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.     

Efficient microwave induced direct α-halogenation of carbonyl compounds

A novel and direct method for the synthesis of α-halocarbonyl compounds using sequential treatment of carbonyl compounds with [hydroxy(tosyloxy)iodo]benzene followed by magnesium halides under solvent-free microwave irradiation conditions is described.     

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 .     

Synthesis and Structure of Novel Organocycloborates

A series of α,ω‐boryl(bromo)alkanes of the general formula R₂B? (CH₂)_n? Br (n=3, 4, 5, 6) was obtained in high yield following a standard hydroboration protocol. Upon treatment with Mg turnings and formation of the respective Grignard species, all alkanes with n=4 to 6 underwent an unprecedented boron‐centered cyclisation reaction with formation of boratacyclopentanes, ‐hexanes, and ‐heptanes, respectively. All new compounds were isolated in high yields as colourless, crystalline materials and characterised in solution by multinuclear NMR spectroscopy. Four representative examples were chosen for X‐ray diffraction studies, thus providing the first structurally characterised ring systems of that size at a tetraalkyl borate centre.     

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?     

MgO在Mg-hBN体系中对合成cBN晶体的影响

 以金属镁粉为触媒，以六角氮化硼为原料，其中加入适量比例的氧化镁，在国产六面顶压机上，在约5.0 GPa压力、1 500～1 800 K温度条件下，合成出了颜色均匀、晶形完整的黄色立方氮化硼单晶体。实验结果表明，在Mg-hBN体系中，氧化镁对合成cBN晶体的颜色及合成温度有很大的影响。