Acta Mathematica Hungarica最新文献

We give a lower bound for the polynomial entropy of the induced map on an (n) -fold symmetric product of (X) , for a homeomorphism (f) with at least one wandering point, on a compact space (X). Also, we compute some polynomial entropies using this result.

Numbers of the form (kcdot p^n+1) with the restriction (k < p^n) are called generalized Proth numbers. For a fixed prime p we denote them by (mathcal{T}_p). The underlying structure of (mathcal{T}_2) (Proth numbers) was investigated in [2]. In this paper the authors extend their results to all primes. An efficiently computable upper bound for the reciprocal sum of primes in (mathcal{T}_p) is presented.All formulae were implemented and verified by the PARI/GP computer algebra system. We show that the asymptotic density of ( bigcup_{pin mathcal{P}} mathcal{T}_p) is (log 2).

Let ( mathcal{F} subseteq 2^{[n]}) be a fixed family of subsets. Let (D( mathcal{F} )) stand for the following set of Hamming distances:

. ( mathcal{F} ) is said to be a Hamming symmetric family, if ( mathcal{F} )X implies (n-din D( mathcal{F} )) for each (din D( mathcal{F} )).

We give sharp upper bounds for the size of Hamming symmetric families. Our proof is based on the linear algebra bound method.

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.