Periodica Mathematica Hungarica最新文献

We study quasi-quadratic modules in a pseudo-valuation domain A whose strict units admit a square root. Let (mathfrak X_R^N) denote the set of quasi-quadratic modules in an R-module N, where R is a commutative ring. It is known that there exists a unique overring B of A such that B is a valuation ring with the valuation group ((G,le )) and the maximal ideal of B coincides with that of A. Let F be the residue field of B. In the above setting, we found a one-to-one correspondence between ({mathfrak {X}}_A^A) and a subset of (prod _{g in G,g ge e} {mathfrak {X}}_{F_0}^F).

We obtain a new bound on certain multiple sums with multidimensional Kloosterman sums. In particular, these bounds show the existence of nontrivial cancellations between such sums in very small families.

For any positive integer m, let (mathbb {Z}_m) be the cyclic group of order m. For any subset (Asubseteq mathbb {Z}_{m}) and any (nin mathbb {Z}_{m}), let (delta _{A}(n)=#{(a,b)|n=a-b, ain A, bin A}). In this paper, we prove that, for any positive integer m, there exists a subset A of (mathbb {Z}_m) such that (delta _A (n)le 5) for all (n in mathbb {Z}_m) with at most 3 exceptions, which improves a 2010 result of Y.–G. Chen & T. Sun.

We characterize a 2-Killing Reeb vector field of a contact metric manifold, we describe the 2-Killing vector fields pointwise collinear with the Reeb vector field of the structure, and we study them in the general Riemannian case. On the other hand, we obtain some properties when the Reeb vector field is 2-Killing and the manifold is a Ricci soliton, a Yamabe soliton, a hyperbolic Ricci soliton, or a hyperbolic Yamabe soliton with potential vector field pointwise collinear with the Reeb vector field of the structure.

We study the semi-symmetry and pseudo-symmetry of almost Kenmotsu 3-manifolds. We prove that non-locally symmetric pseudo-symmetric H-almost Kenmotsu 3-manifolds are certain generalized almost Kenmotsu ((kappa ,mu ,nu ))-spaces.

For any given set A of nonnegative integers and for any given two positive integers (k_1,k_2), (R_{k_1,k_2}(A,n)) is defined as the number of solutions of the equation (n=k_1a_1+k_2a_2) with (a_1,a_2in A). In this paper, we prove that if integer (kge 2) and set (Asubseteq {mathbb {N}}) such that (R_{1,k}(A,n)=R_{1,k}({mathbb {N}}setminus A,n)) holds for all integers (nge n_0), then (R_{1,k}(A,n)gg log n).

In this paper, we first give two fundamental principles to characterize conformal vector fields of ((alpha ,beta ))-spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of ((alpha ,beta ))-spaces under certain curvature conditions. Besides, we construct a family of non-homothetic conformal vector fields on a family of locally projectively flat Randers spaces.

In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most (1+1) contaminated, if it contains at most one failure of type I and at most one failure of type II. The accompanying distribution for the length of the longest at most (1+1) contaminated run is obtained. The proof is based on a powerful lemma of Csáki, Földes and Komlós. Besides a mathematical proof, simulation results supporting our theorem are also presented.

We are concerned with the existence of positive solutions for the boundary value problem

where (a,b:mathbb {Z}rightarrow mathbb {R}), (c:mathbb {Z}rightarrow (0,1)), (p>0), and D is the forward difference operator. The main tools used are fixed point theorems of cone-compressing and cone-condensing type.