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.     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Meromorphic singular foliations on complex projective surfaces

Here we show that many numerical computations and bounds on the degrees of the algebraic leaves for singular meromorphic foliations on ² may be extended to large classes of foliations and complex projective surfaces.The author was partially supported by MURST and GNSAGA of CNR (Italy)     

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.