The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic ω-α-Bloch space and characterize it in terms of \omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{x - y}}} \right| and \omega \left( {{{\left( {1 - {{\left| x \right|}^2}} \right)}^\beta }{{\left( {1 - {{\left| y \right|}^2}} \right)}^{\alpha - \beta }}} \right)\left| {\frac{{f\left( x \right) - f\left( y \right)}}{{\left| x \right|y - x'}}} \right| where ω is a majorant. Similar results are extended to harmonic little ω-α-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G.Ren, U.Kähler (2005)., Xi Fu, Bowen Lu., and Obsahuje seznam literatury
We construct a class of special homogeneous Moran sets, called {mk}-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of {mk}k\geqslant 1, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of ho- mogeneous Moran sets to assume the minimum value, which expands earlier works., Xiaomei Hu., and Obsahuje seznam literatury
Let L1 = −Δ + V be a Schrödinger operator and let L2 = (−Δ)2 + V2 be a Schrödinger type operator on \mathbb{R}^{n}\left ( n\geqslant 5 \right ) where V≠ 0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s\geqslant n/2. The Hardy type space H_{L2}^{1} is defined in terms of the maximal function with respect to the semigroup \left\{ {{e^{ - t{L_2}}}} \right\} and it is identical to the Hardy space H_{L2}^{1} established by Dziubański and Zienkiewicz. In this article, we prove the Lp-boundedness of the commutator Rb = bRf - R(bf) generated by the Riesz transform R = {\nabla ^2}L_2^{ - 1/2} , where b \in BM{O_\theta }(\varrho ) , which is larger than the space BMO\left (\mathbb{R}^{n} \right ). Moreover, we prove that Rb is bounded from the Hardy space H_{L2}^{1} into weak L_{weak}^1 (\mathbb{R}^n )., Yu Liu, Jing Zhang, Jie-Lai Sheng, Li-Juan Wang., and Obsahuje seznam literatury
Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory and combinatorics. In this paper, we obtain three new finite generalizations of Euler's pentagonal number theorem., Ji-Cai Liu., and Seznam literatury
We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals., Lewen Ji, Zhenbing Zeng., and Obsahuje bibliografické odkazy
We find the sum of series of the form \sum\limits_{i = 1}^\infty {\frac{{f(i)}}{{{i^r}}}} or some special functions f. The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mező’s paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of π., Meher Jaban, Sinha Sneh Bala., and Obsahuje seznam literatury
About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let p be a prime, and let N(k; p) denote the number of all 1\leqslant a_{i}\leq p-1 such that a_{1}a_{2}...a_{k}\equiv 1 mod p and 2 | ai + āi + 1, i = 1, 2, ..., k. The main purpose of this paper is using the analytic method, the estimate for character sums and trigonometric sums to study the asymptotic properties of the counting function N(k; p), and give an interesting asymptotic formula for it., Han Zhang, Wenpeng Zhang., and Obsahuje seznam literatury
We study some properties of generalized reduced Verma modules over $\mathbb{Z}$-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for $\mathbb{Z}$-graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules., Keli Zheng, Yongzheng Zhang., and Obsahuje bibliografické odkazy
Let R be a commutative ring. The annihilator graph of R, denoted by AG(R), is the undirected graph with all nonzero zero-divisors of R as vertex set, and two distinct vertices x and y are adjacent if and only if ann(xy) \neqann R(x)\cup annR(y), where for z \in R, annR(z) = {r \in R: rz = 0}. In this paper, we characterize all finite commutative rings R with planar or outerplanar or ring-graph annihilator graphs. We characterize all finite commutative rings R whose annihilator graphs have clique number 1, 2 or 3. Also, we investigate some properties of the annihilator graph under the extension of R to polynomial rings and rings of fractions. For instance, we show that the graphs AG(R) and AG(T(R)) are isomorphic, where T(R) is the total quotient ring of R. Moreover, we investigate some properties of the annihilator graph of the ring of integers modulo n, where n>1., Mojgan Afkhami, Kazem Khashyarmanesh, Zohreh Rajabi., and Obsahuje bibliografii
Let G be a graph of order n and λ(G) the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. One of the main results of the paper is the following theorem Let k \geqslant 2,
n \geqslant k^{3} + k + 4, and let G be a graph of order n, with minimum degree δ(G) \geqslant k. If \lambda \left( G \right) \geqslant n - k - 1, then G has a Hamiltonian cycle, unless G=K_{1}\vee (K_{n-k-1}+K_{k}) or G=K_{k}\vee
(K_{n-2k}+\bar{K}_{k})., Vladimir Nikiforov., and Obsahuje seznam literatury