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1.
Abstract

Existence and location of solutions to a Dirichlet problem driven by (pq)-Laplacian and containing a (convection) multivalued term fully depending on the solution and its gradient are established through the method of subsolution–supersolution. This result extends preceding works, in particular improving the growth condition for the lower order terms and allowing multivalued nonlinearities. A criterion for the existence of positive solutions with a priori estimates is obtained. Finally, an application to hemivariational inequalities is given.  相似文献   

2.
In this paper, we introduce new modifications of Szász–Mirakyan operators based on (p,q)‐integers. We first give a recurrence relation for the moments of new operators and present explicit formula for the moments and central moments up to order 4. Some approximation properties of new operators are explored: the uniform convergence over bounded and unbounded intervals is established, direct approximation properties of the operators in terms of the moduli of smoothness is obtained and Voronovskaya theorem is presented. For the particular case p = 1, the previous results for q‐Sz ász–Mirakyan operators are captured. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

3.
Let G be a connected, semisimple, and simply connected algebraic group defined and split over the finite field of order p, and let G(q) be the corresponding finite Chevalley or twisted group, where q = pr. Recently, Anwar determines the direct sum decomposition of the tensor product of the rth Steinberg module and a simple G-module with a (p,r)-minuscule highest weight λ. In this paper, we determine that of the tensor product regarded as a module for G(q) under some weak assumptions for λ.  相似文献   

4.
In this paper, the concepts of Lorentz inner product with (p, q) form, the Lorentz space and the Lorentz transformation with (p, q) form are given by using Clifford algebra. It is shown that Lmp,q is the Lorentz transformation with (p, q) form, and the matrix equality relation of Minkowski space with (n − 1, 1) form is given. The examples are given to illustrate the corresponding results.  相似文献   

5.
In this paper we show that the q-deformed commutator for a ladder is related to the usual commutator of the modified ladder. In addition, we consider a family of ladders in the (qh)-Weyl algebra, which gives a factorization of certain second order difference equations.  相似文献   

6.
In this article, based on the variational approach, the existence of at least one nontrivial solution is studied for (p, q)‐Laplacian type impulsive fractional differential equations involving Riemann‐Liouville derivatives. Without the usual Ambrosetti‐Rabinowitz condition, the nonlinearity f in the paper is considered under some suitable assumptions.  相似文献   

7.
Walid Al-Kawarit 《代数通讯》2013,41(10):3879-3896
In this article, we compare (n, m)-purities for different pairs of positive integers (n, m). When R is a commutative ring, these purities are not equivalent if R does not satisfy the following property: there exists a positive integer p such that, for each maximal ideal P, every finitely generated ideal of R P is p-generated. When this property holds, then the (n, m)-purity and the (n, m′)-purity are equivalent if m and m′ are integers ≥np. These results are obtained by a generalization of Warfield's methods. There are also some interesting results when R is a semiperfect strongly π-regular ring. We also compare (n, m)-flatnesses and (n, m)-injectivities for different pairs of positive integers (n, m). In particular, if R is right perfect and right self (?0, 1)-injective, then each (1, 1)-flat right R-module is projective. In several cases, for each positive integer p, all (n, p)-flatnesses are equivalent. But there are some examples where the (1, p)-flatness is not equivalent to the (1, p + 1)-flatness.  相似文献   

8.
Yongcai Ren 《代数通讯》2013,41(6):2635-2644
Let G be a finite group. We put ρ(G) = {p|p is a prime dividing χ(1) for some χ ∈Irr(G)}. We define a graph Γ(G), whose vertices are the primes in ρ(G) and p, q ∈ ρ(G) are connected in Γ(G) denoted p ~ q, if pq||χ(1) for some χ ∈Irr(G). For p ∈ ρ(G), we define ord(p) = |{q ∈ ρ(G)|q ~ p}|. We call ord(p) the order of the vertex p of the graph Γ(G). In this article, we discuss orders and the influences of orders on the structure of finite groups.  相似文献   

9.
We study the correlation decay and the expected maximal increments of the exponential processes determined by continuous-time autoregressive moving average (CARMA)-type processes of order (pq). We consider two background driving processes, namely fractional Brownian motions and Lévy processes with exponential moments. The results presented in this paper are significant extensions of those very recent works on the Ornstein–Uhlenbeck-type case (p = 1, q = 0), and we develop more refined techniques to meet the general (pq). In the concluding section, we discuss the perspective role of exponential CARMA-type processes in stochastic modelling of the burst phenomena in telecommunications and the leverage effect in financial econometrics.  相似文献   

10.
Suppose V is a vector space with dim V = p ≥ q ≥ ?0, and let T(V) denote the semigroup (under composition) of all linear transformations of V. For α ∈ T (V), let ker α and ran α denote the “kernel” and the “range” of α, and write n(α) = dim ker α and d(α) = codim ran α. In this article, we study the semigroups AM(p, q) = {α ∈ T(V):n(α) < q} and AE(p, q) = {α ∈ T(V):d(α) < q}. First, we determine whether they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Then, for each semigroup, we describe its maximal regular subsemigroup, and we characterise its Green's relations and (two-sided) ideals. As a precursor to further work in this area,, we also determine all the maximal right simple subsemigroups of AM(p, q).  相似文献   

11.
In this paper, we study the existence of positive smooth solutions for a class of singular (p(x), q(x))-Laplacian systems using sub and supersolution methods.  相似文献   

12.
13.
《偏微分方程通讯》2013,38(7-8):1127-1148
Abstract

In this work we analyze the existence of solutions that blow-up in finite time for a reaction–diffusion equation u t  ? Δu = f(x, u) in a smooth domain Ω with nonlinear boundary conditions ?u/?n = g(x, u). We show that, if locally around some point of the boundary, we have f(x, u) = ?βu p , β ≥ 0, and g(x, u) = u q then, blow-up in finite time occurs if 2q > p + 1 or if 2q = p + 1 and β < q. Moreover, if we denote by T b the blow-up time, we show that a proper continuation of the blowing up solutions are pinned to the value infinity for some time interval [T, τ] with T b  ≤ T < τ. On the other hand, for the case f(x, u) = ?βu p , for all x and u, with β > 0 and p > 1, we show that blow-up occurs only on the boundary.  相似文献   

14.
The goal of this article is two-fold. First, we consider a class of hyperholomorphic functions, the so called B p, q (G) space in ?3. Then, we use the B p, q (G) space to characterize the hyperholomorphic α-Bloch space. Second, we obtain characterizations of the weighted hyperholomorphic B p, q (G)-functions by the coefficients of certain lacunary series expansions in Clifford Analysis.  相似文献   

15.
Jingcheng Dong 《代数通讯》2013,41(12):4673-4678
Let p, q be prime numbers with p > q 3, and k an algebraically closed field of characteristic 0. In this article, we obtain the structure theorems for semisimple Hopf algebras of dimension pq 3.  相似文献   

16.
In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model.  相似文献   

17.
《代数通讯》2013,41(4):1777-1797
Abstract

In this paper we introduce and study the local quiver as a tool to investigate the étale local structure of moduli spaces of θ-semistable representations of quivers. As an application we determine the dimension vectors associated to irreducible representations of the torus knot groups G p,q  = ?a, b ∣ a  p  = b q ?.  相似文献   

18.
If K is a field of finite characteristic p, G is a cyclic group of order q = pα, U and W are indecomposable KG-modules with dim U = m and dim W = n, and λ(m,n,p) is a standard Jordan partition of mn, we describe how to find a generator for each of the indecomposable components of the KG-module U ? W.  相似文献   

19.
Li, Qi, and Rosalsky (Trans. Amer. Math. Soc., 368 (2016), no. 1, 539–561) introduced a refinement of the Marcinkiewicz–Zygmund strong law of large numbers (SLLN), the so-called ( p , q ) $(p,q)$ -type SLLN, where 0 < p < 2 $0<p<2$ and q > 0 $q>0$ . They obtained sets of necessary and sufficient conditions for this new type SLLN for two cases: 0 < p < 1 $0<p<1$ , q > p $q>p$ , and 1 p < 2 , q 1 $1\le p<2,q\ge 1$ . Results for the case where 0 < q p < 1 $0<q\le p<1$ and 0 < q < 1 p < 2 $0<q<1\le p<2$ remain open problems. This paper gives a complete solution to these problems. We consider random variables taking values in a real separable Banach space B $\mathbf {B}$ , but the results are new even when B $\mathbf {B}$ is the real line. Furthermore, the conditions for a sequence of random variables X n , n 1 $\left\lbrace X_n, n \ge 1\right\rbrace$ satisfying the ( p , q ) $(p, q)$ -type SLLN are shown to provide an exact characterization of stable type p Banach spaces.  相似文献   

20.
David E. Dobbs 《代数通讯》2013,41(6):2603-2623
An integer n is called catenarian if, whenever L/K is an n-dimensional field extension, all maximal chains of fields going from K to L have the same length. Catenarian field extensions and catenarian groups are defined analogously. If n is an even positive integer, 6n is non-catenarian. If n ≥ 3 is odd, there exist infinitely many odd primes p such that p 2 n is non-catenarian. A finite-dimensional field extension is catenarian iff its maximal separable subextension is. If q < p are odd primes where q divides p ? 1 (resp., q divides p + 1), every (resp., not every) group of order p 2 q is catenarian.  相似文献   

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