Every separable metric space is Lipschitz equivalent to a subset ofc 0 +

It is shown that there is a constantK so that, for every separable metric spaceX, there is a mapT:X →c _o satisfyingd(x, y)≦‖Tx−Ty‖≦Kd(x, y) for everyx, y ∈ X. This is a part of the author's Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Professor J. Lindenstrauss.     

Effect of the metal fragment in the thermal cycloaddition between alkynyl metal(0) Fischer carbene complexes and nitrones

The thermal cycloaddition between alkynyl metal(0) Fischer carbenes and nitrones has been studied computationally within the Density Functional Theory framework. It is found that the [3 + 2] cycloaddition takes place via transition structures that are more asynchronous and less aromatic than their nonorganometallic analogues. These reactions are also found to be completely regioselective in favor of the cycloadduct possessing the Fischer carbene moiety and the oxygen atom of the nitrone in a 1,3-relative disposition. These results are consistent with the role of the Fischer carbene moiety as an electron withdrawing group that enhances the electrophilic character of the alkyne group acting as a Michael acceptor as a dipolarophile. In terms of the isolobal analogy model, it can be concluded that alkynylalkoxy metal(0) carbene complexes act in this reaction as organometallic analogues of organic alkyl-propiolates with enhanced electrophilic character.     

Enhanced electro-catalytic degradation of chloroorganic compounds in the presence of ultrasound

The application of finely divided (black) Pd and Pd-Fe powder in the sono-electro-catalytic reduction of chlorophenoxy herbicides (2,4-D) and chlorophenols (2,4-DCP) in aqueous solutions allows for effective destruction of toxic chlorinated aromatic compounds. At 20 degrees C complete conversion of these compounds is observed within 10 min. On bimetallic Pd/Fe catalyst, intermediates due to the oxidation reaction are detected in addition to the products of dechlorination. The bimetallic catalyst appears to be energetically and economically superior to the Pd. In both cases, the reaction times were considerably shortened in comparison with traditional electro-catalytic processes.     

Solid-State Supramolecular Chemistry of Porphyrins. Ligand-Bridged Tetraphenylmetalloporphyrin Dimers

Eight new crystalline materialsbased on ligand-bridged dimers of either Zn(II)- orCo(II)-tetraphenylporphyrins have been prepared andcharacterized by X-ray diffraction analysis. These supramolecular entities have a ``wheel-and-axle' typeshape, the elongated bidentate ligands1,3-diaminopropane, 1,4-diaminobutane, 4,4'-bipyridyl, 1,2-bis(4-pyridyl)ethene or1,2-bis(4-pyridyl)ethane coordinating axially on bothsides to the metal centers of the porphyrin species. They vary from one another by the length of the ligandspacer, the distance between the two porphyrincomponents ranging from 9.4 Å to 14.0 Å. Theintermolecular organization in these structures ischaracterized by a similar chain motif in whichadjacent oligomeric units interlock into one another. In spite of the steric constraint imposed by thebridging ligand, this packing preserves the typicalcorrugated stacked arrangement of the porphyrinframeworks which has been commonly observed inclathrates of monomeric tetraarylporphyrins. It alsoinduces in most cases large voids between theinterlocked motifs, causing enclathration of solventmolecules in the crystal lattice. The experimentallyestablished geometries of these oligomers and theircrystal packing modes provide useful information forfurther crystal engineering efforts of polymericmultiporphyrin domains.     

Bis(μ‐pyrrolidine‐N:N)bis(dibromoboron), [(Br)2B(pyrrolidine)2B(Br)2]

The B atoms in the title compound, C₈H₁₆B₂Br₄N₂, bridge between the two monomeric moieties, forming a (BN)₂ four‐membered ring with partial bond orders of the B—N bonds.     

Crystalline complexes of N,N'-ditritylurea (DTU) and N-tritylurea (NTU) hosts with molecular guests

This paper reports crystalline complexes of the new hosts N,N'-ditritylurea (DTU) and N-tritylurea (NTU) with various uncharged molecular guests. The crystal structures of the following complexes were elucidated by single crystal X-ray diffraction analysis at 115^oK: (I) 1:1 DTU-propanamide — space group C2/c, a=15.839Å, b=9.088Å, c=24.584Å, =111.05^o, Z=4; (II) 1:1 DTU-ethyl N-acetylglycinate — space group P1, a=9.010Å, b=10.800Å, c=19.810 Å, =105.29^o =94.33^o, =93.03^o, Z=2; (III) 2:1 NTU-N, N-dimethylformamide — space group Cc, a=29.614Å, b=8.906Å, c=16.127Å, =121.04^o, Z=4. The three crystal structures are stabilized mainly by a cooperative effect of hydrogen bonding between amide fragments displaced along the shortest axis of each crystal. This interaction occurs between host and guest in complexes I and II, and between host and host in complex III. The latter also represents a cage-type clathrate in which the guest molecules are accommodated in voids between the hydrophobic fragments of four neighboring NTU hosts. On the other hand, complexes of DTU are characterized by a more specific interaction between the two components, each guest molecule being inserted between two adjacent hosts (related by translation) and strongly bound to them via hydrogen bridges. These results illustrate a useful concept in the design of molecular species which can be potential hosts upon crystallization with neutral molecular guests. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82022 (7 pages).     

α‐Amino boronates as cyanoborane complexes: crystal structure and inhibition properties for the serine proteases: α‐chymotrypsin and trypsin

The first examples of α‐amino boronate complexes stabilized by amino cyanoborane complexation were tested as trypsin and chymotrypsin inhibitors, and they showed moderate inhibition. The structure of compound 1 that contains two different boron atoms reveals that the geometry around the boron atom in the cyano group is tetrahedral, whereas a trigonal planar geometry exists around the boron atom attached to two oxygen atoms and a carbon atom. Copyright © 2006 John Wiley & Sons, Ltd.     

On negative eigenvalues of selfadjoint eztensions of band matrices

The method of one-step extension is used here to analyse the number of negative eigenvalues of an extension of a selfadjoint band matrix in terms of the entries in the band matrix and the nature of the extension. Applications art; given to selfadjoint Toeplitz matrices and to the problem of determining the size of the singular values of an extension of a lower-triangular matrix.     

On h-unitary and block-toeplitz h-normal operators

A special class of normal operators acting in spaces with indefinite scalar products is studied. The operators from this class are characterized by the property that, in a natural basis, their matrices have diagonal block-Toeplitz forms. The relations between polynomials of self-adjoint operators and operators from this class are established.     

含内环化A_a－B_b，C_c缩聚反应的溶胶－凝胶分配

结合Ａａ－Ｂｂ，Ｃｃ型缩聚反应，给出了溶胶中含内环化的溶胶－凝胶分配公式及凝胶化条件。