1).

We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p − 1) and all others with exactly k(p − 1) colors, where k is arbitrary (but fixed).

We use a convex integration construction from [22] in a Bairecategory argument to show that weak solutions to the transport equation withincompressible vector fields with Sobolev regularity are generic in the Baire categorysense. Using the construction of [7] we prove an analog statement for the3D Navier–Stokes equations.

We consider power means of independent and identically distributed(i.i.d.) non-integrable random variables. The power mean is an exampleof a homogeneous quasi-arithmetic mean. Under certain conditions, several limittheorems hold for the power mean, similar to the case of the arithmetic mean ofi.i.d. integrable random variables. Our feature is that the generators of the powermeans are allowed to be complex-valued, which enables us to consider the powermean of random variables supported on the whole set of real numbers. We establishintegrabilities of the power mean of i.i.d. non-integrable random variablesand a limit theorem for the variances of the power mean. We also consider thebehavior of the power mean as the parameter of the power varies. The complex-valuedpower means are unbiased, strongly-consistent, robust estimators for thejoint of the location and scale parameters of the Cauchy distribution.

A very short inductive proof is given for the maximal size of a k-graph on n vertices in which any two edges overlap in at least t vertices.

Let S be a pseudo-unitary homogeneous (graded) inverse semigroupwith zero 0, that is, an inverse semigroup with zero, and with a family ({S_delta}_{deltainDelta}) of nonzero subsets of S, called components of S,indexed by a partial groupoid (Delta), that is, by a set with a partial binary operation, such that(S=bigcup_{deltainDelta}S_delta), and: i) (S_xicap S_etasubseteq{0}) for all distinct (xi,etainDelta;)ii) (S_xi S_etasubseteq S_{xieta}) whenever (xieta) is defined;iii) (S_xi S_etansubseteq{0}) if and only if the product (xieta) is defined;iv) for every idempotent element (epsiloninDelta), the subsemigroup (S_epsilon) is with identity (1_epsilon;)v) for every (xin S) there exist idempotent elements (xi, etainDelta) such that (1_xi x=x=x1_eta;)vi) (1_xi1_eta=1_{xieta}) whenever (xietainDelta) is an idempotent element, where (xi), (eta) are idempotent elements of (Delta).Let A be a subset of the union of the subsemigroup components of S, which does not contain 0. By (operatorname{Cay}(S^*,A)) we denote a graph obtained from the Cayley graph (operatorname{Cay}(S,A)) by removing 0 and its incidentedges. We characterize vertex-transitivity of (operatorname{Cay}(S^*,A)) and relate it to the vertex-transitivity of its subgraph whose vertex set is (S_musetminus{0}), where (mu) is the maximum element of the set of all idempotent elements of (Delta),with respect to the natural order.