Gradient Young measures generated by sequences in Sobolev spaces

Oscillatory properties of a weak convergent sequence of functions bounded inL ^p , 1 ≤p ≤ ∞, may be summarized by the parametrized measure it generates. When such a measure is generated by the gradients of a sequence of functions bounded inH ^1,p , it must have special properties. The purpose of this paper is to characterize such parametrized measures as the ones that obey Jensen’s inequality for all quasiconvex functions with the appropriate growth at infinity. We have found subtle differences between the casesp < ∞ andp = ∞. A consequence is that any measure determined by biting convergence is in fact generated by a sequence convergent in a stronger sense. We also give a few applications. Research groupTransitions and Defects in Ordered Materials, funded by the NSF, the AFOSR, and the ARO. The work of the second author is also supported by DGICYT (Spain) through “Programa de Perfeccionamiento y Movilidad del Personal Investigador” and through Grant PB90-0245.     

A RIEMANN-TYPE DEFINITION OF N-TH CESARO-PERRON INTEGRALS

In this paper, We give a varlational-type definition of (CnP) integrals. It is equivalent to the original definition of Perron-type and to the definition of Riemann-type, in this way the problem on definition of(CnP)′s Riemann-type has been solved completely.     

OSCILLATION CONVERGENT THEOREMS FOR THE V^2-INTEGRAL

The V^t-integral as defined in[2], which is eqnivalent to M^2-integrsl as defined in Trigonometre series by Zygmund is used to sum trigonometric seies in[1]. In this paper, some convergent theorems of V^2-integral are established.     

ON SOME INTEGRATION BY PARTS FORMULATE FOR THE ASP-INTEGRAL

The main results of this paper are as follows；Let F be approximately continuous on[a,b]and g be of bounded variation on[a,b]. Then (APS)∫^ba Fexists if and only if (APS)∫^ba gdf existe. Furthermore,suppose (APS)∫^ba Fdy or (APS)∫^ba gdF exists, then we have (APS)∫^ba Fdg (APS)∫^bagdf=F(b)g(b)-F(a)g(a)     

Comparison of Boolean algebras

In this work, some results related to superatomic Boolean interval algebras are presented, and proved in a topological way. Let x be an uncountable cardinal. To each I x, we can associate a superatomic interval Boolean algebra B _I of cardinality x in such a way that the following properties are equivalent: (i) I I x, (ii) B _I is a quotient algebra of B _J, and (iii) there is an homomorphism f from B _J into B _I such that for every atom b of B _I, there is an atom a of B _J satisfying f(a)=b. As a corollary, there are 2 ^x isomorphism types of superatomic interval Boolean algebras of cardinality x. This case is quite different from the countable one.     

On top-down splaying

The splay tree is a self-adjusting binary search tree which has a good amortized performance. This paper studies some properties of top-down splay trees. Different ways to charge for the primitive operations of top-down splaying are discussed. We also give some empirical results concerning the behaviour of different top-down restructuring algorithms.This work was supported by the Academy of Finland.     

Optimal impulse control problems for degenerate diffusions with jumps

Optimal stopping and impulse control problems for degenerate diffusion with jumps are studied in this paper. Lipschitzian coefficients for the diffusion process, data with polynomial growth, and evolution in the whole space are the main assumptions on the models. Several characterizations of the optimal cost functions are given. Existence of optimal policies is obtained.This research has been supported in part by Army Research Office Contract DAAG29-83-K-0014 and by National Science Foundation Grant DMS-8601998.     

Confirmation of far infrared laser assignments from CH3-deformation and CH3-rocking states of optically pumped methanol

High-resolution Fourier transform spectroscopy has been applied to confirm previously proposed assignments for nine far infrared (FIR) laser lines from the CH₃-deformation state of CH₃OH and one line from the CH₃-rocking state. Accurate frequencies are deduced for the observed and other predicted FIR laser transitions. FIR torsional branch frequencies in the ground state which were used in the confirmation are presented. Comments are also made on the OH-bending mode of CH₃OH.