Periodica Mathematica Hungarica最新文献

It is proved that the (*)-Ricci operator of a real hypersurface in a nonflat complex space form is Reeb parallel if and only if the hypersurface is Hopf. As an application of this result, we obtain a classification theorem of real hypersurfaces with parallel (*)-Ricci operators. These results answer some open questions posed by Kaimakamis and Panagiotidou a decade ago.

We introduce the concept of (epsilon )-homoclinic points for invertible linear operators on Banach spaces. We establish that an operator is hyperbolic if and only if it possesses the shadowing property without any nonzero (epsilon )-homoclinic points (for some (epsilon >0)). Additionally, we demonstrate that a linear operator on a Banach space X exhibiting the shadowing property is uniformly contracting, uniformly expanding, possesses a nontrivial invariant closed subspace, or has a dense set of bounded orbits in X. Moreover, we demonstrate the invariance of the set of generalized hyperbolic operators under (lambda )-Aluthge transforms, where (lambda in left( 0, 1right) ). Additionally, we establish that the Aluthge iterates of an invertible operator converge to a hyperbolic operator solely when the initial operator is hyperbolic. Finally, we prove that the Aluthge iterates of hyponormal shifted hyperbolic weighted shifts diverge and also the existence of hyperbolic weighted shifts with divergent Aluthge iterates.

A set S of vertices in a hypergraph is strongly independent if every hyperedge shares at most one vertex with S. We prove a sharp result for the number of maximal strongly independent sets in a 3-uniform hypergraph analogous to the Moon-Moser theorem. Given an r-uniform hypergraph ({{mathcal {H}}}) and a non-empty set A of non-negative integers, we say that a set S is an A-transversal of ({{mathcal {H}}}) if for any hyperedge H of ({{mathcal {H}}}), we have (|Hcap S| in A). Independent sets are ({0,1,dots ,r{-}1})-transversals, while strongly independent sets are ({0,1})-transversals. Note that for some sets A, there may exist hypergraphs without any A-transversals. We study the maximum number of A-transversals for every A, but we focus on the more natural sets, (A={a}), (A={0,1,dots ,a}) or A being the set of odd integers or the set of even integers.

In this paper we obtain refinement of Sherman’s generalization of classical majorization inequality for convex functions (2-convex functions). Using some nice properties of Green’s functions we introduce new identities that include Sherman’s difference, deduced from Sherman’s inequality, which enable us to extend Sherman’s results to the class of convex functions of higher order, i.e. to n-convex functions ((nge 3)). We connect this approach with Csiszár f-divergence and specified divergences as the Kullback–Leibler divergence, Hellinger divergence, Harmonic divergence, Bhattacharya distance, Triangular discrimination, Rényi divergence and derive new estimates for them. We also observe results in the context of the Zipf–Mandelbrot law and its special form Zipf’s law and give one linguistic example using experimentally obtained values of coefficients from Zipf’s law assigned to different languages.

For fixed positive numbers (alpha ne beta ), we consider the multiplicative group ({mathcal {F}}_{alpha ,beta }) generated by the rational numbers of the form (frac{lfloor alpha nrfloor }{lfloor beta nrfloor }), where (n in {mathbb {N}}) and (n ge max big (frac{1}{alpha },frac{1}{beta }big )). For (0<alpha <1) and (beta =1), we prove that ({mathcal {F}}_{alpha ,1}) is the maximal possible group, namely, it is the multiplicative group of all positive rational numbers ({mathbb {Q}}^{+}). The same equality ({mathcal {F}}_{alpha ,beta }={mathbb {Q}}^{+}) holds in the case when (0< 10 alpha le beta <1). These results produce infinitely many pairs ((alpha ,beta )), (alpha ne beta ), for which a conjecture posed by Kátai and Phong can be confirmed. The only previously known such example is ((alpha ,beta )=(sqrt{2},1)). We also give a new proof in that case, which is much simpler than the original proof of Kátai and Phong. More generally, we conjecture that ({mathcal {F}}_{alpha ,beta }={mathbb {Q}}^{+}) for (alpha ne beta ) if at least one of the numbers (alpha ,beta >0) is not an integer.

Let A be a nonempty subset of the integers and G a finite group written multiplicatively. The constant (eta _A(G)) ((s_A(G))) is defined to be the smallest positive integer t such that any sequence of length t of elements of G contains a nonempty A-weighted product one subsequence (that is, the terms of the subsequence could be ordered so that their A-weighted product is the multiplicative identity of the group G) of length at most (exp (G)) (of length (exp (G))). In this note, we shall calculate the value of (eta _pm (G),D_pm (G),E_pm (G) text{ and } s_pm (G)) for some metacyclic groups. In 2007, Gao et al. conjectured that (s(G)=eta (G)+exp (G)-1) holds for any finite abelian group G (see Gao et al. in Integers 7:A21, 2007). We will prove that this conjecture is true for some metacyclic groups. Furthermore, we study the Harborth constant (mathfrak {g}_pm (G)), where G is a group among one specific class of metacyclic groups.

Dartyge and Sárközy introduced the notion of digits in finite fields and studied the properties of polynomial values of ({mathbb {F}}_q) with a fixed sum of digits. Swaenepoel provided sharp estimates for the number of elements of special sequences of ({mathbb {F}}_q) whose sum of digits is prescribed. In this paper we study the sum-of-digits function in rings of residue classes and give a few asymptotic formulas and exact identities by using estimates for character sums and exponential sums modulo prime powers.

Suppose that N is a sufficiently large real number and E is an arbitrarily large constant. In this paper, it is proved that, for (1< c < frac{7}{6}), the Diophantine inequality

is solvable in prime variables (p_1,p_2,p_3) so that each of the numbers (p_i+2,,i=1,2,3), has at most (big [3.43655+{frac{12.12}{7-6c}}big ]) prime factors counted with multiplicity.

We prove Wittmann’s SLLN (see Wittmann in Stat Probab Lett 3:131–133, 1985) for (psi )-mixing sequences without the rate assumption.

In this paper we consider the (topological) lattice cohomology (mathbb {H}^*) of a surface singularity with rational homology sphere link. In particular, we will be studying two sets of (topological) invariants related to it: the weight function (upchi ) that induces the cohomology and the topological subspace arrangement (T(ell ,I)) at each lattice point (ell ) — the latter of which is the weaker of the two. We shall prove that the two are in fact equivalent by establishing an algorithm to compute (upchi ) from the subspace arrangement. Replacing the topological arrangements with the analytic, we get another formula — one that connects them with the analytic lattice cohomology introduced and studied in our earlier papers. In fact, this connection served as the original motivation for the definition of the latter. Aside from the historical interest, this parallel also provides us with tools to study more easily the connection between the two cohomologies.