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191. Some finite generalizations of Euler's pentagonal number theorem

Creator:
Liu, Ji-Cai
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, q-binomial coefficient, q-binomial theorem, pentagonal number theorem, 13, and 51
Language:
English
Description:
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
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192. Some inequalities for radial Blaschke-Minkowski homomorphisms

Creator:
Ji, Lewen and Zeng, Zhenbing
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, radial Blaschke-Minkowski homomorphism, Orlicz radial sum, 13, and 51
Language:
English
Description:
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
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193. Some infinite sums identities

Creator:
Jaban, Meher and Bala, Sinha Sneh
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
mathematics, multiple zeta values, multiple Hurwitz zeta values, 13, and 51
Language:
English
Description:
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
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194. Some new sums related to D. H. Lehmer problem

Creator:
Zhang, Han and Zhang, Wenpeng
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
Lehmer number, analytic method, trigonometric sums, asymptotic formula, 13, and 51
Language:
English
Description:
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
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195. Some properties of generalized reduced Verma modules over $\mathbb{Z}$-graded modular Lie superalgebras

Creator:
Zheng, Keli and Zhang, Yongzheng
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
modular Lie superalgebra, generalized reduced Verma module, coinduced module, invariant form, mixed product, 13, and 51
Language:
English
Description:
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
Rights:
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196. Some results on the annihilator graph of a commutative ring

Creator:
Afkhami, Mojgan, Khashyarmanesh, Kazem, and Rajabi, Zohreh
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, kruhový graf, číslo kliky, chromatická čísla, annihilator graph, zero-divisor graph, outerplanar, ring-graph, cut-vertex, clique number, weakly perfect, chromatic numbers, polynomial ring, ring of fractions, 13, and 51
Language:
English
Description:
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
Rights:
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197. Spectral radius and Hamiltonicity of graphs with large minimum degree

Creator:
Nikiforov, Vladimir
Format:
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Type:
model:article and TEXT
Subject:
matematika, mathematics, Hamiltonian cycle, Hamiltonian path, minimum degree, spectral radius, 13, and 51
Language:
English
Description:
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
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198. The basic construction from the conditional expectation on the quantum double of a finite group

Creator:
Xin, Qiaoling, Jiang, Lining, and Ma, Zhenhua
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, conditional expectation, basic construction, quantum double, quasi-basis, 13, and 51
Language:
English
Description:
Let G be a finite group and H a subgroup. Denote by D(G;H) (or D(G)) the crossed product of C(G) and \mathbb{C}H (or \mathbb{C}G) with respect to the adjoint action of the latter on the former. Consider the algebra \left \langle D(G), e\right \rangle generated by D(G) and e, where we regard E as an idempotent operator e on D(G) for a certain conditional expectation E of D(G) onto D(G; H). Let us call \left \langle D(G), e\right \rangle the basic construction from the conditional expectation E: D(G) → D(G; H). The paper constructs a crossed product algebra C(G/H ×G) \rtimes \mathbb{C}G, and proves that there is an algebra isomorphism between \left \langle D(G), e\right \rangle and C(G/H×G) \rtimes \mathbb{C} G., Qiaoling Xin, Lining Jiang, Zhenhua Ma., and Obsahuje seznam literatury
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199. The Bergman kernel: Explicit formulas, deflation, Lu Qi-Keng problem and Jacobi polynomials

Creator:
Beberok, Tomasz
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Jacobi polynomial, Lu Qi-Keng problem, Bergman kernel, Routh-Hurwitz theorem, 13, and 51
Language:
English
Description:
We investigate the Bergman kernel function for the intersection of two complex ellipsoids {(z,w1,w2) 2 Cn+2 : |z1|2+. . .+|zn|2+|w1|q <1, |z1|2+. . .+|zn|2+|w2|r < 1}. We also compute the kernel function for {(z1,w1,w2) 2 C3 : |z1|2/n + |w1|q < 1, |z1|2/n + |w2|r < 1} and show deflation type identity between these two domains. Moreover in the case that q = r = 2 we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem., Tomasz Beberok., and Seznam literatury
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200. The Cauchy problem for the liquid crystals system in the critical Besov space with negative index

Creator:
Ming, Sen, Yang, Han, Chen, Zili, and Yong, Ls
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, systém kapalných krystalů, záporný index, liquid crystals system, critical Besov space, negative index, well-posedness, blow-up, 13, and 51
Language:
English
Description:
The local well-posedness for the Cauchy problem of the liquid crystals system in the critical Besov space is established by using the heat semigroup theory and the Littlewood-Paley theory. The global well-posedness for the system is obtained with small initial datum by using the fixed point theorem. The blow-up results for strong solutions to the system are also analysed., Sen Ming, Han Yang, Zili Chen, Ls Yong., and Obsahuje bibliografii
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