Singular integral operators on 53-0153-0153-01-spaces

Summary It is shown that certain singular integral operators with variable kernels leave invariant theL ^v, -spaces studied by Campanato, Stampacchia, Peetre and others. Our results extend Peetre's work on convolution operators.     

Association Schemes and Fusion Algebras (An Introduction)

We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establish the condition when the matrix S of a fusion algebra at algebraic level is unitary or symmetric. We construct integral fusion algebras at algebraic level, from association schemes, in particular from group association schemes, whose matrix S is unitary and symmetric. Finally, we consider whether the modular invariance property is satisfied or not, namely whether there exists a diagonal matrix T satisfying the condition (ST)³ = S ². We prove that this property does not hold for some integral fusion algebras at algebraic level coming from the group association scheme of certain groups of order 64, and we also prove that the (nonintegral) fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) has the modular invariance property.     

Strategy-proofness, solidarity, and consistency for multiple assignment problems

We consider a problem of allocating indivisible objects when agents may desire to consume more than one object and no monetary transfers are allowed. We are interested in allocation rules that satisfy desirable properties from an economic and social point of view. In addition to strategy-proofness and Pareto efficiency, we consider consistency and two solidarity properties (replacement-domination and population-monotonicity). In most of the cases, these properties are satisfied only by serially dictatorial rules. Received: November 1999/Final version: December 2001     

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind

Positivity - In the present paper, we will characterize the boundedness of the generalized fractional integral operators $$I_{rho }$$ and the generalized fractional maximal operators $$M_{rho }$$...     

Construction of an atomic decomposition for functions with compact support

Chang, Krantz and Stein [D.-C. Chang, S.G. Krantz, E.M. Stein, Hp theory on a smooth domain in Rn and elliptic boundary value problems, J. Funct. Anal. 114 (1993) 286-347] proved that if f∈Hp(Rn) and f vanishes outside , then f has an atomic decomposition whose atoms are contained in Ω. The purpose of this paper is to give another proof for the case n/(n+1)<p?1 and Ω a cube. Our argument provides a simple, direct construction of the desired atomic decomposition, and it works in a class of function spaces more general than the usual Hardy spaces.     

Two-dimensional measurement of laser-induced target movement by face-on interferometry

Initial movement of laser irradiated foil targets has been measured by face-on interferometry with two-dimensional resolution. This interferometric method provides direct and precise information about the initial movement of the rear surface of the target compared with conventional diagnostics. Target movement of 20–500 nm from the original position has been observed.     

Anisotropic excitonic molecules in CdS and CdSe

Luminescence lines due to excitonic molecules are observed in CdS and CdSe. The line shape is analyzed by taking account of the broadening due to elastic collision. It is pointed out that the anisotropy of the effective hole masses makes the molecular binding energies much larger than evaluated by using the geometrical means of the hole masses.     

Long rod-like array of bis(imidazolyl)porphyrinatocobalt(III) by successive complementary coordination

Simple bis(imidazolyl)porphyrin cobalt(III) complex was found to form a long polymeric array by complementary coordination of imidazole to cobalt ion. Formation of higher ordered assemblies was also observed.     

Chemical compositional separation of styrene-methyl methacrylate copolymers using high-performance liquid chromatography with liquefied carbon dioxide as eluent

Chromatographic separation of styrene-methyl methacrylate (MMA) copolymers depending on the chemical composition was studied using liquefied carbon dioxide as an adsorption promoting solvent, and tetrahydrofuran, chloroform containing ethanol as a desorption promoting solvent in the mobile phase and the column packed non-bonded silica gel by a solvent gradient method. With the increase of MMA content, the elution was retarded indicating that the typical normal-phase type of adsorption occurred. The effects of type of desorption solvents, molecular mass of sample, and column temperature on the elution were investigated.