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.     

Some developments in reaction and solution microcalorimetry,with particular reference to its use in biochemistry and cellular biology

The field of isothermal microcalorimetry as applied to systems of interest for aqueous solution chemistry, biochemistry and in cellular biology is briefly reviewed. Some techniques recently developed in the author's laboratory are described.     

Standard pseudo-Hermitian structure on manifolds and seifert fibration

A strictly pseudoconvex pseudo-Hermitian manifoldM admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function onM. AsM supports a contact form, there exists a characteristic vector field dual to the contact structure. If induces a local one-parameter group ofCR transformations, then a strictly pseudoconvex pseudo-Hermitian manifoldM is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature or of nonpositive curvature . By the definition, standard pseudo-Hermitian manifolds are calledK-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant curvature turn out to be Sasakian space forms. It is well known that a conformally flat manifold contains a class of Riemannian manifolds of constant curvature. A sphericalCR manifold is aCR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a sphericalCR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When 0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a sphericalCR structure.Dedicated to Professor Sasao Seiya for his sixtieth birthday     

CHAOS FOR MIXING TRANSFORMATIONS

ＣＨＡＯＳＦＯＲＭＩＸＩＮＧＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳ￥ＬＩＡＯＧＯＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈａｎｇｃｈｕｎ１３００２３,Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｆｏｒａｃｌａｓｓｏｆｍ...     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.     

Comprehensive DFT and MO studies on glyoxilic acid oxime and related ions in gas phase and solution: Conformations,basicities and acidities

Density functional (BLYP, B3LYP and BHLYP) and highly correlated MP2 and CCSD(T) calculations have been performed to investigate conformers, energy barriers, intramolecular H-bond strength, gas-phase basicity and deprotonation energies of glyoxilic acid oxime (gao) and related ions in gas phase and in aqueous solution (SCRF-PCM method). BHLYP/6-311G(d,p) and B3LYP/6-31++G(d) predictions for the global minimum conformer of gao were consistent with experiment. BLYP level overestimated the H-bond and stabilized incorrectly the H-bonded conformer. The calculations in solution indicated destabilization of H-bonded conformers due to the small polarizability and weaken of the H-bond. The same global minimum structures in gas phase and aqueous solution were found for gao-neutral (ectt) and gao-dianion (e⁻²), whereas they were different for gao-anion because of the strong decrease of the conformational energies in solution. The global minimum structures of the neutral, anion and dianion of gao, obtained in solution, are in agreement with experiment. The gas-phase basicity (GB) and molecular electrostatic potential (MEP) calculations revealed the same sites for electrophilic attack, supported by the nature of HOMO: the carbonylic oxygen for the neutral, the carboxylic oxygen for the anion and the oxime nitrogen for the dianion. MEP results in gas phase and in solution suggested a region between the two atoms, but not on one atom in accordance with bidentate binding of gao ions to a metal. The BHLYP/6-31++G(d,p) molecular properties of gao were in best consistent with CCSD(T) results. The thermodynamical properties (GB and bond deprotonation energy) of gao were better estimated at B3LYP level.     

The convergence of the Rayleigh-Ritz Method in quantum chemistry

Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L ²-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent.     

Problems with the ζ-function method

The -function method for evaluating effective actions is applied to an operator containing a potential localized on two parallel planes. This operator is characterized by a continuous spectrum and broken translation invariance. In this case, the -method leads to a divergent volume factor independent of the physical parameters. In a suitable regularization scheme, only the next to leading order term reproduces a physically interesting result.