含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*

在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|²dx) Δu + λV (x)u = μf(x)|u|^q?2u + |u|^p?2u, x ∈ R³,u ∈ H¹(R³),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到.     

光氧化还原碘盐引发阳离子固化的研究

合成了二苯基碘六氟磷酸盐光引发剂。研究了染料的种类和浓度对碘盐引发阳离子光固化速度的影响，用光致电子转移（光氧化还原）理论解释了这些光敏染料的光敏机理。     

Potential reduction method for harmonically convex programming

In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and them constraint functions are allk-harmonically convex in the feasible set, then the number of iterations needed to find an -optimal solution is bounded by a polynomial inm, k, and log(1/). The method requires either the optimal objective value of the problem or an upper bound of the harmonic constantk as a working parameter. Moreover, we discuss the relation between the harmonic convexity condition used in this paper and some other convexity and smoothness conditions used in the literature.The authors like to thank Dr. Hans Nieuwenhuis for carefully reading this paper and the anonymous referees for the worthy suggestions.     

Hydrodynamic thickness and deformational properties of adsorption layers of poly(ethyleneoxides)

From the measurements of surface potentials of quartz capillaries before and after adsorption of poly(ethylene oxides) (PEO) of various molecular mass, an assessment of the equilibrium hydrodynamic thickness of the adsorption layers has been obtained. The results have been compared with those of independent measurements of . The flow of the polymer solution under increasing pressure drops at the ends of a capillary, which causes the corresponding shear stress () on the surface of adsorbed PEO layers, results in the deformation of the latter, which manifests itself in decreasing 5. The values decrease by several times when the shear stress rises to 2×10₂ N m^–2. Such values of have been obtained using thin capillaries (r = 5÷6 mm) and by application of the capillary electrokinetic method with pressure drops up to 5÷6 MPa.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 31–37, January, 1994.     

Virial expansion for a polymer with a realistic pair-potential interaction

No modern theory of polymer excluded volume adequately describes the crossover from poor solvent to good solvent conditions; a fundamental difficulty is a singularity in the binary cluster integral. Mayer expansion techniques are applied to a model with a pair interaction between monomers to clarify the distinction between geometric and solvent contributions to excluded volume. Detailed calculations are undertaken for a hard-core potential and a mimic Lennard-Jones potential. The significance of the singularity in the binary cluster integral for calculations in the crossover regime is discussed.     

Phipps's lagrangian and hamiltonian

In this work it is derived Phipps's Lagrangian function and Phipps's Hamiltonian function. This allows the utilization of Phipps's interaction in the Lagrangian and Hamiltonian frameworks.Dedicated to Thomas E. Phipps, Jr. on the occasion of his 70th birthday (1995).     

Spatial chaotic structure of attractors of reaction-diffusion systems

The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

     

On the electrostatic and steric similarity of lactam compounds and the natural substrate for bacterial cell-wall biosynthesis

Summary Electrostatic and structural properties of a set of -lactam, -lactam and nonlactam compounds have been analyzed and compared with those of a model of the natural substrate d-alanyl-d-alanine for the carboxy- and transpeptidase enzymes. This first comparison of the electrostatic properties has been based on a distributed multipole analysis of high-quality ab initio wave functions of the substrate and potential antibiotics. The electrostatic similarity of the substrate and active compounds is apparent, and contrasts with the electrostatic properties of the noninhibitors. This has been quantified to give a reasonable correlation with the MIC (Minimum Concentration for Inhibition) and with kinetic data (k₂/K) in accordance with the model for interaction of the lactam compounds with dd-peptidase. These correlations provide a better prediction of antibacterial activity than purely structural criteria.     

The role of radicals in metal-assisted oxygenation reactions

The oxo-functionalization of organic substrates with the aid of metal oxo moieties is of fundamental importance not only in nature but also in academic and industrial research. Nevertheless the corresponding reaction mechanisms remain among the most enigmatic in chemistry and few of them are understood in detail. Recent research efforts have resulted in significantly improved information: in the cases of many oxygenation reactions evidence has been provided for the occurrence radical intermediates, even though the high selectivity observed suggests to a different mechanism. Examples stem from various areas of chemistry and include processes involving molecular metal oxo complexes, gas-phase and matrix-isolated species, metalloenzymes, and solid-state oxide surfaces. This review treats this seemingly wide variety of systems with the aim of providing an overview of common reactivity patterns and principles, as well as open problems.