NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE

The nonlocal initial problem for nonlinear nonautonomous evolution equati-ons in a Banach space is considered. It is assumed that the nonlinearities havethe local Lipschitz properties. The existence and uniqueness of mild solutionsare proved. Applications to integro-differential equations are discussed.The main tool in the paper is the normalizing mapping (the generalizednorm).     

The Spaces b~p with 0 < p < 1

Let 0 < p < 1. In this paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = Rn-1 × R is the upper half space. As an application, we get the boundedness of harmonic conjugation operators on bp(H).     

Self-assembling Characteristics of Amphiphilic Star Block Copolymers with a Polyelectrolyte Shell

1 Results Amphiphilic block copolymers are capable of forming supramolecular assemblies resembling those observed in nature,such as spherical micelles,worm micelles,and vesicles.Changing the solvent composition,ionic strength or pH of the polymer solution may induce the self-assembly of block copolymers or trigger the transition between the geometries of noncovalent assemblies.In the current work,we have synthesised starlike amphiphilic block copolymers having hydrophobic poly(methyl methacrylate),PMMA,core,and hydrophilic poly(acrylic acid),PAA,shell.The self-assembling characteristics of these polymers have been investigated in aqueous solutions by light scattering and direct visualisation by cryo-transmission electron microscopy (cryoTEM)[1]. Computer simulations along with the theoretical predictions made for the star-like system based on mean-field theory have been used to support the experimental observations[2]. The association of the starlike macromolecules resembles that of charged biopolymers,such as actin,since a balance between attractive and repulsive forces is required for the formation of cylindrical assemblies and can be manipulated by changing the pH or the ionic strength of the solvent[3].     

CRYSTAL STRUCTURE AND MORPHOLOGY OF NASCENT SAMPLES OF SYMMETRIC AROMATIC POLYESTERS——Ⅱ. POLY(p-PHENYLENE 2,6-NAPHTHALATE)

Confined thin film melt polymerization (CTFMP) of naphthalene chloride/hydroquinone (NCMQ, 1/1, molar)mixtures at polymerization temperatures (T_p) below ca. 300℃ resulted in relatively thick, elongated crystals. Polymerizationof NC/HQ above 300℃ between glass yielded well-formed lamellar crystals ca. 100 A thick. Phase Ⅰ and Ⅱ [001] EDpatterns were obtained for all T_p, the relative amount of phase Ⅰ increasing with T_p. Polymerization of naphthalenedicarboxylic acid/hydroquinione diacetate 1/1 mixtures at high T_p also yielded lamellar crystals that "curled up" off of thesubstrate. When the high temperature CTFMP polymerization was conducted between mica, aggregates of lamellae on-edgedeveloped but epitaxial growth did not occur. Epitaxial growth of lamellae between mica could be obtained, however, byconfined thin film solution polymerization, with both of the latter samples yielding apparently related ED patterns from adifferent unit cell than phase Ⅰ or Ⅱ. Fiber patterns, obtained from sheared samples, indicated considerably greater crystaldisorder than in the nascent crystals. Refinement of the phase Ⅰ unit cell parameters, based on the [001] and [01 1] EDpatterns, with modeling based on Cerius~2, suggests a monoclinic phase Ⅰ unit cell with a = 7.76, b = 5.71, c = 14.99 A, α = γ= 90°, β= 99.7°, ρ = 1.47 g/cm~3, space group P12_1/al.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

UNIFORM CONVERGENCE OF CESARO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES

In this paper we prove that iff ∈ C([-π,π]2) and the function f is bounded partial p-variation for some p ∈ [1, ∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α β＜ 1/p,α,β＞ 0) in the sense of Pringsheim. If α β≥ 1/p, then there exists a continuous function f0 of bounded partial double trigonometric Fourier series of fo diverge over cubes.     

纳米尺寸的ZnO晶体高压相变的拉曼散射研究(英文)

Weperformedthehigh-pressureRaman measurementofthethreenanosizedZnOcrystals. Wefoundthesmallerthesize,thehigherthe pressuretoinducethephasetransitionfrom w櫣rzitetorock-saltstructure. High-pressureRamanmeasurementsof nona-shapedZnOcrystalswerepreformed.The…     

ON THE UNIFORM DISSIPATIVITY OF SOME FIFTH-ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

This paper studies the problem of uniformly dissipative solutions of somefifth order non-linear differential equations by the use of frequency domaintechnique. We use the generalized theorem of Yacubovich on dissipativity toobtain some new sufficient conditions of the existence of solutions that aredissipative for (1.1) and (1.2).     

Study on Inhibitors of Methionine Synthase Ⅷ: Synthesis of 2,5-Diamino-4-oxo-6- (3-butenyl) pyrimidine

Cobalamin-dependent methionine synthase plays a crucial role in folate metabolism and such would appear to be an excellent target for rational antifolate drug design. However, to date, no anticancer agents directed at this enzyme are available, but the enzyme is efficiently and specifically inhibited by N2O and this has proven invaluable for evaluating the biochemical consequence of enzyme inhibition and for mechanistic studies. [1,2] 2,5-Diamino-4-oxo-6-(3-butenyl) pyrimidine, a key intermediate in synthetic inhibitors of methionine synthase, was first synthesized using γbutenyl-β-ketoester and guanidine carbonate (Scheme 1). [3]     

A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case.