Computing global minima to polynomial optimization problems using Gröbner bases

The local optimality conditions to polynomial optimization problems are a set of polynomial equations (plus some inequality conditions). With the recent techniques of Gröbner bases one can find all solutions to such systems, and hence also find global optima. We give a short survey of these methods. We also apply them to a set of problems termed with exact solutions unknown in the problem sets of Hock and Schittkowski. To these problems we give exact solutions.     

Molar heat capacities and volumes of transfer of cytosine,thymine, caffeine and 1,3-diethylthymine to aqueous solutions of glycyl-glycine and L-α-alanyl-L-α-alanine at 25°C

Densities and specific heat capacities of ternary aqueous systems containing dipeptides (glycyl-glycine or L--alanyl-L--alanine) and nucleic acid bases (cytosine or thymine) or their alkyl derivatives (1,3-diethylthymine or caffeine) were determined at 25°C by flow calorimetry and flow densimetry. The partial molar volumes and heat capacities of transfer at infinite dilution of the different nucleic acid bases from water to water+dipeptide solutions were obtained therefrom. Except for the case of the transfer of cytosine to aqueous glycyl-glycine solutions where a small positive dependence of the transfer quantities was observed with the dipeptide concentration, the values of the heat capacities of transfer were in general low, positive or negative, depending on the compensation of hydrophobic-hydrophilic interactions between the dipeptide and the base. The volumes of transfer of most of the bases are very small, within the limit of the experimental error.     

Synthesis of alkylN-(α-amidomethyl)glycinates from glycine esters,aroylamides, and formaldehyde

A one-step synthesis of alkylN-(-amidomethyl)glycinates from glycine esters or their salts, formaldehyde, and aroylamides was developed. The effect of the structure of the amide component and the reaction conditions on the yields of the products was investigated.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1078–1080, June, 1994.     

Analysis of grid file algorithms

Grid file algorithms were suggested in [12] to provide multi-key access to records in a dynamically growing file. We specify here two algorithms and derive the average sizes of the corresponding directories. We provide an asymptotic analysis. The growth of the indexes appears to be non-linear for uniform distributions:O(v ^c ) orO(v ), wherec=1+b^–1, =1+(s-1)/(sb+1),s is the number of attributes being used,v the file size, andb the page capacity of the system. Finally we give corresponding results for biased distributions and compare transient phases.     

Enantioselective catalytic epoxidation of nonfunctionalized prochiral olefins by dissymmetric chiral Schiff base complexes of Mn(III) and Ru(III) metal ions II

A series of new dissymmetric chiral Schiff base complexes has been obtained by a systematic condensation of (1S,2S)(+)-diaminocyclohexane and 3-acetyl-4-hydroxy-6-methyl-2-pyrone with salicylaldehyde, 5-chloro-, 5-methoxy-and 5-nitrosalicylaldehyde and by subsequent metallation with manganese and ruthenium. The characterization of the complexes 1–8 was accomplished by physico chemical studies viz. microanalysis, IR-, UV/VIS-, and CD spectral studies, optical rotation, molar conductance measurements and cyclic voltammetry. Enantioselective epoxidation of non functionalised olefins, viz. cis-stilbene, trans-3-nonene and trans-4-octene with iodosyl benzene as oxidant was demonstrated in the presence of catalytic amounts of chiral Mn(III) and Ru(III) dissymmetric Schiff base complexes. Good optical yields of epoxides were obtained for the catalyst 4 with the substrates trans-3-nonene and cis-stilbene.     

Enantiopure Chiral Macrocyclic Lanthanide Complexes Derived from (R)-2,2′-Diamino-1,1′-binaphthyl and 2,6-Diformylpyridine

The template condensation of (R)-2,2′-diamino-1,1′-binaphthyl and 2,6-diformylpyridine leads to lanthanide(III) complexes of the new chiral hexaaza macrocycle L that adopts highly twisted conformation in [LnL](NO₃)₃ complexes. The complexes have been characterised by ESI MS spectrometry and NMR spectroscopy. The analogous N₂O₄ chiral crown ether L2 that has the same carbon skeleton as L does not exhibit tendency to bind lanthanide(III) ions. The X-ray crystal structure of L2 exhibit squeezed conformation of the macrocycle and spatial disposition of donor atoms that does not predispose it for coordination of lanthanide(III) ions.     

Thermodynamics of formation of nitrogen bases and d-ribose from mineral substances in light of the problem of origination of simplest elements of living matter

The paper represents a further development of our hydrate hypothesis of simplest living matter origination (SLMO) from inorganic and simplest organic mineral substances. It is supposed that the sources of SLMO are simplest aliphatic hydrocarbons, niters, and phosphates. Thermodynamic calculations demonstrating a principal possibility for simultaneous syntheses of different nitrogen bases, d-ribose, and desoxy-d-ribose from these source substances are presented. The most probable principal mechanism of SLMO and the principal conditions necessary for realization of the proposed chemism of SLMO in the framework of the proposed mechanism are considered. A principal means for testing the hypothesis is proposed.     

Two‐ and Three‐Dimensional Molecular Organization of Schiff‐Base Derivatives

We have designed and synthesized a series of Schiff base derivatives, and studied their structural features in two‐dimensional (2D) and three‐dimensional (3D) states by combining scanning tunneling microscopy (STM) and X‐ray diffraction experiments. The Schiff‐base derivatives with short alkyl chains crystallize easily, which allows a detailed structural analysis by X‐ray diffraction. Due to the strong adsorbate–substrate interactions, those bases with long alkyl chains easily form 2D assemblies on highly oriented pyrolytic graphite (HOPG). The STM images indicate also that the introduction of two methoxy groups into the molecule can change the structure of these 2D assemblies as a result of the increased steric hindrances, for example: the Schiff‐base derivative, bearing both methoxy groups and C₁₆H₃₃ tails, forms 2D Moiré patterns, and an alignment of pairing Schiff‐base molecules may be easily resolved. Conversely, the Schiff base derivative, bearing solely C₁₆H₃₃ tails, forms 2D non‐Moiré patterns. It is demonstrated that the 3D structural features result from the compromise of intermolecular interactions of different molecular moieties. However, there is one more factor, which also governs the 2D structure: the adsorbate‐substrate interaction. The 3D crystal structure may thus help to understand many factors involved in the formation of 2D structures, and would be helpful for designing new molecular assemblies with tailoring functions.     

Synthesis and catalytic activity of new chiral unsymmetrical Mn(III)-Schiff-base complexes containing salicylaldehyde and 1-(2-hydroxyphenyl)ketone units

Two new chiral unsymmetrical (non-C₂-symmetric) Schiff-base ligands containing salicylaldehyde and 1-(2-hydroxyphenyl)ketone units were synthesized from (R,R)-1,2-diphenylethylenediamine as the chiral diamine using a stepwise approach. The Mn(III) complexes of the ligands were subsequently used as catalysts in asymmetric epoxidation of unfunctionalized alkenes and the results were compared with those obtained using typical C₂-symmetric Mn(III)–salen complexes. Possible reasons for the differences in reactivity and selectivity between the two types of catalysts are briefly discussed.     

Matrix-isolation FT-IR and DFT theoretical studies of the intramolecular hydrogen bonding in Mannich bases

FT-IR Ar-matrix isolated spectra were studied for dichloro- (Cl₂-MB) and tetrachloroderivatives (Cl₄-MB) of the ortho Mannich base. The spectra were analyzed based on the DFT calculated frequencies and intensities and compared with those recorded in CCl₄ solution in the region of the ν(OH) and ν(OD) vibrations. The matrix-isolated spectra are characterized by narrower ν(OH) and ν(OD) bands with much better resolved fine structure than in solution. The fine structure originates from the anharmonic coupling with the low frequency modes as well as from Fermi resonance. The ν(OD) band shapes can be reproduced exclusively by assuming the Fermi resonance with overtones and summation of the frequencies of modes into which the bridge atoms are involved. The frequency isotopic ratio (ISR) is for both compounds 1.33 while the half-width ratios are equal to 1.82 and 1.94, for Cl₂-MB and Cl₄-MB, respectively.