LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

HOMOCLINIC SOLUTIONS FOR AUTONOMOUS DIFFERENTIAL EQUATIONS

ＨＯＭＯＣＬＩＮＩＣ　ＳＯＬＵＴＩＯＮＳ　ＦＯＲ　ＡＵＴＯＮＯＭＯＵＳ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳ￥ＺｅｎｇＷｅｉｙａｏ（曾唯尧）（ＨｕｎａｎＬｉｇｈｔＩｎｄｕｓｔｒｉａｌＣｏｌｌｅｇｅ）＆ＷａｎｇＸｕｅｘｉｎ（王学鑫）（Ｚｈｅｊｉ...     

MULTIVARIATE EXTREME VALUE DISTRIBUTION AND ITS FISHER INFORMATION MATRIX

ＭＵＬＴＩＶＡＲＩＡＴＥＥＸＴＲＥＭＥＶＡＬＵＥＤＩＳＴＲＩＢＵＴＩＯＮＡＮＤＩＴＳＦＩＳＨＥＲＩＮＦＯＲＭＡＴＩＯＮＭＡＴＲＩＸ￥ＳＨＩＤＡＯＪＩ（史道济）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ，Ｔｉａ...     

THE MAXIMUM AND MINIMUM SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE WITH IMPULSES IN BANACH SPACES

ＴＨＥＭＡＸＩＭＵＭＡＮＤＭＩＮＩＭＵＭＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲ　ＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＭＩＸＥＤＴＹＰＥＷＩＴＨＩＭＰＵＬＳＥＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＬｉｕＷｅｉａｎ（刘伟安）（Ｗｕｈａｎ...     

A NEW DETECTING METHOD FOR CONDITIONS OF EXISTENCE OF HOPF BIFURCATION

ＡＮＥＷＤＥＴＥＣＴＩＮＧＭＥＴＨＯＤＦＯＲＣＯＮＤＩＴＩＯＮＳＯＦＥＸＩＳＴＥＮＣＥＯＦＨＯＰＦＢＩＦＵＲＣＡＴＩＯＮＳＨＥＮＪＩＡＱＩ（沈家骐）；ＪＩＮＧＺＨＵＪＵＮ（井竹君）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎ...     

ASYMPTOTIC CHARACTERISTIC AND OSCILLATION OF HIGH ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

ＡＳＹＭＰＴＯＴＩＣＣＨＡＲＡＣＴＥＲＩＳＴＩＣＡＮＤＯＳＣＩＬＬＡＴＩＯＮＯＦＨＩＧＨＯＲＤＥＲＮＥＵＴＲＡＬＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＷｅｎＸｉａｎｇｃａｉ（温香彩）（ＨｅｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ...     

TURNING POINT PROBLEMS FOR THE THIRD ORDER DIFFERENTIAL EQUATIONS EXHIBITING RESONANCE

ＴＵＲＮＩＮＧＰＯＩＮＴＰＲＯＢＬＥＭＳＦＯＲＴＨＥＴＨＩＲＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＥＸＨＩＢＩＴＩＮＧＲＥＳＯＮＡＮＣＥＸＩＡＯＣＨＥＮＧＹＯＵ（肖成猷）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉ...     

THE SOLUTION OF _b－EQUATION OF （P，Q）－FORMS AND IT＇S L~P＆HOLDER ESTIMATES ON A STEIN MANIFOLD

ＴＨＥＳＯＬＵＴＩＯＮＯＦ_ｂ－ＥＱＵＡＴＩＯＮＯＦ（Ｐ，Ｑ）－ＦＯＲＭＳＡＮＤＩＴ＇ＳＬ￣Ｐ＆ＨＯＬＤＥＲＥＳＴＩＭＡＴＥＳＯＮＡＳＴＥＩＮＭＡＮＩＦＯＬＤ￥ＷｕＸｉａｏｑｉｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉｍｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｇｅＸｉａ?..     

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＡＷＥＡＫＳＯＬＵＴＩＯＮＯＦＱＵＡＳＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＷＩＴＨＣＲＩＴＩＣＡＬＳＯＢＯＬＶＥＸＰＯＮＥＮＴＯＮＵＮＢＯＵＮＤＥＤＤＯＭＡＩＮＬｉＧｏｎｇｂａｏ（李工宝）（Ｉｎｓｔ．ｏｆＭａｔｈ...     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR A CLASS OF THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

Regularity of ∫Ω|∇u|2 + λ∫Ω|u−f{2 and some gap phenomenon

We study the regularity of the minimizer u for the functional F (u,f)=|u|² + |u–f{² over all maps uH ¹(, S ²). We prove that for some suitable functions f every minimizer u is smooth in if ₀ and for the same functions f, u has singularities when is large enough.

---

Résumé On étudie la régularité des minimiseurs u du problème de minimisation min_ueH ¹(,S²)(|u|² + |u–f{². On montre que pour certaines fonctions f, u est régulière lorsque ₀ et pour les mêmes f, si est assez grand, alors u possède des singularités.

     

φ-Factors for Function Seminorms

Let (, A, ) be a measure space, a function seminorm on M, the space of measurable functions on , and M the space {f M : (f) < }. Every Borel measurable function : [0, ) [0, ) induces a function : M M by (f)(x) = (|f(x)|). We introduce the concepts of -factor and -invariant space. If is a -subadditive seminorm function, we give, under suitable conditions over , necessary and sufficient conditions in order that M be invariant and prove the existence of -factors for . We also give a characterization of the best -factor for a -subadditive function seminorm when is -finite. All these results generalize those about multiplicativity factors for function seminorms proved earlier.     

Approximate maximum likelihood estimation in linear regression

The application of the ML method in linear regression requires a parametric form for the error density. When this is not available, the density may be parameterized by its cumulants ( _i ) and the ML then applied. Results are obtained when the standardized cumulants ( _i ) satisfy _i = _i+2/ ₂ ^(i+2)/2 =O(v ⁱ ) asv 0 fori>0.Research financed in part by the Research Center of the Athens University of Economics and Business.     

First order properties of random posets

Let =(n,p) be a binary relation on the set [n]={1, 2, ..., n} such that (i,i) for every i and (i,j) with probability p, independently for each pair i,j [n], where i<j. Define as the transitive closure of and denote poset ([n], ) by R(n, p). We show that for any constant p probability of each first order property of R(n, p) converges as n .     

Two congruence lattices of completely simple semigroups

For a Rees matrix semigroupS with normalized sandwich matrix and C(S), the congruence lattice ofS, we consider the lattice generated by {itpT_l, pK, pT_r, pt_l, pk, pt_r}. HerepT ₁ andpt _l are the upper and lower ends of the interval which makes up the _i -class of , _i being the left trace relation onC(S). The remaining symbols have the analogous meaning relative to the kernel and the right trace relations. We also consider the lattice generated by {T _l, K, T_r, t_l, _k, t_r} where and are the equality and the universal relations onS, respectively. In both cases, we find lattices freest relative to these lattices and represent them as distributive lattices with generators and relations.With 3 Figures     

An Inequality Involving the Local Eigenvalues of a Distance-Regular Graph

Let denote a distance-regular graph with diameter D 3, valency k, and intersection numbers a _i, b _i, c _i. Let X denote the vertex set of and fix x X. Let denote the vertex-subgraph of induced on the set of vertices in X adjacent X. Observe has k vertices and is regular with valency a ₁. Let _{1 2} ··· _k denote the eigenvalues of and observe ₁ = a ₁. Let denote the set of distinct scalars among ₂, ₃, ..., _k . For let mult denote the number of times appears among ₂, ₃,..., _k . Let denote an indeterminate, and let p ₀, p₁, ...,p _D denote the polynomials in [] satisfying p ₀ = 1 andp _i = c _i+1 p _i+1 + (a _i – c _i+1 + c _i)p _i + b _i p _i–1 (0 i D – 1),where p _–1 = 0. We show where we abbreviate = –1 – b ₁(1+)^–1. Concerning the case of equality we obtain the following result. Let T = T(x) denote the subalgebra of Mat _X ( ) generated by A, E*₀, E*₁, ..., E* _D , where A denotes the adjacency matrix of and E* _i denotes the projection onto the ith subconstituent of with respect to X. T is called the subconstituent algebra or the Terwilliger algebra. An irreducible T-module W is said to be thin whenever dimE* _i W 1 for 0 i D. By the endpoint of W we mean min{i|E* _i W 0}. We show the following are equivalent: (i) Equality holds in the above inequality for 1 i D – 1; (ii) Equality holds in the above inequality for i = D – 1; (iii) Every irreducible T-module with endpoint 1 is thin.     

Limits of certain iterates of Post-Widder operators

The paper is a study of the limiting behaviour of the [n t]-th iterates of the well-known Post-Widder operatorsL _{n, x} used in the real inversion of the Laplace transform. It is shown that the limiting operators constitute a semigroup T _t;t0 of class (C ₀) on a family C _,; , >0 of Banach spaces. Applications of the semigroup structure lead to a pointwise saturation theorem forL _{n, x} and a characterization of convex functions inC _, through an inequality involving the action ofL _{n, x}.     

The regularity of Lagrangiansf(x, ξ)=254-01254-01254-01with Hölder exponents α(x)

In this paper the regularity of the Lagrangiansf(x, )=||^(x)(1< ₁(x)₂< +) is studied. Our main result: If(x) is Holder continuous, then the Lagrangianf(x, )=f(x, )=||^(x) is regular. This result gives a negative answer to a conjecture of V. Zhikov.Supported by the National Natural Science Foundation of China.     

Local isometric immersions of two-dimensional metrics inE 4 with prescribed Gaussian torsion

Suppose that in a domain R(, B) of variables (r, ): (0 r , ₁ +B(r–r ₀ ) ₂–B(r–r₀), where > 0, B > 0, ₁ < 0 < ₂ are numbers) a metric ds² = dr² +G(r, )d ² and a function k(r, ) are given. The problem of isometrically immersing ds² in E ⁴ with prescribed Gaussian torsion is considered. The following is proved: The class C ⁵ metric ds ² is locally realized in the form of a class C ³ surface F ² whose Gaussian torsion is the prescribed class C ³ function (r, ).Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 38–47, 1992.     

Solution of a problem on the identification of parameters by the distribution of the maximum random variable: a multivariate normal case

In this paper we solve the problem of unique factorization of products ofn-variate nonsingular normal distributions with covariance matrices of the form , _ij =p _{i j} forij, = _i ² ,j=j,p0.