Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Photografting of vinyl polymers onto ultrafine inorganic particles: Photopolymerization of vinyl monomers initiated by AZO groups introduced onto these surfaces

The photografting of polymers onto ultrafine inorganic particles, such as silica and titanium oxide, initiated by azo groups introduced onto these surfaces was investigated. The introduction of azo groups onto the particles was achieved by the reaction of 4,4′-azobis(4-cyanopentanoic acid) with surface isocyanate groups, which were introduced by the treatment with tolylene 2,4-diisocyanate. It was found that the photopolymerization of vinyl monomers, such as methyl methacrylate (MMA), styrene, and N-vinylcarbazole, is initiated by ultrafine particles having azo groups. The corresponding polymers were effectively grafted onto these surfaces through the propagation of the polymer from the surface radicals formed by the photodecomposition of the azo groups: e.g., the percentage of grafting of PMMA and polystyrene onto silica was reached to 112 and 176%, respectively. The percentage of grafting onto silica in the graft polymerization initiated by photodecomposition of surface azo groups was much larger than that initiated by thermal decomposition. Polymer-grafted ultrafine particles thus obtained gave a stable colloidal dispersion in good solvents for the grafted chain. © 1994 John Wiley & Sons, Inc.     

The effect of side substituents on rotation hindrance in polyheteroarylenes

Hindered rotation was considered in calculations of the conformational parameters of a series of polyheteroarylenes with bulky side substituents by the Monte-Carlo method. Within the range of experimental errors, the results of calculations for several polyarylates coincide with the values of conformational rigidity, determined from hydrodynamic experimental data. The proposed procedure was used to estimate the rigidities of a number of polymers with bulky side substuents for which experimental determination is difficult. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1287–1296, July, 1998.     

Oxobenzo[f]benzopyrans as new fluorescent photolabile protecting groups for the carboxylic function

The properties of three oxobenzo[f]benzopyrans as new fluorogenic photolabile protecting groups for the carboxylic function of amino acids were studied. Fluorescent amino acid conjugates were efficiently prepared and characterised. Photodeprotection of these compounds was carried out by irradiation at 300, 350 and 419 nm, the most suitable wavelength being 350 nm, on account of short irradiation times and good deprotection yields.     

Synthesis and characterization of surface-cyanofunctionalized poly (N-isopropylacrylamide) latexes

 A series of P[N-isopropylacrylamide (NIPAM)] latexes with different contents of cyano groups were successfully prepared by either seeded or shot-growth polymerizations of an aqueous solution containing acrylonitrile (AN) onto a seed P[NIPAM] latex, respectively, and further characterized by FT-IR, ¹H-NMR, elemental analysis, as well as by quasielastic light scattering (QELS) and scanning electron microscopy (SEM). All prepared surface-cyanofunctionalized P[NIPAM] latexes exhibited the same range of lower critical solution temperature (LCST) as a pure P[NIPAM] latex. The shot polymerization process proved more efficient at yielding cyano derivatized latexes than the seeded polymerization technique. The amount of incorporated cyano groups onto the particles was determined with a good correlation both by ¹H-NMR and elemental analysis. The higher the amount of initially introduced AN monomer in the reaction mixture, the more cyano groups were incorporated onto the particles. The surface of the particles with high content of cyano groups appeared quite rough by SEM in comparison with that of the pure P[NIPAM] particles. Received: 25 February 1998 Accepted: 23 June 1998     

The free loop space and the algebraic k-theory of spaces

Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let . Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces.     

A generalized sandwich theorem

It is proved for an arbitrary commutative ring A with identity and any integer n3 that if H is a subgroup of GL_n(A) normalized by E _n(A,q), then there is an ideal of A such that E _n(A,) H GL _n (A, (:q⁴⁰).Furthermore, is uniquely determined up to a certain equivalence relation on the set of ideals of A. The result extends a theorem of Bak, by removing a stability condition he uses on A.