Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

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.     

Stability properties of collocation methods

Lower bounds for are given for which equidistant s-point collocation methods areA()-stable for arbitrarys.     

Adaptive boundary element methods for strongly elliptic integral equations

Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.This work was carried out while Dr. De-hao Yu was an Alexander-von-Humboldt-Stiftung research fellow at the University of Stuttgart in 1987, 1988     

On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

四（对羟基苯基）卟啉—硅胶固定相的合成及在核苷酸分析中的应用

以大孔微硅胶作基体，经γ－氨丙基三乙氧基硅烷活化与间隔臂氯代环内烷反应后，再与预先合成的四（对羟基苯基）卟啉配体键合，构成电荷转移型亲和色谱固定相。以ＰＨ＝７．０的磷酸盐缓冲溶液作流动相，成功实现对一些核苷酸的高效液相亲和色谱分离。     

反相高效液相色谱法半制备分离[T(4-MOP)PS4]卟啉的研究

本文研究了新水溶性５，１０，１５，２０－四（４－甲氧基－３－磺酸苯基）卟啉［Ｔ（４－ＭＯＰ）ＰＳ４］的反相高效液相色谱（ＨＰＬＣ）分离条件。采用ＳｈｉｍｐａｃｋＰＲＥＰ－ＯＤＳ半制备色谱柱，用含有１０ｍｍｏｌ／Ｌ四乙基碘化铵的乙腈－水（体积比２５：７５）为流动相，流速１８ｍＬ／ｍｉｎ，于４１８ｎｍ波长下检测。［Ｔ（４－ＭＯＰ）ＰＳ４］与合成中生成的杂质组分完全分离。经此制备的卟啉纯度高，已成功地应用于自来水样中微量钴、锌、铜离子的ＨＰＬＣ测定中。