A Variational ODE and its Application to an Elliptic Problem

In this paper,we consider the following ODE problem(P)where f ∈ C((0, ∞)×R,R),f(r,s)goes to p(r)and q(r)uniformly in r>0 as s→0 and s→ ∞,respectively,0≤p(r)≤q(r)∈ L~∞(0,∞).Moreover,for r>0,f(r,s)is nondecreasing in s≥0.Some existenceand non-existence of positive solutions to problem(P)are proved without assuming that p(r)≡0 and q(r)hasa limit at infinity.Based on these results,we get the existence of positive solutions for an elliptic problem.     

一类脉冲微分方程边值问题的特征值

Consider the following equations: Where 0 <η< 1,0 <α< 1, and f : [0,1]×[0,∞)→[0,∞), Ii,Li : [0,∞)→R, (i = 1,2,…, k) are continuous functions. We prove the existence of eigenvalues for the problem under a weaker condition, moreover we do not require the monotonicity of the impulsive functions.     

UNIQUENESS OF THE MILD SOLUTION OF SEMILINEAR STOCHASTIC EVOLUTION EQUATION IN HILBERT SPACE

In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y,f(t, y): [0, T]×Y→Y, and G(t, y): [0, T]×Y→L(H, Y), y_0: Ω→Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in [4].     

EXISTENCE OF SIGN-CHANGING SOLUTION FOR THREE-POINT BOUNDARY VALUE PROBLEM

In this paper,by using the fixed-point index theory,we study the existence of sign-changing solution to some three-point boundary value problem {y″(t) f(y)=0,t∈[0,1], y(0)=0,y′(1)=αy′(η), where 0<α<1,0<η<1,f:R→R is continuous,strictly increasing and f(0)=0.     

非线性分数次边值问题改进的ADM解法(英文)

We use the modified Adomian decomposition method（ADM） for solving the nonlinear fractional boundary value problem {D（^α₀） + u（x） = f（x, u（x））, 0 < x < 1, 3 < α≤ 4 u（0） = α₀ , u’’ （0） = α₂ u（1） = β₀ , u’’（1） = β₂} （1） where D（₀^α）+u is Caputo fractional derivative and α₀,α₂,β₀,β₂ is not zero at all,and f:[0,1]×R→ R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems.     

LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

We obtain a local regularity result for solutions to Kψ,θ-obstacle problem of A-harmonic equation divA(x,u(x),▽u(x))=0,where A:Ω× R×Rn → Rn is a Carath'eodory function satisfying some coercivity and growth conditions with the natural exponent 1pn,the obstacle function ψ≥0,and the boundary data θ∈W1,p(?).     

CONVERGENCE PROPERTIES OF IMPROVED SECANT METHODS WITH TRUST REGION MULTIPLIER

§ 1　 IntroductionWe consider the following equality contrained minimization problem:minf(x)s.t.c(x) =0 , (1 .1 )wheref :Rn→ R1 and c:Rn→ Rmare twice continuously differentiable.In[1 ] ,Fontecilla proposed the secant methods and proved their localq -superlineartwo-step convergence property under certain conditions.However,the global convergenceis not concerned in this paper,since Fontecilla did not discuss the important question ofensuring progress towards the solution of the problem(1 .1…     

Problem with Critical Sobolev Exponent and with Weight

The authors consider the problem: -div(p▽u) = uq-1 λu, u > 0 inΩ, u = 0 on (?)Ω, whereΩis a bounded domain in Rn, n≥3, p :Ω→R is a given positive weight such that p∈H1 (Ω)∩C(Ω),λis a real constant and q = 2n/n-2, and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.     

DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL HALF SPACE

This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t > 0, x = (x 1 , x ′ ) ∈ R n + := R + × R n 1 , u(0, x) = u 0 (x) → u + , as x 1 → + ∞ , u t (0, x) = u 1 (x), u(t, 0, x ′ ) = u b , x ′ = (x 2 , x 3 , ··· , x n ) ∈ R n 1 . (I) For the non-degenerate case f ′ 1 (u + ) < 0, it was shown in [10] that the above initialboundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave φ(x 1 ) uniformly in x 1 ∈ R + as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t → + ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ (u) < 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 (u b ) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.     

SINGULAR PERTURBATIONS OF BOUNDARY VALUE PROBLEMS FOR THIRD ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

In this paper we obtain some results about the convergence of aolutions of the boundary value problems of the third order nonlinear ordinary differential equation with a small parameter ε>0: (i=0, 1, 2) to a solution of their reduced problem as ε→0, hero z=ψ(t, x, y) is a root of the equation f(t, x, y, z, 0)=0, and about the existence of solutions of the reduced problem. In addition, under certain conditions we prove the existence of solutions of the boundary value problems (1), (2_i) (i=1, 2), and give their asymptotic estimations.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.