On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian

In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p > 1):where Ω is a bounded domain in Rn (A≥1) and f(x,u) is quasi-asymptotically linear with respect to |u|p-2 u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f(x, s)/sp-1 is nondecrcasing with respect to s for all x ∈Ω and some others. In this paper. by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x, s)/sp-1 isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.     

On the Stability of Eaton’s Characterization by the Properties of Linear Forms

We consider a population and a sample X ₁,X ₂,…,X _n of n independent observations drawn from this population. We assume that two suitably chosen linear statistics of X ₁,X ₂,…,X _n are given. The assumption that these statistics are identically distributed or have the same distribution as the monomial X ₁ can be used to characterize various populations. This is an object of the so-called characterization theorems. But if the assumptions of a characterization theorem are fulfilled only approximately, then can we state that the conclusion of this characterization is also fulfilled approximately? Theorems concerning problems of this type are called stability theorems. By Eaton’s theorem, if, under additional conditions, two linear statistics $(X_{1}+\cdots +X_{k_{1}})/k_{1}^{1/\alpha}We consider a population and a sample X ₁,X ₂,…,X _n of n independent observations drawn from this population. We assume that two suitably chosen linear statistics of X ₁,X ₂,…,X _n are given. The assumption that these statistics are identically distributed or have the same distribution as the monomial X ₁ can be used to characterize various populations. This is an object of the so-called characterization theorems. But if the assumptions of a characterization theorem are fulfilled only approximately, then can we state that the conclusion of this characterization is also fulfilled approximately? Theorems concerning problems of this type are called stability theorems. By Eaton’s theorem, if, under additional conditions, two linear statistics and have the same distribution as the monomial X ₁, then this monomial has a symmetric stable distribution of order α. The stability estimation in this theorem is investigated in the λ ₀-metric.      

On a Problem of Approximation by Linear Means

is valid, where ω(f,δ) is the modulus of continuity of f. Furthermore they asked that: (1.3) If Theorem A can be extended to matrix summability? Later, P. D. Kathal, A. S. B. Holland and B. N. Sahney partially answered this problem. They proved the following Theorem B If {Λ_(n,k)} is monotonic non-increasing for all 0≤k≤n and Λ_(n,k)≥0 (0≤k≤n),Λ_(n,k)=0 (k>n), then we have     

On the Edge-forwarding Indices of Frobenius Graphs

A G-Frobenius graph F, as defined by Fang, Li, and Praeger, is a connected orbital graph of a Frobenius group G = K × H with Frobenius kernel K and Frobenius complement H. F is also shown to be a Cayley graph, F = Cay（K, S） for K and some subset S of the group K. On the other hand, a network N with a routing function R, written as （N, R）, is an undirected graph N together with a routing R which consists of a collection of simple paths connecting every pair of vertices in the graph. The edge-forwarding index π（N） of a network （N, R）, defined by Heydemann, Meyer, and Sotteau, is a parameter to describe tile maximum load of edges of N. In this paper, we study the edge-forwarding indices of Frobenius graphs. In particular, we obtain the edge-forwarding index of a G-Frobenius graph F with rank（G） ≤ 50.     

On the Problem of Heilbron Type

ＯｎｔｈｅＰｒｏｂｌｅｍｏｆＨｅｉｌｂｒｏｎＴｙｐｅ￥ＴｉａｎＺｈｅｎｇｐｉｎｇ（田正平）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＲｏｙａｌＨｏｌｌｏｗａｙａｎｄＢｅｄｆｏｒｄＮｅｗＣｏｌｅｇｅ，ＵｎｉｖｅｒｓｉｔｙｏｆＬｏｎｄｏｎ，Ｅｇｈ...     

On Rubel’s Problem in the Class of Linear Operators on the Space of Analytic Functions

In this paper, we describe all derivation pairs of linear operators that act in spaces of functions analytic in domains.     

On the Approximation of Combination of Linear Operators

Let f(x)∈C_(2π).For Valle-Poussin integrals V_n(f,x)=(2n)!! 1(2n-1)!! 2πintegral grom -πto π(f(x 1)cos~(2n)t/2 dt), Z.Ditzian and G.Freud considered the approximation of their combination writingV_(n,1)(f,x)=2V_(2n-1)(f,x)-V_(n-1)(f,x),V_(n,2)(f,x)=8/3V_(4n-1)(f,x)-2V_(2n-1)(f,x) 1/3V_(n-1)(f,x), they proved that V_(n,1)(f,x)-f(x)=O(ω_4(f,1/n~(1/2))), V_(n,2)(f,x)-f(x)=O(ω_6(f,1/n(1/2))) In this paper, using the asymptotic expansions of linear operators with many terms,we generalize the above result to the case of eombination of m terms, where mis an arbtirary positive integer.     

On the Irredundant Forms of Fuzzy Switching Functions

ＯｎｔｈｅＩｒｒｅｄｕｎｄａｎｔＦｏｒｍｓｏｆＦｕｚｚｙＳｗｉｔｃｈｉｎＦｕｎｃｔｉｏｎｓTXＯｎｔｈｅＩｒｒｅｄｕｎｄａｎｔＦｏｒｍｓｏｆＦｕｚｚｙＳｗｉｔｃｈｉｎｇＦｕｎｃｔｉｏｎｓＰｅｉＤａｏｗｕ（ＹａｎｃｈｅｎｇＴｅａｃｈｅｒｓＣｏｌｅｇｅ，...     

On the Syskin Problem of Finite Groups

In 1980, at the Seventh All-Union Symposium on Group Theory, ProfessorS.A .Syskin raised the following well-known problem: In a finite group G, supposeany two elemeuts of the same order are conjugate. Is |G|≤6? It is quite easy to     

On the Equation and the Number of Solution of Znam's Problem

§1. In 1972,St.Znam posed the problem whether for every s>1 thereexist integers x_i>1,i=1,…,s such that x_i is a proper divisor of the numberx_1…x_(i-1)x_(i 1)…x_s 1 for i=1,…, s.Without loss of generality, we may assume1相似文献   

On a Model Problem for the Orr–Sommerfeld Equation with Linear Profile

A model spectral problem of the form -i)y+xy= y on the finite interval [-1,1] with the Dirichlet boundary conditions is considered. Here is the spectral parameter and is positive. The behavior of the spectrum of this problem as 0 is completely investigated. The limit curves are found to which the eigenvalues concentrate and the counting eigenvalue functions along these curves are obtained.     

On the Number and Locations of the Eigenvalues of Generalized Eigenvalue Problem

The gerleralized eigenvalue problem Aχ=λBχ (1) where A and B are teal symmetric n×n matrices,is one 0f the basie Problems in matrix theory,which apPears in many fields,Such as physics,mechanics and engineering.When B is a positiVe definite matrix(1)can be solved by reducing it to the form     

The Uniqueness Problem of Non-Gaussian Linear Processes

Consider a linear time series which is represented aswhere u_t is an independent and identically distributed random series with Eu_t=0,Eu_t~2=σ~2>0,w_t is a square-summable sequence     

On a Problem of Hayman

ＯｎａＰｒｏｂｌｅｍｏｆＨａｙｍａｎＣｈｅｎＨｕａｉｈｕｉ（陈怀惠）ＦａｎｇＭｉｎｇｌｉａｎｇ（方明亮）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ，Ｊｉａｎｇｓｕ，２１００２４）Ｃ...     

On “Pre-historic” Linear Programming and the Figure of the Earth

In this paper, we develop algorithms to solve generalized Fermat–Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.     

On the Pal‘s Problem

The correct answer of Pal‘s interpolation polynomial problem has been given is this paper,espe-cially,the explict form of this polynomial has been obtained.     

On the Construction of Indecomposable Definite Hermitian Forms(Ⅲ)

ＯｎｔｈｅＣｏｎｓｔｒｕｃｔｉｏｎｏｆＩｎｄｅｃｏｍｐｏｓａｂｌｅＤｅｆｉｎｉｔｅＨｅｒｍｉｔｉａｎＦｏｒｍｓ（Ⅲ）ＺｈｕＦｕｚｕ（朱福祖）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎ...     

On the Closure of Translation–Dilation Invariant Linear Spaces of Polynomials

Assume that a linear space of real polynomials in d variables is given which is translation and dilation invariant. We show that if a sequence in this space converges pointwise to a polynomial, then the limit polynomial belongs to the space, too.     

On Fast Polynomial Algorithms and Lower Bounds of the Linear Complexity

ＯｎＦａｓｔＰｏｌｙｎｏｍｉａｌＡｌｇｏｒｉｔｈｍｓａｎｄＬｏｗｅｒＢｏｕｎｄｓｏｆｔｈｅＬｉｎｅａｒＣｏｍｐｌｅｘｉｔｙＬｉＬｅｉ（李磊）（Ｘｉ＇ａｎＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｘｉ＇ａｎ，Ｃｈｉｎａ，＆ＡｏｍｏｒｉＵｎｉｖｅｒｓｉｔｙ，...