Sharp frequency bounds for eigenfunctions of the Ornstein–Uhlenbeck operator

We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein–Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.     

Sharp bounds for multilinear Hausdorff operators北大核心CSCD

We give the necessary conditions of boundedness of multilinear Hausdorff operators on Lebesgue spaces and λ-central Morrey spaces, respectively, when the kernel functions are nonnegative. Meanwhile, the corresponding operator norms are worked out. ©, 2015, Chinese Academy of Sciences. All right reserved.     

On the reliability bounds in κ-HNBUE and κ-HNWUE classes

-HNBUE class and its dual were introduced by Basu and Ebrahimi [2]. In this paper we give a generalized definition, and discuss their reliability bounds based on the known mean.     

Sharp weighted bounds for the Hardy–Littlewood maximal operators on Musielak–Orlicz spaces

Let \({\varphi}\) be a Musielak–Orlicz function satisfying that, for any \({(x,\,t)\in{\mathbb R}^n \times [0, \infty)}\), \({\varphi(\cdot,\,t)}\) belongs to the Muckenhoupt weight class \({A_\infty({\mathbb R}^n)}\) with the critical weight exponent \({q(\varphi) \in [1,\,\infty)}\) and \({\varphi(x,\,\cdot)}\) is an Orlicz function with uniformly lower type \({p^{-}_{\varphi}}\) and uniformly upper type \({p^+_\varphi}\) satisfying \({q(\varphi) < p^{-}_{\varphi}\le p^{+}_{\varphi} < \infty}\). In this paper, the author obtains a sharp weighted bound involving \({A_\infty}\) constant for the Hardy–Littlewood maximal operator on the Musielak–Orlicz space \({L^{\varphi}}\). This result recovers the known sharp weighted estimate established by Hytönen et al. in [J. Funct. Anal. 263:3883–3899, 2012].     

Traveling wave solutions for the mKdV equation and the Gardner equations by new approach of the generalized (G′/G)-expansion method

In this paper, we demonstrate the effectiveness of the new generalized (G′/G)-expansion method by seeking more exact solutions via the mKdV equation and the Gardner equations. The method is direct, concise and simple to implement compared to other existing methods. The traveling wave solutions obtained by this method are expressed in terms of hyperbolic, trigonometric and rational functions. The method shows a wide application for handling nonlinear wave equations. Moreover, the method reduces the large amount of calculations.     

New generalized and improved (G′/G)-expansion method for nonlinear evolution equations in mathematical physics

In this article, new extension of the generalized and improved (G′/G)-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV) equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.     

Two upper bounds for the Erd?s-Hooley Delta-function

For integer n≥1 and real u,let Δ(n,u):=|{d:d] n,e^u u+1}|.The Erd?s-Hooley Deltafunction is then defined by Δ(n):=Max_u∈R Δ(n,u).We improve the current upper bounds for the average and normal orders of this arithmetic function.     

Order of magnitude bounds for expectations of Δ2-functions of generalized random bilinear forms

Let Φ be a symmetric function, nondecreasing on [0,∞) and satisfying a Δ₂ growth condition, (X ₁,Y ₁), (X ₂,Y ₂),…,(X _n ,Y _n ) be arbitrary independent random vectors such that for any given i either Y _i =X _i or Y _i is independent of all the other variates. The purpose of this paper is to develop an approximation of

Sharp bounds of the zeroth-order general Randi? index of bicyclic graphs with given pendent vertices

Let G be a simple connected graph and α be a given real number. The zeroth-order general Randi? index of ⁰R_α(G) is defined as ∑_v∈V(G)[d_G(v)]^α, where d_G(v) denotes the degree of the vertex v of G. In this paper, for any α(≠0,1), we give sharp bounds of the zeroth-order general Randi? index ⁰R_α of all bicyclic graphs with n vertices and k pendent vertices.     

Error bounds of Rayleigh–Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems

We investigate contour integral-based eigensolvers for computing all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we focus on a Rayleigh–Ritz type method and analyze its error bounds. From the results of our analysis, we conclude that the Rayleigh–Ritz type contour integral-based eigensolver with sufficient subspace size can achieve high accuracy for target eigenpairs even if some eigenvalues exist outside but near the region.     

Lower bounds¶for the relative Lusternik–Schnirelmann category

We give estimates of numerical homotopy invariants of the pair (X,X×S ^p ) in terms of homotopy invariants of X. More precisely, we prove that σ ^{p +1} cat(X) + 1 ≤ cat(X,X×S ^p }), that and that e(X,X×S< ^p )=e(X)+1, where σ ^{p +1} cat is the (relative) σ category of Vandembroucq and e is the (relative) Toomer invariant. The proof is based on an extension of Milnor's construction of the classifying space of a topological group to a relative setting (due to Dold and Lashof). Received: 14 October 1998 / Revised version: 5 November 1999