Some models for evaluating the cavity formation energies in liquids

In the mixing process of solutes into solvents, the cavity formation energy is generally introduced into the energy balance. In this study, models for calculating this type of energy are proposed. These models are based on the Hansen's partial solubility parameters δ_d (MPa^1/2) dispersive, δ_p (MPa^1/2) polar and δ_h (MPa^1/2) hydrogen-bonding, and on the internal pressure P_j (J cm^?3) of the solvents.     

On Galois cohomology of semisimple groups over local and global fields of positive characteristic, II

We show that the recent results of Prasad and Rapinchuk (Adv. Math. 207(2), 646–660, 2006) on the existence and uniqueness of certain global forms of semisimple algebraic groups with given local behaviour in the case of number fields still hold in the case of global function fields.     

Hilbert polynomials of non-standard bigraded algebras

This paper investigates Hilbert polynomials of bigraded algebras which are generated by elements of bidegrees $(1,0), (d_1,1),\ldots,(d_r,1)$, where $d_1,\ldots,d_r$ are non-negative integers. The obtained results can be applied to study Rees algebras of homogeneous ideals and their diagonal subalgebras. Mathematics Subject Classification (1991):13D40, 13H15.The authors are partially supported by the National Basic Research Program of\break Vietnam.     

Galois Cohomology of Unipotent Algebraic Groups and Field Extensions

In this note we discuss, in the case of unipotent groups over nonperfect fields k of characteristic p, an analog of a theorem of Steinberg (formely a Serre's conjecture) for unipotent algebraic group schemes, which relates properties of Galois (or flat) cohomology of unipotent group schemes to finite extensions of k of degree divisible by p.     

The negative answer to Kameko's conjecture on the hit problem

The goal of this paper is to give a negative answer to Kameko's conjecture on the hit problem stating that the cardinal of a minimal set of generators for the polynomial algebra Pk, considered as a module over the Steenrod algebra A, is dominated by an explicit quantity depending on the number of the polynomial algebra's variables k. The conjecture was shown by Kameko himself for k?3 in his PhD thesis in the Johns Hopkins University in 1990, and recently proved by us and Kameko for k=4. However, we claim that it turns out to be wrong for any k>4.In order to deny Kameko's conjecture we study a minimal set of generators for A-module Pk in some so-call generic degrees. What we mean by generic degrees is a bit different from that of other authors in the fields such as Crabb-Hubbuck, Nam, Repka-Selick, Wood …We prove an inductive formula for the cardinal of the minimal set of generators in these generic degrees when the number of the variables, k, increases. As an immediate consequence of this inductive formula, we recognize that Kameko's conjecture is no longer true for any k>4.     

The shift of the curie temperature due to spin-phonon interaction

By means of the method of double-time Green's functions with Callen's decoupling scheme an expression for the energy of a spin-phonon interaction system was derived. Using this result a formula for the shift of the Curie temperature due to spin-phonon interaction was obtained.I would like to thank my professor Dr. D. Fraitová for her valuable help.     

Simple prediction of cycloaddition orientation: I—Diels-alder reactions

Application of the “hard and soft” concept to the Woodward-Katz model allows simple and accurate prediction of the structure of the major adduct in Diels-Alder reactions. About 100 examples have been examined. Agreement with experimental results is excellent: therefore, the doubts expressed by Houk et al.³⁶ are groundless.Two special cases deserve mention. First, for compounds with heteroatoms at reactive sites, it is necessary to introduce explicity the overlap integrals in the perturbational treatment. Second, in the reactions between electron-poor dienes and nitrosobenzene derivatives the adjacent lone pairs on N and O play an important role.     

Generalization of a theorem of Gonchar

Let X and Y be two complex manifolds, let D⊂X and G⊂Y be two nonempty open sets, let A (resp. B) be an open subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Under a geometric condition on the boundary sets A and B, we show that every function locally bounded, separately continuous on W, continuous on A×B, and separately holomorphic on (A×G)∪(D×B) “extends” to a function continuous on a “domain of holomorphy” and holomorphic on the interior of .