Problem with conditions similar to Neumann conditions for φ-Laplacian

A boundary value problem with functional boundary conditions, with the Neumann problem as its special case, is considered for the ?-Laplacian.     

广义Mbius变换和算术Fourier变换

离散Fourier变换(DFT)在数字信号处理等许多领域中占有重要地位.近年来,出现一种优于FFT的算术Fourier变换来计算DFT.在广义M     

Cuspidal integrals for SL(3)∕Kϵ

We show that for the symmetric spaces $\mathrm{SL}(3,\mathbb{R})∕{\mathrm{SO}(1,2)}_e$ and $\mathrm{SL}(3,\mathbb{C})∕\mathrm{SU}(1,2)$ the cuspidal integrals are absolutely convergent. We further determine the behavior of the corresponding Radon transforms and relate the kernels of the Radon transforms to the different series of representations occurring in the Plancherel decomposition of these spaces. Finally we show that for the symmetric space $\mathrm{SL}(3,\mathbb{H})∕\mathrm{Sp}(1,2)$ the cuspidal integrals are not convergent for all Schwartz functions.     

Operator conditions for ℂ-differentiability

The concepts of dilation and rotation operators are introduced for maps of domains of infinite-dimensional Hibert spaces. Sufficient conditions for -differentiability along subspaces are established and theorems on operator conditions for IR-differentiable maps to be monogenic and holomorphic are proved.Translated from Ukrainskii Matematicheskii Zhurnal,42, No. 11, pp. 1448–1454, November, 1990.     

Necessary conditions for Gabor frames

The goal of this paper is to establish a set of necessary conditions for Gabor frames. These conditions are also sufficient for tight frames.     

Nodal standing waves for a gauged nonlinear Schrödinger equation in R2

This paper investigates the existence and asymptotic behavior of nodal solutions to the following gauged nonlinear Schrödinger equation

$\{\begin{array}{c}?\mathrm{\Delta }u+\omega u+(\frac{h^2(\left|x\right|)}{{\left|x\right|}^2}+\underset{\left|x\right|}{\overset{+\infty }{\int }}\frac{h(s)}{s}{u}^2(s)ds)u=\lambda {\left|u\right|}^{p?2}u,x\in {\mathbb{R}}^2,\hfill \\ u(x)=u(|x|)\in H^1({\mathbb{R}}^2),\hfill \end{array}$

where $\omega ,\lambda >0$, $p>6$ and

$h(s)=\frac{1}{2}\underset{0}{\overset{s}{\int }}r{u}^2(r)dr$

is the so-called Chern–Simons term. We prove that for any positive integer k, the problem has a sign-changing solution ${u^{\lambda }}_k$ which changes sign exactly k times. Moreover, the energy of $u_k^{\lambda }$ is strictly increasing in k, and for any sequence $\{{\lambda }_n\}\to +\infty (n\to \infty )$, there exists a subsequence $\{{\lambda }_{n_s}\}$, such that ${({\lambda }_{n_s})}^{\frac{1}{p?2}}{u}_k^{{\lambda }_{n_s}}$ converges in $H^1({\mathbb{R}}^2)$ to $w_k$ as $s\to \infty$, where $w_k$ also changes sign exactly k times and solves the following equation

$?\mathrm{\Delta }u+\omega u=|u{|}^{p?2}u,u\in H^1({\mathbb{R}}^2).$

     

Curved fronts in the Belousov–Zhabotinskii reaction–diffusion systems in R2

In this paper we consider a diffusion system with the Belousov–Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in ${\mathbb{R}}^2$ by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in ${\mathbb{R}}^2$.     

Avkhadiev–Becker type <Emphasis Type="Italic">p</Emphasis>-valence conditions for harmonic mappings of a disc

We obtain Avkhadiev–Becker type p-valence conditions for locally univalent harmonic mappings defined in the unit disc.     

On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

We consider a two-dimensional Ginzburg–Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg–Landau parameter vs. hole radius) is motivated by a recently discovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg–Landau problems in the classes of ${\mathbb{S}}^1$-valued and $\mathbb{C}$-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques.     

Multiplicity and concentration behaviour of positive solutions for Schrödinger-Kirchhoff type equations involving the p-Laplacian in RN

In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type

$-{\in }^{p}M\left({\in }^{p-N}{\int }_{{\mathbb{R}}^N}{\left|?u\right|}^p\right){\Delta }_{p}u+V\left(x\right){\left|u\right|}^{p-2}u=f\left(u\right)$

in ${\mathbb{R}}^N$, where Δ_p is the p-Laplacian operator, 1 < p < N, M: ${\mathbb{R}}^{+}\to {\mathbb{R}}^{+}$ and V: ${\mathbb{R}}^{\text{N}}\to {\mathbb{R}}^{+}$ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and Lyusternik-Schnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.     

The benefit of preemption with respect to the ℓp norm

We establish tight bounds on the benefit of preemption with respect to the ${?}_p$ norm minimization objective for identical machines and for two uniformly related machines (based on their speed ratio). This benefit of preemption is the supremum ratio between the optimal costs of non-preemptive and preemptive schedules.     

Density conditions for interpolation inA −∞

We give a necessary and sufficient density condition for a sequence {a _k} _k in the unit disk ofC to be interpolating for the classA ^−∞ of holomorphic functions with polynomial growth. The condition goes along the lines of those found by Seip for the analogous problem in Bergman spaces of the disk and by Berenstein and Li for some weighted spaces of entire functions. The result complements an earlier characterization given by Bruna and Pascuas. Partially supported by DGICYT grant PB95-0956-C02-02 and CIRIT grant 1998 SGR 00052. Also supported by a program of the Comunitat de Treball dels Pirineus.     

Finite groups with ℱ-subnormal conditions

Let ? be a subgroup-closed saturated formation. A finite group G is called an ?_pc-group provided that each subgroup X of G is ?-subabnormal in the ?-subnormal closure of X in G. Let ?_pc be the class of all ?_pc-groups. We study some properties of ? _pc-groups and describe the structure of ?_pc-groups when ? is the class of all soluble π-closed groups, where π is a given nonempty set of prime numbers.     

A bijective proof of Amdeberhan’s conjecture on the number of (s,s+2)-core partitions with distinct parts

Amdeberhan conjectured that the number of $(s,s+2)$-core partitions with distinct parts for an odd integer $s$ is $2^{s?1}$. This conjecture was first proved by Yan, Qin, Jin and Zhou, then subsequently by Zaleski and Zeilberger. Since the formula for the number of such core partitions is so simple one can hope for a bijective proof. We give the first direct bijective proof of this fact by establishing a bijection between the set of $(s,s+2)$-core partitions with distinct parts and a set of lattice paths.     

关于树T的的界

控制数γ和连通控制数γc是图的两个重要的控制参数.本文通过对树中的点进行恰当分类,给出了树中的γ/γc值的最好界,为刻画单圈图和双圈图中γ/γc值的界打下良好的基础.