A Criterion for Finite Topological Determinacy of Map-Germs

Let f, g: (Rⁿ, 0) (R^p, 0) be two C map-germs. Then f and gare C⁰-equivalent if there exist homeomorphism-germs h and lof (Rⁿ, 0) and (R^p, 0) respectively such that g = l f h^–1.Let k be a positive integer. A germ f is k-C⁰-determined ifevery germ g with j^k g(0) = j^k f(0) is C⁰-equivalent to f. Moreover,we say that f is finitely topologically determined if f is k-C⁰-determinedfor some finite k. We prove a theorem giving a sufficient conditionfor a germ to be finitely topologically determined. We explainthis condition below. Let N and P be two C manifolds. Consider the jet bundle J^k(N,P) with fiber J^k(n, p). Let z in J^k(n, p) and let f be suchthat z = j^kf(0). Define Whether (f) < k depends only on z, not on f. We can thereforedefine the set Let W^k(N, P) be the subbundle of J^k(N, P) with fiber W^k(n, p).Mather has constructed a finite Whitney (b)-regular stratificationS^k(n, p) of J^k(n, p) – W^k(n, p) such that all strata aresemialgebraic and K-invariant, having the property that if S^k(N,P) denotes the corresponding stratification of J^k(N, P) –W^k(N, P) and f C(N, P) is a C map such that j^kf is multitransverseto S^k(N, P), j^kf(N) W^k(N, P) = and N is compact (or f is proper),then f is topologically stable. For a map-germ f: (Rⁿ, 0) (R^p, 0), we define a certain ojasiewiczinequality. The inequality implies that there exists a representativef: U R^p such that j^kf(U – 0) W^k (Rⁿ, R^p = and suchthat j^kf is multitransverse to S^k (Rⁿ, R^p) at any finite setof points S U – 0. Moreover, the inequality controlsthe rate j^kf becomes non-transverse as we approach 0. We showthat if f satisfies this inequality, then f is finitely topologicallydetermined. 1991 Mathematics Subject Classification: 58C27.     

Generation of a polyclonal Fab phage display library to the protozoan parasite Cryptosporidium parvum

We had developed a technology for creation of recombinant polyclonal antibody libraries, standardized perpetual mixtures of polyclonal whole antibodies for which the genes are available and can be altered as desired. We report here the first phase of generating a polyclonal antibody library to Cryptosporidium parvum, a protozoan parasite that causes severe disease in AIDS patients, for which there is no effective treatment. BALB/c mice, immunized by neonatal oral infection with oocysts followed by intraperitoneal immunization with a sporozoite/oocyst preparation of C. parvum, were used for construction of a Fab phage display library in a specially-designed bidirectional vector. This library was selected for reactivity to an oocyst/sporozoite preparation, and was shown to be antigen-specific and diverse. Following mass transfer of the selected variable region gene pairs to appropriate mammalian expression vectors, such anti-C. parvum Fab phage display libraries could be used to develop chimeric polyclonal antibody libraries, with mouse variable regions and human constant regions, for passive immunotherapy of C. parvum infection.     

Preparation and characterization of MgB2 superconductor

The MgB₂ superconductor, synthesized using solid-state and liquid-phase sintering methods, have been characterized for various properties. The upper critical field, irreversibility line and critical current density have been determined using magnetization data. The current-voltage characteristics recorded under an applied magnetic field revealed the existence of vortex glass transition. The surface analysis using X-ray photoelectron spectroscopy shows that MgB₂ is sensitive to atmospheric degradation.     

Recombinant polyclonal antibody libraries

We describe a technology for generating recombinant polyclonal antibody libraries (PCALs) that enables the creation and perpetuation of standardized mixtures of polyclonal whole antibodies specific for a multiantigen (or polyantigen). Therefore, this technology combines the advantages of targeting multiple antigenic determinants -- high avidity, low likelihood of antigen 'escape variants', and efficient mediation of effector functions, with the advantages of using monoclonal antibodies -- unlimited supply of standardized reagents and the availability of the genetic material for desired manipulations. The technology for generating recombinant polyclonal antibody libraries begins with the creation of phage display Fab (antibody) libraries. This is followed by selection of sublibraries with desired antigen specificities, and mass transfer of the variable region gene pairs of the selected sublibraries to a mammalian expression vector for generation of libraries of polyclonal whole antibodies. We review here our experiments for selection of phage display antibody libraries against microbes and tumor cells, as well as the recent literature on the selection of phage display antibody libraries to multiantigen targets.