QUASI-CONFORMING FINITE ELEMENT APPROXIMATION FOR A FOURTH ORDER VARIATIONAL INEQUALITY WITH DISPLACEMENT OBSTACLE

In this paper, unconventional quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle is considered, the optimal order of error estimate O(h) is obtained which is as same as that of the conventional finite elements.     

一类拟线性椭圆方程组的Dirichlet问题

The homogeneous Dirichlet problem(1) for quasilinear elliptic system in a bounded domain Ω is investigated in this paper. The existence of generalized solutions in [H₀¹(Ω)]^N is obtained by using the contructive Galerkin method. For the case of a_ij^lm=0 when i≠j, it is estatablished that such generalized solutions have bounded [L_∞(Ω)]N norm and possess Holeler continuity. Even in the particular case that f_i are independent of Du, our results have improved those of A. V. Lair [Ann. Mat. Pura Appl., 116(1978)], allowing b_i¹(x,u) and f_i(x,u) to have a growth in u arbitrarily close to 1.     

Generalized Persistence of Entropy Weak Solutions for System of Hyperbolic Conservation Laws

Let u(t, x) be the solution to the Cauchy problem of a scalar conservation law in one space dimension. It is well known that even for smooth initial data the solution can become discontinuous in finite time and global entropy weak solution can best lie in the space of bounded total variations. It is impossible that the solutions belong to, for example, H¹ because by Sobolev embedding theorem H¹ functions are H¨older continuous. However, the author notes that from any point (t, x), he can draw a generalized characteristic downward which meets the initial axis at y = α(t, x). If he regards u as a function of (t, y), it indeed belongs to H¹ as a function of y if the initial data belongs to H¹ . He may call this generalized persistence (of high regularity) of the entropy weak solutions.The main purpose of this paper is to prove some kinds of generalized persistence (of high regularity) for the scalar and 2 × 2 Temple system of hyperbolic conservation laws in one space dimension.     

6q+1级2—传递置换群,q为素数

In [ 3 ] M. D. Atkinson conjectured that if G is a doubly transitive but not doubly primitive permutation group on Ω, then G is of one of the following four types: i) Metacyclic groups of prime degree p and of order p(p -1); ii) Groups of degree 2^p and of order 2^p(2^p-1)or 2^p(2^p-l)p for some prime p;iii)Gr-oups of automorphisms of a block design with λ=1; iv) Sz(q)≤G≤Aut(Sz(g)).In this paper we proved this conjecture in a special case without using the result of classification of finte simple groups, Qur explicit result is as follows: Theorem. Let G be a doubly transitive group on set Ω,where |Ω|=6q+1 and q is a prime, then one of the following holds: i)G is doubly primitive on Ω;ii) G is sharply doubly transitive on Ω; iii) G is a groups of automorphisms of a block design with λ=1.     

A variational inequality arising from European option pricing with transaction costs

In this paper we present a method which can transform a variational inequality with gradient constraints into a usual two obstacles problem in one dimensional case.The prototype of the problem is a parabolic variational inequality with the constraints of two first order differential inequalities arising from a two-dimensional model of European call option pricing with transaction costs.We obtain the monotonicity and smoothness of two free boundaries.     

一类广义Schr?dinger型非线性高阶方程组

In this paper we consider a class of semilinear systems of partial differential equations of higher order A(t)u₁+(-1)^Mu_x^ZM=f(u), which contain a class of the nonlinear Schr?dinger equations, where the matrix A(t) is nonsingular, nonnegative definite and f(u) satisfy the conditions (i) f(u) = -grad F(u), F(u)≥0(ii) (g(u),u)≤α(u,u) + b, g = A^－1f. The existence, uniqueness and regularity of solutions for periodic boundary problems and Cauchy problems in global are proved.     

EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

This paper deals with the existence of solutions to the elliptic equation -△uμu/|x|2=λu |u|2*-2u f(x, u) in Ω, u = 0 on ( a)Ω, where Ω is a bounded domain in RN(N≥3),0∈Ω,2*=2N/N-2,λ＞0,λ(a)σμ, σμ is the spectrum of the operator -△- μI/|x|2with zero Dirichlet boundary condition, 0 ＜μ＜-μ,-μ=(N-2)2/4,f(x,u) is an asymmetric lower order perturbation of |u|2*-1 at infinity. Using the dual variational methods, the existence of nontrivial solutions is proved.     

Terzo problema al contorno per una classe di equazioni ellittiche del secondo ordine a coefficienti discontinui

Summary The solvability of the boundary value problem Lu=f a.e. in Ω, u ε H²(Ω), ∂u/∂β+μu=0 on ∂Δ is studied, where L is a linear second order elliptic partial differential operator in non-divergence form with discontinuous coefficients, and β is a vector field which forms with the normal axe to ∂Ω an angle smaller than π/2.

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Entrata in Redazione il 6 febbraio 1976.

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Lavoro eseguito nell’ambito del ? Centro di Studio per la Matematica e la Fisica Teorica ? del C.N.R., Genova.     

Picard-Type Theorem and Curvature Estimate on an Open Riemann Surface with Ramification*

Let M be an open Riemann surface and G : M → Pⁿ(C) be a holomorphic map. Consider the conformal metric on M which is given by ds² = k e Gk^2m|ω|², where eG is a reduced representation of G, ω is a holomorphic 1-form on M and m is a positive integer. Assume that ds² is complete and G is k-nondegenerate(0 ≤ k ≤ n). If there are q hyperplanes H₁, H₂, · · · , H_q Pⁿ(C) located in general position such that G is ramified over H_j with multiplicity at least γ_j (> k) for each j ∈ {1, 2, · · · , q}, and it holds that Xj=1 1 -k/γ_j> (2n - k + 1) （mk/2+ 1）,then M is flat, or equivalently, G is a constant map. Moreover, one further give a curvature estimate on M without assuming the completeness of the surface.     

Local Well-posedness of the Derivative Schr¨odinger Equation in Higher Dimension for Any Large Data

In this paper, the authors consider the local well-posedness for the derivative Schr¨odinger equation in higher dimension u_t ? i△u + |u|²(?→γ · ?u) + u²(?→λ · ?u) = 0, (x, t) ∈ Rⁿ × R,?→γ ,?→λ ∈ Rⁿ; n ≥ 2.It is shown that the Cauchy problem of the derivative Schr¨odinger equation in higher dimension is locally well-posed in H^s(Rⁿ) (s > n/2) for any large initial data. Thus this result can compare with that in one dimension except for the endpoint space H^n/2.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.