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     

Differential form methods in the theory of variational systems and Lagrangian field theories

This paper will attempt to unify diverse material from physics and engineering in terms of differential forms on manifolds. A variational system will be defined by means of a scalar-valued differential form on a manifold and an ideal in the Grassmann algebra of differential forms on that manifold to serve as constraints. Two types of extremal submanifolds will be defined. The first-called the Euler-Lagrange extremals-will be defined by a method that is the generalization of the classical methods in the calculus of variations. The second—a generalization of a method used by Cartan in his treatise Leçons sur les invariants intégraux-will define extremals as integral submanifolds of an exterior differential system invariently attached to the variational system. As examples, the variational systems attached to string theories in Riemannian manifolds and Yang-Mills fields will be discussed from this differential form point of view. Finally, as application, the differential geometric properties and definition of energy will be presented from the differential form point of view.This work was supported by a grant from the Applied Mathematics program of the National Science Foundation.     

Dual vectors and lower bounds for the nearest lattice point problem

We prove that given a point outside a given latticeL then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanesH _i, such thatL _iH_i andd( _iH_i)(6n ²+1)^–1 d( ,L).Supported by an IBM fellowship.     

ZnO超微粒子光催化氧化降解n-C7H16的研究

利用ZnO光催化氧化技术对气相n-C7H16进行了降解研究，考察了氧气、水燕气体积分数等因素对n-C7H16光催化氧化的影响，利用气相色谱－质谱联用仪和气相色谱仪对气相光催化反应过程中的气体组成进行了定性分析，并对主要中间产物丙醛进行了定量分析，结果发现，ZnO超微粒子光催化氧化n-C7H16的降解率较高，n-C7H16绝大部分被完全氧化成CO2，探讨了n-C7H16光催化氧化反尖的动力学行为及机理。     

On copowers of an ordered skew field

It is shown that the double of an ordered skew fieldE over a subfieldK, which is its own bicentralizer, can again be ordered, and a corresponding result for groups is deduced.     

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.     

The Study of Anti-tumor Activity of Trichosanthin by Cyclic Voltammogram

IthasbeenreportedthatTrichosanthi11(TCS),isolatedfromrkiI-ilolt)ii,hasanti-tumorI-4andanti-vira1activities5-'.Someanti-tun1orremedies,whicharedesignedfromTCS,arebeingtestedanddeveloped'-.'.StudyingthebioIogicalphenomenonbyelectrochemicalmethodsisanewhotresearchspotemerginginrecentyears".Manyresultsshowedthatnotonlytheenzymesystemsuchassuccinatedehydrogenasedisplayedthediode-likebehaviorduringtheelectrontransferprocess",butalsothehigh1yorganizedorganeIle,forexample,mitochondria,andevenintac…