Simple Constructions of Almost k-wise Independent Random Variables

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity.     

Conservation Laws of K(m, n) and mK(m, n) Equations

Based on the rank analysis method, algorithmization idea, and symbolic computation, in this paper we have presented a method to construct the conservation laws for nonlinear evolution equations. The polynomial conservation laws for K (n 2, n) equations and mnK(m, n) equations are found by using of this approach and some new results have been obtained.     

Temperature Development of Homo- and Hetero-Clustering in Saturated Vapors

Computational findings of temperature increase of clustering degree in saturated vapors are analyzed. A thermodynamic proof is presented and a simple criterion derived. Illustrations are based on saturated steam, magnesium and carbon vapor. The results are applicable to synthesis of fullerenes, metallofullerenes, and heterofullerenes, chemical vapor deposition technique, or atmospheric chemistry.     

Molecular caps for full quantum mechanical computation of peptide-water interaction energy

We present a systematic study of numerical accuracy of various forms of molecular caps that are employed in a recently developed molecular fractionation scheme for full quantum mechanical computation of protein-molecule interaction energy. A previously studied pentapeptide (Gly-Ser-Ala-Asp-Val) or P5 interacting with a water molecule is used as a benchmark system for numerical testing. One-dimensional potential energy curves are generated for a number of peptide-water interaction pathways. Our study shows that various forms of caps all give consistently accurate energies compared to the corresponding full system calculation with only small deviations. We also tested the accuracy of cutting peptide backbone at different positions and comparisons of results are presented.     

Theoretical studies of molecular conformation. Derivation of an additive procedure for the computation of intramolecular interaction energies. Comparison withab initio SCF computations

An additive procedure (SIBFA) is developed for the rapid computation of conformational energy variations in very large molecules. The macromolecule is built out of constitutive molecular fragments and the intramolecular energy is computed as a sum of interaction energies between the fragments. The electrostatic and the polarization components are calculated using multicenter multipole expansions of theab initio SCF electron density of the fragments. The repulsion component is obtained as a sum of bond and lone pair interactions.Tests of the procedure on a series of model compounds containing ether oxygens and pyridine-like nitrogens are reported and compared with the results of correspondingab initio SCF calculations. The resulting methodology is compatible with the simultaneous computation of intermolecular interactions.     

Synthesis of N-（α-Alkoxyalkyl）benzotriazoles Catalyzed by Acidic Ionic Liquid at Room Temperature

N-（α-Alkoxyalkyl）benzotriazoles were synthesized via the condensation of benzotriazole with various aldehydes and alcohols catalyzed by acidic ionic liquid [hmim]HSO4 at room temperature. The yield was up to 99%. This novel method was effective when triethoxymethane was utilized instead of alcohols. Moreover, acidic ionic liquid could be reused easily with no significant degradation of its catalytic activity.     

Complete solutions of a family of quartic Thue and index form equations

Continuing the recent work of the second author, we prove that the diophantine equation

for has exactly 12 solutions except when , when it has 16 solutions. If denotes one of the zeros of , then for we also find all with .

     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

Polarographic study of Tl+, Li+, Na+, K+, and Cs+ complexes with monensin anion in dipolar aprotic solvents

Summary The stability constants,K _sof monensin complexes with Li⁺, Na⁺, K⁺ and Cs⁺ ions were studied by a competitive polarographic method using the Tl⁺/Tl(Hg) redox couple as a sensitive electrochemical probe. TheK _svalues are strongly influenced by the solvents (acetonitrile, propionitrile, acetone, N,N-dimethylformamide, N-methyl pyrolidinone, N,N-dimethylacetamide, dimethylsulfoxide, N,N-diethylformamide and N,N-diethylacetamide were used in experiments) and vary inversely with the Gutmann donicity scale. Molecular mechanics computations revealed the probable structures of the complexes.

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Polarographische Untersuchung von Tl⁺-, Li⁺-, Na⁺- und Cs⁺-Komplexen mit Monesin-Anion in dipolaren aprotischen Lösungsmitteln

Zusammenfassung Es wurden die StabilitätskonstantenK _svon Monesin-Komplexen mit Li⁺-, Ma⁺- und Cs⁺-Ionen mittels einer competitiven polarographischen Methode unter Verwendung der Tl⁺/Tl(Hg)-Redoxelektrode als sensitiver elektrochemischer Sonde bestimmt. DieK _s-Werte werden stark vom Lösungsmittel (Acetonitril, Propionitril, Aceton, N,N-Dimethylformamid, N-Methylpyrrolidinon, N,N-Dimethylacetamid, Dimethylsulfoxid, N,N-Diethylformamid und N,N-Diethylacetamid) beeinflußt, wobei sie invers zurGutmann schen Donizitätsskala variieren. Die wahrscheinliche Struktur der Komplexe wurde mittels molekularmechanischer Berechnungen ermittelt.

     

A Robust and Efficient Method for the Computation of Equilibrium Composition in Gaseous Mixtures

This paper presents in detail a robust, efficient and accurate methodology for the computation of equilibrium composition in gaseous mixtures. The methodology is founded on the concept of the chemical basis, which is defined and formalized using a powerful matricial approach. The method is specially designed to be general, thus providing basic thermodynamic data in several areas, such as combustion, plasma chemistry and, more generally speaking, computational fluid dynamics. The performance of the method is given in terms of CPU usage and the computed results are compared with those in the published literature. The method is shown to yield results of very high quality in terms of accuracy and smoothness.