作者机构：
[Yu Long; Zheng Dabin] Hubei Univ, Fac Math & Stat, Wuhan 430062, Peoples R China.;[Yu Long] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Hu Lei] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China.
通讯机构：
[Zheng Dabin] H;Hubei Univ, Fac Math & Stat, Wuhan 430062, Peoples R China.
关键词：
Block cyclic matrix;Greatest common divisor;Quadratic bent function;Quadratic semi-bent function
摘要：
Let n = me and p be an odd prime. Let Fpbe a finite field and Fpnbe its nth field extension. By some polynomial GCD computations, this paper characterize the bentness and semi-bentness of two classes of p-ary quadratic functions from Fpnto Fpwith coefficients in Fpe. Moreover, the enumeration formulas of constructed bent functions are obtained for some special cases of m. The results generalize some previous related work.
摘要：
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameter α goes to zero.
摘要：
We study the following singular elliptic equation -div(vertical bar x vertical bar(-2a) del u) - mu u/vertical bar x vertical bar(2(1+a)) = vertical bar u vertical bar(p-2)u/vertical bar x vertical bar(bp) + lambda u/vertical bar x vertical bar(dD) with Dirichlet boundary condition, which is related to the well-known Caffarelli-Kohn-Nirenberg inequalities. By virtue of variational method and Nehari manifold, we obtain least energy sign-changing solutions in some ranges of the parameters mu and lambda. In particular, our result generalizes the existence results of sign-changing solutions to lower dimensions 5 and 6.
摘要：
In this paper, we prove the following Myers type theorem: If (M
n
,g), n≥3, is an n-dimensional complete locally conformally flat Riemannian manifold with bounded Ricci curvature satisfying the Ricci pinching condition Rc≥ϵRg, where R>0 is the scalar curvature and ϵ>0 is a uniform constant, then M
n
must be compact.
摘要：
This paper is concerned with the existence of positive solutions for a class of quasilinear Schrodinger equations in R-N with critical growth and potential vanishing at in finity. By using a change of variables, the quasilinear equations are reduced to semilinear one. Since the potential vanish at in finity, the associated functionals are still not well de fined in the usual Sobolev space. So we have to work in the weighted Sobolev spaces, by Hardy-type inequality, then the functionals are well defined in the weighted Sobolev space and satisfy the geometric conditions of the Mountain Pass Theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is classical arguments used by H. Brezis and L. Nirenberg in [13].
作者：
Kuo, David Li-Wei;Tsai, Ming-Cheng;Wong, Ngai-Ching;Zhang, Jun*
期刊：
Abstract and Applied Analysis,2014年2014(SI52):1-5 ISSN：1085-3375
通讯作者：
Zhang, Jun
作者机构：
[Tsai, Ming-Cheng; Wong, Ngai-Ching; Kuo, David Li-Wei] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 80424, Taiwan.;[Zhang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Zhang, Jun] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
We study maps ϕ of positive operators of the Schatten p -classes ( 1 < p < + ∞ );which preserve the p -norms of convex combinations;that is;∥ t � + ( 1 - t ) σ ∥ p = ∥ t ϕ ( � ) + ( 1 - t ) ϕ ( σ ) ∥ p;σ ∈ � p + ( H ) 1;t ∈ [ 0;1 ] . They are exactly those carrying the form ϕ ( � ) = U � U * for a unitary or antiunitary U . In the case p = 2;we have the same conclusion whenever it just holds ∥ � + σ ∥ 2 = ∥ ϕ ( � ) + ϕ ( σ ) ∥ 2 for all the positive Hilbert-Schmidt class operators �;σ of norm 1 . Some examples are demonstrated. Published: 2014 First available in Project Euclid: 26 March 2014 zbMATH: 07022546 MathSciNet: MR3166627 Digital Object Identifier: 10.1155/2014/520795
