NEW WAVELET BASES FOR NON－HOMOGENEOUS SYMBOLIC SPACE OpS1,1^m AND RELATED KERNEL－DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.     

Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

A constructive characterization of the split closure of a mixed integer linear program

Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel.     

Chemical reactivity of hypervalent silicon compounds: The local hard and soft acids and bases principle viewpoint

The silicon atom may increase its coordination number to values greater than four, to form pentacoordinated compounds. It has been observed experimentally that, in general, pentacoordinated compounds show greater reactivity than tetracoordinated compounds. In this work, density functional theory is used to calculate the global softness and the condensed softness of the silicon atom for SiH _n F_4−n and SiH _n F _5−n ¹⁻ . The values obtained show that the global and condensed softness are greater in the pentacoordinated compounds than in the tetracoordinated compounds, a result that explains the enhanced reactivity. If the results are analysed through a local version of the hard and soft acids and bases principle, it is possible to suggest that in nucleophilic substitution reactions, soft nucleophiles preferably react with SiH _n F _5−n ¹⁻ , and hard nucleophiles with SiH _n F_4−n .     

Catalytic Hydrosilylation of Furan, Thiophene, and Pyridine Aldimines

The addition of hydrosilanes (HSiEt₃, HSiMe₂Ph, H₂SiPh₂) to the CH=N bond of heterocyclic azomethines has been studied in the presence of monovalent complexes of rhodium and palladium. The effect on the reaction of the CF₃ group of the aldimines, which were obtained from O-, S-, and N-heteroaromatic aldehydes and 2-trifluoromethylaniline, has been clarified, as were other regularities of the processes being studied. A series of corresponding furans, thiophenes, and pyridine amines has been synthesized.     

Pseudoaffinity, de Boor algorithm, and blossoms

In order to ensure existence of a de Boor algorithm (hence of a B-spline basis) in a given spline space with (n+1)-dimensional sections, it is important to be able to generate each spline by restriction to the diagonal of a symmetric function of n variables supposed to be pseudoaffine w.r. to each variable. We proved that a way to obtain these three properties (symmetry, n-pseudoaffinity, diagonal property) is to suppose the existence of blossoms on the set of admissible n-tuples, given that blossoms are defined in a geometric way by means of intersections of osculating flats. In the present paper, we examine the converse: do symmetry, n-pseudoaffinity, and diagonal property imply existence of blossoms?     

On the local structure of doubly laced crystals

Let g be a Lie algebra all of whose regular subalgebras of rank 2 are type A₁×A₁, A₂, or C₂, and let B be a crystal graph corresponding to a representation of g. We explicitly describe the local structure of B, confirming a conjecture of Stembridge.     

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between "punctured" Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.     

The world according to Rényi: thermodynamics of multifractal systems

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs-Shannon entropy into more general framework—Rényi’s information entropy. We address the renormalization issue for Rényi’s entropy on (multi)fractal sets and consequently show how Rényi’s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Rényi’s information entropy and thermodynamics of multifractals. Important issues such as Rényi’s entropy versus Tsallis-Havrda-Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed.