Nonlinear stability and convergence of finite-difference methods for the “good” Boussinesq equation

Summary The good Boussinesq equationu _tt =–u _xxxx +u _xx +(u ²) _xx has recently been found to possess an interesting soliton-interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the good Boussinesq equation. Numerical experimentas are also reported.     

A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

Finding numerical solution of linear partial differential equations of first order with real coefficients

Applying Bittner's operational calculus we present a method to give approximate solutions of linear partial differential equations of first order

Lattice-point examples for a question of Erdős

Here we establish a set of eight points in general position in the plane, i.e. no three on a line, no four on a circle, and they determine 7 distinct distances, so that, thei-th distance occursi times,i = 1, 2, , 7. The points are embedded in a triangular net, and the distances are not ordered by size or in any other way. We shall show that some known and unknown examples forn < 8 with the above properties may also be lattice points of a similar net.Research (partially) supported by the Hungarian National Foundation for Scientific Research (OTKA) grant, no. 1808.     

晶化温度对中孔分子筛（M41S）结构转变的影响

在低表面活性剂浓度及低表面活性剂与氧化硅比的条件下，研究了十六烷基三甲基溴化铵－硅酸钠体系中晶化温度对中孔分子筛Ｍ４１Ｓ材料结构转变的影响。结果有，晶化温度提高至１３５℃改变了原六方晶相ＭＣＭ－４１的结构，晶化温度提高到１５０℃后，中孔结构六方ＭＣＭ－４１晶格转变为变不稳定的层状相，     

Thermal evolution of ferromagnetic metallic glasses

A traditional TG apparatus was modified by placing two permanent magnets producing a controlled magnetic field (TG(M): Magneto Thermogravimetry). This technique proved to be useful to study both structural relaxation and crystallisation of ferromagnetic metallic glasses. Results obtained for the amorphous alloys Fe₄₀Ni₄₀P₁₄B₆ and Fe_62.5Co₆Ni_7.5Zr₆Nb₂Cu₁B₁₅, are reported in this paper. Structural relaxation can be evaluated by measuring changes in Curie temperature induced by thermal treatments. Crystallisation in TG(M) is detected through a change in the measured apparent mass (difference between the sample mass and magnetic force driving it upward). These results were confirmed by DSC analysis. Whether the obtained crystalline phase is ferromagnetic, it can be identified through its Curie temperature, measured by TG(M). In fact the value of 770°C measured as Curie temperature of crystallised Fe_62.5Co₆Ni_7.5Zr₆Nb₂Cu₁B₁₅led to conclude that the only ferromagnetic crystalline phase is a-Fe. These hypothesis was confirmed by XRD analysis, showing that the first crystallisation yields to a-Fe nanocrystals. This revised version was published online in July 2006 with corrections to the Cover Date.     

用透射积分法研究的穆斯堡尔谱学——一个在聚合二茂铁研究中的应用

本文利用透射积分法，在聚合二茂铁研究中发现，这种方法不但能够得到超精细参数，而且能够得到一般拟合方法得不到的另外两个重要参数—样品的无反冲分数和相应的德拜温度，由此能进一步了解到样品在结合中晶格的质量及化学键的强弱，为穆斯堡尔谱研究提供了一条新的途径。     

固体CD光谱研究及其应用于手性席夫碱M(II)配合物

结合课题组近期的相关研究,对固体CD光谱在手性配合物研究中的应用,特别是手性样品固体CD光谱的测试方法进行了概述,通过对四对手性席夫碱M(II)(M=Ni、Cu)配合物的固体和溶液CD光谱进行比较研究,发现配合物的手性构型在固液相中保持一致,但其固液CD光谱之间存在不同程度的差异,可能是由于相应配合物在固体和溶液相中的四面体扭曲或构象的微妙不同所致.     

Peptides-XXXXVI: Studies in the synthesis of an analogue of hen egg white lysozyme

The previously synthesised (1–37), (38–75), (76–93), (94–104), (105–117) and (118–129) fragments of the analogue were combined making extensive use of the DCCI/HONSu method. The final coupling involved the (1–75) and (76–129) sub-fragments. Aggregation of the latter fragment caused problems in purification by routine gel filtration methods employing Enzacryl K2 or Sephadex LH60. The fully protected (1–129) product was partially purified by washing, then deprotectcd and purified by gel filtration and ion exchange chromatography. Satisfactory removal of the acetamidomethyl group used for cysteine protection could not be achieved.     

A particle method for first-order symmetric systems

Summary We present and study a conservative particle method of approximation of linear hyperbolic and parabolic systems. This method is based on an extensive use of cut-off functions. We prove its convergence inL ² at the order as soon as the cut-off function belongs toW ^m+1.1.Dedicated to Professor Joachim Nitsche on the occasion of his 60th birthday