Constrained minima of nonlocal free energy functionals

We consider variational problems involving nonlocal free energy functionals that arise from Gibbs measures with Kac potentials and are related to the characterization of the optimal (i.e., typical) shape of an interface under given constraints on the magnetization profile.     

一个新的单调类定理

定义了集类的ｗ类的概念,给出了ｗ类的单调类定理．     

Enantioselective synthesis of hydroxy-substituted α-methyl-α-amino acids using Al and Mn derivatives of cyclo-(L-Ala-L-AIa) bis-Iactim ethers

Aluminum and manganese derivatives of lithiated bis-lactim ethers of cyclo-(L-Ala-L-Ala) were used for the enantioselective synthesis of w2x3j22hh/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-hydroxy and polyhydroxy w2x3j22hh/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-amino acids of the 2-methyIserine series. A new variant of the synthesis of these acids via 3-acyl-2, 5-dialkoxy-3, 6-dimethyl-3, 6-dihydropyrazines is proposed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 590–595, March, 1993.     

Primal-dual interior point approach for computingl 1-solutions andl ∞-solutions of overdetermined linear systems

This paper concerns solving an overdetermined linear systemA ^T x=b in the leastl ₁-norm orl _{w6217143228kv283/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">}-norm sense, whereAw6217143228kv283/xxlarge8712.gif" alt="isin" align="MIDDLE" BORDER="0">w6217143228kv283/xxlarge8477.gif" alt="Ropf" align="BASELINE" BORDER="0"> ^m×n ,m<n. We show that the primal-dual interior point approach for linear programming can be applied, in an effective manner, to linear programming versions of thel ₁ andl _{w6217143228kv283/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0">}-problems. The resulting algorithms are simple to implement and can attain quadratic or superlinear convergence rate. At each iteration, the algorithms must solve a linear system with anm×m positive-definite coefficient matrix of the formADA ^T , whereD is a positive diagonal matrix. The preliminary numerical results indicate that the proposed algorithms offer considerable promise.This research was supported in part by Grants NSF DMS-91-02761 and DOE DE-FG05-91-ER25100.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the w6795/xxlarge603.gif" alt="epsiv" align="BASELINE" BORDER="0">=d–2 expansion, the w6795/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">=4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

Spin density distributions in radical anions of heterocyclic amine N-oxides

The unrestricted Hartree-Fock (UHF) method of Snyder and Amos is used to calculate, in the w1625gn8w5g2064q/xxlarge960.gif" alt="pgr" align="BASELINE" BORDER="0">-electron approximation, the spin density distributions in radical anions of heterocyclic amine N-oxides. The computed spin densities are observed to be in good agreement with the experimental values. The computed spin density distribution of the radical anion of pyridine N-oxide is consistent with the greater susceptibility of pyridine N-oxide relative to pyridine to electrophilic nitration. Also, the calculations are consistent with the lower basicity of the N-oxides relative to the parent bases.     

Synthese und Geruch von Tricyclo[6.2.2.02, 7]dodecan-Derivaten

Summary The acetale-ketone9 was synthesized as precursor for the preparation of w137/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-santalol derivatives posessing a bicyclo[2.2.2]octane nucleus. After methylenation of the keto-group the subsequent acidic hydrolysis of the acetal leads via a Prins reaction of the liberated aldehyde with the methylene group to tricyclo[6.2.2.0^{2, 7}]dodecane derivatives. Their olfactory properties are described.

     

Spin-transition behaviour of transition metal complexes with 2,6-bis-(benzimidazol-2′-yl)-pyridine induced by deprotonation of the complex

Summary 2,6-bis-(Benzimidazol-2w1gu2xg187vrh330/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-yl)-pyridine (bzimpy = H₂ L) acts as a bidentate ligand when combining with transition metal ions. The complexes [M(bzimpy)₂](ClO₄)₂ (M = Fe²⁺, Mn²⁺, Zn²⁺, Co²⁺, and Ni²⁺) were obtained as solids. The protonation constants (logK) for the ligand and the complexes were evaluated in 30:70 (v/v) H₂O:EtOH at 293 K and at constant ionic strength of 0.12M KCl. Coordination of the ligand to the metal ions leads to an increase of acidity of the imino-hydrogen of the benzimidazole group of the ligand as a function of the complex stability. Deprotonation leads to a spin-state transition (intermediate spin-state w1gu2xg187vrh330/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> low-spin) of the iron(II)-complex, followed by a shift of the metal-to-ligandcharge transfer band (MLCT) to lower energies (w1gu2xg187vrh330/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0">_max=563 to 580 nm). The d-d absorption bands are found to shift to higher energies and the low-spin isomer is favoured at room temperature. An opposite shift of theMLCT band (w1gu2xg187vrh330/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0">_max=563 to 557 nm) is observed when HClO₄ is added to the complex solution, rendering the high-spin state of the complex more favourable.On leave from the Chemistry Department, Jahangirnagar University, Dhaka, Bangladesh     

Die Berechnung von Einelektronen-Integralen in der SCF-Xα-SW-Methode: I. Die Normierung

A normalization of the wave functions by means of the theoretical exact Multiple-Scattering-(MS)-formalism is discussed within the framework of the SCF-X_{w7t2458r0417822n/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">}-SW-method. For the atomic and extramolecular regions the integrals of normalization can be easily determined and the results can be described by the corresponding electronic charges. The calculation of the integral of the interatomic region is problematic. The needful volume integration is only necessary to theGreen's functions of the wave functions and can be solved by means of the residual theory. The further analytical calculation of the surface integrals leads to a complicated formalism which can be numerically evaluated.

     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for w447641987403344/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">iterative evaluationw447641987403344/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.