A SECOND-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SINGULAR AND DISCONTINUOUS NONLINEARITY

1. Introduction and Main ResultsIn recent years, singular nonlinear two-point boundary value problems have been studied. For details, see, for instance, [1--14] and references therein. However, the periodicboundary problems with singlllar and discontinuous nonlinearity are quite rarely studied.Motivated by [12,14], we study in this paper a periodic boundary value problem with singularand discontinuous nonlinearity of the form{;<;';<2;::<'> =:<u:>::<,.>,, 5 t 5 27, (1 1)where p is a positi…     

A new way to Prepare ts-2 with Silica sol as Silicon Source

The addition of suitable amounts of aqueous ammonia into precursor gel with silica sol as silicon source, TS-2 with small particle size and high titanium content has been successfully synthesized. It displays the same excellent performance in hydroxylation of phenol as the sample prepared with TEOS as silicon source.     

一个超导理论中的反应扩散系统的解析解

A reaction diffusion system arising in the theory of superconductivity is considered and its many kinds of analytic solutions are constructed by the Painlev analysis and similarity reduction methods.     

Inclined circular flat punch on a transversely isotropic piezoelectric half-space

Summary Utilizing the general solution of transversely isotropic piezoelectricity, the paper analyzes the problem of an inclined rigid circular flat punch indenting a transversely isotropic piezoelectric half-space. The potential theory method is employed and generalized to take into account the effect of the electric field in piezoelectric materials. Assuming that the punch is maintained at a constant electric potential, exact expressions for the elastoelectric field are derived in terms of elementary functions. It is noted that the solution corresponding to a flat circular punch centrally loaded by a concentrated force can be obtained as a special case. Received 15 December 1998; accepted for publication 9 March 1999     

Wettability of model fountain solutions: The influence on topo-chemical and -physical properties of offset paper

The surface chemical and physical character of offset paper was studied before and after application of model fountain solutions based on isopropyl alcohol and an alcohol-free surfactant solution. The paper surface features were characterised with atomic force microscopy and the surface energies were determined by contact angle measurements. Changes in the surface chemical properties induced by the fountain solutions were investigated with X-ray photoelectron spectroscopy and time-of-flight secondary ion mass spectroscopy. Coated papers wetted with the surfactant solution revealed a slight increase in the root mean square roughness, but the isopropyl alcohol solution led to no observable changes. The change in sub-micro roughness is ascribed not only to substrate swelling or migration of coating constituents but also to the presence of surfactant on the surface. A change in the surface energy and particularly the polar contribution was observed after application of the surfactant solution. The X-ray photoelectron spectroscopy showed an increase in the oxygen-to-carbon ratio, which confirms the presence of surfactant on the surface. Time-of-flight secondary ion mass spectroscopy showed that the isopropyl alcohol solution did not change the elemental composition of the surface whereas the surfactant solution clearly did so. The distribution of surfactant on the surface was confirmed by mapping the characteristic fragments of the molecule.     

Small divisor problem for an analytic q-difference equation

Similar to the problem of linearization, the “small divisor problem” also arises in the discussion of invertible analytic solutions of a class of q-difference equations. In this paper we give the existence of such solutions under the Brjuno condition and prove that the equation may not have a nontrivial analytic solution when the Brjuno condition is violated. These results are applied to discussing a nonlinear iterative equation.     

DMABN测定含溴化钠或正丁醇水溶液中表面活性剂的临界胶团浓度

以对二甲氨基苯甲腈(DMABN)为探针, 测定它在含NaBr或n-C4H9OH的表面活性剂十二烷基三甲基溴化铵(C12TABr)、季铵盐Gemini表面活性剂C12-3-C12·2Br和十二烷基硫酸钠(SDS)水溶液中的第二重荧光对应的强度(Ia)和特征波长(λa)对表面活性剂浓度(c)曲线. 由Ia-c曲线的转折点或λa-c曲线对应的一阶导数极小点可以获得临界胶团浓度(cmc), 扩展了DMABN探针测定表面活性剂cmc的适用性.     

General Analytic Solutions and Complementary Variational Principles for Large Deformation Nonsmooth Mechanics

This paper presents a nonlinear dual transformation method and general complementary energy principle for solving large deformation theory of elastoplasticity governed by nonsmooth constitutive laws. It is shown that by using this method and principle, the nonconvex and nonsmooth total potential energy is dual to a smooth complementary energy functional, and fully nonlinear equilibrium equations in finite deformation problems can be converted into certain tensor equations. The algebraic relation between the first and the second Piola–Kirchhoff stresses are revealed. A closed form solution for general three-dimensional large deformation boundary value problems is obtained. The properties of this general solution are clarified by a triality extremum principle. This triality theory reveals an important phenomenon in nonconvex variational problems. Applications are illustrated by nonlinear, nonsmooth equilibrium problems in Hencky's plasticity, 3D cylindrical structures and post buckling analysis of elastoplastic bar with jumping and hardening effects. The idea and methods presented in this paper can be used and generalized to solve many nonlinear boundary value problems in finite deformation theory.Sommario. Il lavoro presenta un metodo di trasformazione duale nonlineare ed un principio generale di energia complementare per la soluzione di problemi di teoria elastoplastica in grandi deformazioni governati da leggi costitutive con discontinuità. Si mostra come, usando il metodo ed il principio proposti, l' energia potenziale totale discontinua e nonconvessa duale di un funzionale energia complementare continuo, e le equazioni di equilibrio nonlineare in problemi di deformazione finita, possano essere convertite in equazioni tensoriali. Vengono mostrate le relazioni algebriche fra il primo ed il secondo tensore delle tensioni di Piola–Kirchhoff. Si ottiene una soluzione in forma chiusa per problemi al contorno generali tridimensionali in grandi deformazioni. Le proprietà di tale soluzione generale vengono chiarite per mezzo di un principio estremale di trialità. La eoria della trialità evidenzia un fenomeno importante in problemi variazionali nonconvessi. Vengono presentate applicazioni a problemi di equilibrio nonlineare con discontinuità in situazioni di plasticità alla Hencky, strutture cilindriche in 3D, e nell'analisi postcritica di una barra elastoplastica con effetti hardening e di jumping. L'idea ed i metodi presentati in questo lavoro possono essere usati e generalizzati per risolvere molti problemi al contorno nonlineari nella teoria delle deformazioni finite.     

一个断语的推广及应用

将一个断语进行推广,并借助它介绍一类问题的通用解法.