“断块”与 “板块”

从“断块”学说的观点看,“板块”是断块的一种特殊类型,它是被巨大的深切整个岩石圈的断裂带所围限的断块,是最大一级的断块,称做“岩石圈断块”. 板块学说主要是在对海洋的研究与地球物理研究的基础上发展起来的,它提出了一些有价值的新论点.但大多数研究板块的人,对大陆地区的地质情况还缺乏深入研究,不能充分利用本世纪以来在大陆地质构造研究方面所获得的科学结论与思想方法,这就使板块学说的进一步发展受到了阻碍。 本文先对断块学说的历史发展与现阶段理论作一简单介绍,然后应用断块构造的力学分析与历史分析方法,对板块构造研究中出现的一些主要问题谈一些看法.作者认为板块边界的力学机制主要是受基底锯齿状断裂的活动方式控制的,板块内部的应力分布也主要与板块内部次一级强度不同的断块的复杂活动有关。关于板块运动的驱动力,不但应考虑地球内部的热运动,而且应考虑到重力作用和地球作为一个旋转天体所具有的各种动力学行为.     

Quincunx multiresolution analysis for <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>(ℚ<Stack><Subscript>2</Subscript><Superscript>2</Superscript></Stack>)

With an eye on applications in quantum mechanics and other areas of science, much work has been done to generalize traditional analytic methods to p-adic systems. In 2002 the first paper on p-adic wavelets was published. Since then p-adic wavelet sets, multiresolution analyses, and wavelet frames have all been introduced. However, so far all constructions have involved dilations by p. This paper presents the first construction of a p-adic wavelet system with a more general matrix dilation, laying the foundation for further work in this direction.     

Approximation of the classes <Emphasis Type="Italic">C</Emphasis><Stack><Subscript>β</Subscript><Superscript>ψ</Superscript></Stack><Emphasis Type="Italic">H</Emphasis><Subscript>ω</Subscript> by generalized Zygmund sums

We obtain asymptotic equalities for the least upper bounds of approximations by Zygmund sums in the uniform metric on the classes of continuous 2π-periodic functions whose (ψ, β)-derivatives belong to the set H _ω in the case where the sequences ψ that generate the classes tend to zero not faster than a power function.     

Regular<Emphasis Type="Italic">n</Emphasis>-simplices in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> with vertices in ℤ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper theI andII regularn-simplices are introduced. We prove that the sufficient and necessary conditions for existence of anI regularn-simplex in ℝ ⁿ are that ifn is even thenn = 4m(m + 1), and ifn is odd thenn = 4m + 1 with thatn + 1 can be expressed as a sum of two integral squares orn = 4m - 1, and that the sufficient and necessary condition for existence of aII regularn-simplex in ℝ ⁿ isn = 2m ² - 1 orn = 4m(m + 1)(m ∈ ℕ). The connection between regularn-simplex in ℝ ⁿ and combinational design is given.     

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An extremal problem in the Hardy space <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> for 0&lt;<Emphasis Type="Italic">p</Emphasis>&lt;∞

We prove that if the function determining a linear functional over the Hardy space is analytic on the disk of radius greater than 1 then the extremal function of this functional is analytic on the same disk.     

Equitable total coloring of <Emphasis Type="Italic">F</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> ⋁ <Emphasis Type="Italic">W</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

The minimum number of total independent partition sets of V ∪ E of graph G(V,E) is called the total chromatic number of G denoted by χ _t (G). If the difference of the numbers of any two total independent partition sets of V ∪ E is no more than one, then the minimum number of total independent partition sets of V ∪ E is called the equitable total chromatic number of G, denoted by χ _et (G). In this paper, we obtain the equitable total chromatic number of the join graph of fan and wheel with the same order. Supported by the National Natural Science Foundation of China (No. 10771091).     

The number of S-precomplete classes in the functional system <Emphasis Type="Italic">P</Emphasis><Stack><Subscript><Emphasis Type="Italic">κ</Emphasis></Subscript><Superscript><Emphasis Type="Italic">τ</Emphasis></Superscript></Stack>

The problem on the number of precomplete classes in the functional system P _κ ^τ is considered, elements of P _κ ^τ are deterministic S-functions defined on words of length τ composed from letters of an alphabet of cardinality κ. An asymptotics for the number of S-precomplete classes in P _κ ^τ is obtained for arbitrary fixed κ and τ tending to infinity.     

Weak-Polynomial Convergence on Spaces ℓ<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> and <Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

This paper is concerned with the study of the set P ^-1(0), when P varies over all orthogonally additive polynomials on _p and L _p spaces. We apply our results to obtain characterizations of the weak-polynomial topologies associated to this class of polynomials.     

Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition

In this paper, we prove the existence of nontrivial nonnegative solutions to a class of elliptic equations and systems which do not satisfy the Ambrosetti–Rabinowitz (AR) condition where the nonlinear terms are superlinear at 0 and of subcritical or critical exponential growth at ∞. The known results without the AR condition in the literature only involve nonlinear terms of polynomial growth. We will use suitable versions of the Mountain Pass Theorem and Linking Theorem introduced by Cerami (Istit. Lombardo Accad. Sci. Lett. Rend. A, 112(2):332–336, 1978 Ann. Mat. Pura Appl., 124:161–179, 1980). The Moser–Trudinger inequality plays an important role in establishing our results. Our theorems extend the results of de Figueiredo, Miyagaki, and Ruf (Calc. Var. Partial Differ. Equ., 3(2):139–153, 1995) and of de Figueiredo, do Ó, and Ruf (Indiana Univ. Math. J., 53(4):1037–1054, 2004) to the case where the nonlinear term does not satisfy the AR condition. Examples of such nonlinear terms are given in Appendix A. Thus, we have established the existence of nontrivial nonnegative solutions for a wider class of nonlinear terms.     

Existence and Multiplicity of Solutions for a Class of Quasilinear Elliptic Equations with Exponential Growth北大核心CSCD

本文研究一类具有次临界多项式增长或次临界指数型(临界指数型)增长的(p,2)-拉普拉斯方程一个正解及无穷多非平凡解的存在性,运用山路定理及喷泉定理,得到了拉普拉斯方程非平凡解的一些存在性结果.     

An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p–Laplacian operator and subcritical nonlinearities satisfying Ambrosetti–Rabinowitz type conditions. Using Morse theory and a cohomological local splitting as in Degiovanni et al. (Commun Contemp Math 12:475–486, 2010), we prove the existence of a nontrivial weak solution for all (real) values of the eigenvalue parameter. Our result is new even in the semilinear case p = 2 and complements some recent results obtained in Autuori et al. (Adv Anal Equ 18:1–48, 2013).     

一类拟线性椭圆方程的非平凡解

运用环绕理论和对称型山路理论对一类具有次临界多项式增长和次临界指数增长的$p$-Laplacian方程建立一个非平凡解(无穷多个非平凡解)的存在性结果.     

Nonlinear Nonhomogeneous Dirichlet Equations Involving a Superlinear Nonlinearity

We consider a nonlinear elliptic Dirichlet equation driven by a nonlinear nonhomogeneous differential operator involving a Carathéodory function which is (p?1)-superlinear but does not satisfy the Ambrosetti–Rabinowitz condition. First we prove a three-solutions-theorem extending an earlier classical result of Wang (Ann Inst H Poincaré Anal Non Linéaire 8(1):43–57, 1991). Subsequently, by imposing additional conditions on the nonlinearity \({f(x,\cdot)}\), we produce two more nontrivial constant sign solutions and a nodal solution for a total of five nontrivial solutions. In the special case of (p, 2)-equations we prove the existence of a second nodal solution for a total of six nontrivial solutions given with complete sign information. Finally, we study a nonlinear eigenvalue problem and we show that the problem has at least two nontrivial positive solutions for all parameters \({\lambda > 0}\) sufficiently small where one solution vanishes in the Sobolev norm as \({\lambda \to 0^+}\) and the other one blows up (again in the Sobolev norm) as \({\lambda \to 0^+}\).     

Existence of entire solutions for a class of quasilinear elliptic equations

The paper deals with the existence of entire solutions for a quasilinear equation ${(\mathcal E)_\lambda}$ in ${\mathbb{R}^N}$ , depending on a real parameter λ, which involves a general elliptic operator in divergence form A and two main nonlinearities. The competing nonlinear terms combine each other, being the first subcritical and the latter supercritical. We prove the existence of a critical value λ* > 0 with the property that ${(\mathcal E)_\lambda}$ admits nontrivial non-negative entire solutions if and only if λ ≥ λ*. Furthermore, when ${\lambda > \overline{\lambda} \ge \lambda^*}$ , the existence of a second independent nontrivial non-negative entire solution of ${(\mathcal{E})_\lambda}$ is proved under a further natural assumption on A.     

Eigenvalue problems with weights in Lorentz spaces

Given V, w locally integrable functions on a general domain Ω with V ≥  0 but w allowed to change sign, we study the existence of ground states for the nonlinear eigenvalue problem:

$-\Delta u + V u = \lambda w |u|^{p-2} u, \quad u|_{\partial \Omega} =0,$

with p subcritical. These are minimizers of the associated Rayleigh quotient whose existence is ensured under suitable assumptions on the weight w. In the present paper we show that an admissible space of weight functions is provided by the closure of smooth functions with compact support in the Lorentz space \({L(\tilde p,\infty)}\) with \({\frac{1}{{\widetilde p}} + \frac{p}{2^{\star}} =1}\) . This generalizes previous results and gives new sufficient conditions ensuring existence of extremals for generalized Hardy–Sobolev inequalities. The existence in such a generality of a principal eigenfunction in the linear case p = 2 is applied to study the bifurcation for semilinear problems of the type

$-\Delta u= \lambda (a(x)u + b(x) r(u)),$

where a, b are indefinite weights belonging to some Lorentz spaces, and the function r has subcritical growth at infinity.

     

Variable Exponent Sobolev Spaces for Semilinear Elliptic Systems

In this work, the semilinear elliptic systems with Dirichlet boundary value are considered. We extend the notion of subcritical growth from polynomial growth to variable exponent growth. Under the variable exponent growth, nontrivial solutions are obtained via variable exponent Sobolev spaces and variational methods. In article final, we make a remark to explain that our main result is a extention of a recent result of D. G. de Figueiredo, J. M. do Óand B. Ruf [D. G. de Figueiredo, J. M. do Ó, B. Ruf, An Orlicz-space approach to superlinear elliptic systems, J. Funct. Anal. 224 (2005) 471–496].     

Quasilinear asymptotically periodic Schrödinger equations with critical growth

It is established the existence of solutions for a class of asymptotically periodic quasilinear elliptic equations in ${\mathbb{R}^N}$ with critical growth. Applying a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in ${H^1(\mathbb{R}^N)}$ and satisfy the geometric hypotheses of the Mountain Pass Theorem. The Concentration–Compactness Principle and a comparison argument allow to verify that the problem possesses a nontrivial solution.     

Existence of a ground state solution for a nonlinear scalar field equation with critical growth

In the present paper, we establish the existence of Ground State Solutions for some class of Elliptic problems with Critical Growth in ${\mathbb{R}^{N}}$ for N ≥ 2. Our results complete the study made in Berestycki and Lions (Arch Rat Mech Anal 82:313–346, 1983) and Berestycki, Gallou?t and Kavian (C R Acad Sci Paris Ser I Math 297:307–310, 1984), in the sense that, in those papers only the subcritical growth was considered.