Blossoming stories

We review the main properties of blossoms along with their important repercussions in all aspects of geometric design. Not only are they an elegant and efficient tool to express all classical algorithms, but they are also a fundamental concept, as proven by the fact that their existence is equivalent to the existence of B-spline bases. AMS subject classification 65D17     

Undecidable and decidable restrictions of Hilbert's Tenth Problem: images of polynomials vs. images of exponential functions

Classical results of additive number theory lead to the undecidability of the existence of solutions for diophantine equations in given special sets of integers. Those sets which are images of polynomials are covered by a more general result in the second section. In contrast, restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of Schiff's bases from furylacroleins and aminopyridines in the presence of molecular sieves

We have studied the reactions of (hetero)aromatic aldehydes with 2-aminopyridines. The results obtained suggest that molecular sieves play a role in these processes not only as a dehydrating agent but also as an acid catalyst. We have synthesized a series of novel heterocyclic azomethines.Dedicated to Professor M. A. Yurovskaya on her Jubilee.Latvian Institute of Organic Synthesis, Riga LV-1006 Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 324–335, March, 2000.     

The limitations of nice mutually unbiased bases

Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets.     

A construction of multiscale bases for Petrov–Galerkin methods for integral equations

In this paper, a construction of multiscale bases for Petrov–Galerkin methods for Fredholm integral equations of the second kind is proposed. The properties of multiscale bases are presented including additional order of vanishing moments, compact supports and stability. Communicated by A. Zhou Dedicated to Professor Charles A. Micchelli on the occasion of his sixtieth birthday with friendship and esteem Mathematics subject classifications (2000) 41A10, 65R20, 65D15. Min Huang: Supported in part by Professor Yuesheng Xu's support under the program of “One Hundred Distinguished Young Scientists” of the Chinese Academy of Sciences and by the Graduate Innovation Foundation of the Chinese Academy of Sciences.     

A characterization of L p(ℝ) by local trigonometric bases with 1<p<∞

We show that the local trigonometric bases introduced by Malvar, Coifman and Meyer constitute bases, but not unconditional bases, for L^p(ℝ) with 1<p<∞, p≠2. In addition, we characterize the functions in L^p(ℝ) for 1<p<∞ in terms of their local trigonometric basis coefficients. Dedicated to Dr. Charles A. Micchelli for his 60th birthday Mathematics subject classification (2000) 42C15. Supported by Prof. Y. Xu under his grant in program of “One Hundred Distinguished Chinese Scientists” of the Chinese Academy of Sciences, the National Natural Science Foundation of China (No. 10371122), and the second author is supported by Tianyuan Fund for Mathematics (No. A0324648).     

Metal‐based antibacterial and antifungal amino acid derived Schiff bases: their synthesis,characterization and in vitro biological activity

A new series of antibacterial and antifungal amino acid derived Schiff bases and their cobalt(II), copper(II), nickel(II) and zinc(II) metal complexes have been synthesized and characterized by their elemental analyses, molar conductances, magnetic moments, IR and electronic spectral measurements. The spectral data indicated the Schiff base ligands ( L ₁– L ₅) derived by condensation of salicylaldehyde with glycine, alanine, phenylalanine, methionine and cysteine, to act as tridentate towards divalent metal ions (cobalt, copper, nickel and zinc) via the azomethine‐N, deprotonated carboxyl group of the respective amino acid and deprotonated oxygen atom of salicylaldehyde by a stoichiometric reaction of M: L (1:2) to form complexes of the type K₂[M( L )₂] [where M = Co(II), Cu(II), Ni(II) and Zn(II)]. The magnetic moments and electronic spectral data suggested that all complexes have an octahedral geometry. Elemental analyses and NMR spectral data of the ligands and their Zn (II) complexes agree with their proposed structures. The synthesized ligands, along with their metal complexes, were screened for their in‐vitro antibacterial activity against four Gram‐negative (Escherichia coli, Shigella flexeneri, Pseudomonas aeruginosa and Salmonella typhi) and two Gram ‐ positive (Bacillus subtilis and Staphylococcus aureus) bacterial strains and for in‐vitro antifungal activity against Trichophyton longifusus, Candida albicans, Aspergillus flavus, Microsporum canis, Fusarium solani and Candida glaberata. The results of these studies show the metal complexes to be more antibacterial/antifungal against one or more species as compared with the uncomplexed Schiff base ligands. The brine shrimp bioassay was also carried out to study their in‐vitro cytotoxic properties. Only three compounds ( 2, 11 and 17 ) displayed potent cytotoxic activity as LD₅₀ = 8.196 × 10^?4, 7.315 × 10^?4 and 5.599 × 10^?4 M /ml respectively, against Artemia salina. Copyright © 2007 John Wiley & Sons, Ltd.     

Structural Features of ONS-Donor Salicylidene <Emphasis Type="Italic">Schiff</Emphasis> Base Complexes

Summary. This review article summarizes the structural features of complexes of salicylidene Schiff bases containing, in addition to the phenolic-OH and the azomethine (–RC=N–) groups, a thiole group, and/or a sulfur atom participating in coordination. Structural aspects of metal complexes of salicylidene-2-aminothiophenol, salicylidene-3-aminothiophenol, salicylidenethiosemicarbazone, salicylidenedithiocarbazates, salicylidenedithiocarbazates, salicylideneaminopropyleneaminocyclopentenedithiocarboxylates, salicylideneimidazoles, and salicylidene-thiosalicylidene-1,3-propanediamine are reported.     

Cyclopalladation of Schiff's bases in the ruthenocene series. The possibility of application of the asymmetric version of the reaction to metalloceneimines

p-Tolyliminoalkylruthenocenes—Schiff's bases of the ruthenocene series—react with sodium tetrachloropalladate in the presence of carboxylate anion similarly to their ferrocenyl analogs to give cyclopalladation products. The optical rotation values of the products resulting from carbonylation of palladated ferrocene and ruthenocene aldimines, prepared under conditions of asymmetric catalysis, followed by liberation of the aldehyde group were used to determine the stereochemistry and enantiomeric purity of the cyclopalladation products. Centre Nationale de Recherches Scientifiques, URA 419 4, pl. Jussieu, Bat. F, 75252 Paris, France. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1421–1424, July, 1998.