Irregular Behavior of Solutions for Fisher’s Equation

This paper is concerned with the irregular behavior of solutions for Fisher’s equation when initial data do not decay in a regular way at the spatial infinity. In the one-dimensional case, we show the existence of a solution whose profile and average speed are not convergent. In the higher-dimensional case, we show the existence of expanding fronts with arbitrarily prescribed profiles. We also show the existence of irregularly expanding fronts whose profile varies in time. Proofs are based on some estimate of the difference of two distinct solutions and a comparison technique. Dedicated to Professor Pavol Brunovsky on his 70th birthday.     

A MORPHOLOGICAL STUDY OF POLY（DIVINYLBENZENE-co-ACRYLIC ACID） IN CROSSLINKING PRECIPITATION POLYMERIZATION

Divinylbenzene-80 （DVB-80） and polar monomer acrylic acid （AA） having hydrogen bonding at a total monomer loading of 5 vol% were precipitated-copolymerized in a variety of organic solvents with 2,2＇-azobis（isobutyronitrile） （AIBN） as initiator. The experiments were investigated from a two-dimensional matrix, i.e., the actual crosslinking degree of DVB varying from 0 to 80% and the solvent composition varying from 0 to 100% of toluene mixture with acetonitrile, when the mixture of acetonitrile and toluene was used as the reaction solvent. Under various reaction conditions, six distinct morphologies including soluble polymers, swellable microgels, coagulum, irregular microparticles, and nano-/micrometer microspheres were formed and the structures of these polymer architectures were described. A morphological map was utilized to discuss the effects of both crosslinking degree of DVB and composition of solvent on the transitions between morphology domains. The results demonstrated that the microspheres are formed by an internal contraction due to the marginal solvency of the continuous phase and the crosslinking of the polymer network through the covalent bonding from DVB as well as the interchain hydrogen-bonding between the carboxylic acid units.     

New Ni(II)Cu(II)Ni(II) trinuclear complexes with an 5=3/2 high-spin ground

Four new heterotrinuclear complexes have been synthesized and characterized, namely {[Ni(L)₂]₂[Cu(opba)]}(ClO₄)₂, where opba denotes o-phenylenebis(oxamato) and L stands for 1,10-phenanthroline(phen) (1), 5-nitro-l,10-phenanthroline(NO₂-phen) (2), 2,2′-bipyridyl(bpy) (S) and 4,4′-dimethyl-2,2′-bipyridyl(Me₂bpy) (4). The temperature dependence of the magnetic susceptibility of {[Ni(phen)₂]₂[Cu(opba)]}(ClO₄)₂3H₂O has been studied in the 4–300 K range, giving the exchange integral J—109 cm^?1. The HMT vs. T plot exhibits a minimum at about 100 K, characteristic of this kind of coupled polymetallic complex with an irregular spin-state structure.     

Studies on the Particle Morphology of Waterborne Cationic Polyurethane/Polyacrylate Microemulsions

Polyurethane containing tertiary nitrogen atoms was synthesized from polyol, diphenylmethane diisoccyanate (MDI) and N‐methyl diethanolamine. The polymer was converted into cationomers by quarternizing with methacrylic acid (MAA) and then dispersed in water. In this reaction, methyl methacrylate (MMA) was used to decrease viscosity; at the same time, it was the monomer in the later reaction. Finally the cationic polyurethane dispersions were further polymerized with an oil‐soluble initiator, azobisisobutyronitrile (AIBN), water‐soluble initiator, K₂S₂O₈ (KPS) and the mixture of AIBN and KPS. The different emulsion particles with shell‐core structure, “invert” shell‐core structure and “irregular” sandwich structure were obtained; the morphological structures were characterized by TEM observation, FT‐IR and particle size analysis.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

热传导方程的一类无网格方法

构造求解热传导方程的一类无网格方法,只要选择好每个节点的适当的邻点集合,便可利用节点信息顺利进行计算.作为特殊情形,也可在各种结构或非结构网格上进行计算.在矩形或均匀平行四边形网格上进行计算时具有二阶精度,当在任意的不规则四边形或三角形网格上计算时仍然是守恒的和相容的,且至少具有一阶精度.作为数值试验,将该方法用于在不规则四边形网格上及四边形与三角形混合网格上求解二维非线性抛物型方程,并在不规则四边形网格上求解二维三温辐射热传导方程,均获得了较为理想的数值结果.     

Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type

In many applications one seeks to recover an entire function of exponential type from its non-uniformly spaced samples. Whereas the mathematical theory usually addresses the question of when such a function in can be recovered, numerical methods operate with a finite-dimensional model. The numerical reconstruction or approximation of the original function amounts to the solution of a large linear system. We show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite-dimensional reconstruction problem. This legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results. The main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values. From another point of view our approach provides a new method for proving sampling theorems.

     

Algorithms for nonlinear piecewise polynomial approximation: Theoretical aspects

In this article algorithms are developed for nonlinear -term Courant element approximation of functions in ( ) on bounded polygonal domains in . Redundant collections of Courant elements, which are generated by multilevel nested triangulations allowing arbitrarily sharp angles, are investigated. Scalable algorithms are derived for nonlinear approximation which both capture the rate of the best approximation and provide the basis for numerical implementation. Simple thresholding criteria enable approximation of a target function to optimally high asymptotic rates which are determined and automatically achieved by the inherent smoothness of . The algorithms provide direct approximation estimates and permit utilization of the general Jackson-Bernstein machinery to characterize -term Courant element approximation in terms of a scale of smoothness spaces (-spaces) which govern the approximation rates.

     

The derivation of explicit solutions to Wannier–Stark resonances for electrons on coupled chains

Electrons on infinite coupled chains with nearest neighbour couplings under uniform electric and magnetic fields can be expressed as conditionally solvable systems, which concerns both discrete coordinate and wavenumber representations. We then have to account for multiparameter extra-conditions relying on the single chain phase of the system, which amounts to perform a suitable selection of parameters. The implicit plots provided by such conditions exhibit both regular and irregular patterns. This results in the onset of a finite number of Wannier–Stark resonances, now by performing rescalings needed. However, this time the resonance width is sensitive to the quantum number characterizing the Stark-ladder. Bound-state limits, rescalings and approximations proceeding irrespective of the wavenumber have also been presented.     

MgO缺陷和不规则表面吸附Cl2的电子结构研究

采用从头算程序对MgO表面 3种不同配位位置吸附Cl2 的构型进行优化 ,并用扩展休克尔紧束缚 (EHT)晶体轨道方法对MgO的缺陷和不规则表面吸附Cl2的可能构型进行能带计算 ,讨论了吸附前后能带组成和成键性质的变化。研究表明 :MgO表面吸附Cl2 将更趋向于吸附在O原子上而非Mg原子上 ,而且在 3种配位中MgO表面三配位氧最有利于吸附Cl2 ;吸附时 ,电子从O原子转移到Cl2 分子的反键轨道 ,但是各种吸附构型的MgO表面对Cl2 的吸附作用均比较微弱 ,是典型的物理吸附。