The η-Invariant of Twisted Dirac Operators of S3/Γ

The aim of this paper is to compute the and ~-invariants for the Dirac operator of the quotient of the sphere S ³ by a finite subgroup, twisted by a representation of its fundamental group.     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20     

Optimal Ternary Linear Rate 1/2 Codes

In this paper, we classify all optimal linear[n, n/2] codes up to length 12. We show that thereis a unique optimal [10, 5, 5] code up to equivalence.     

Generalized Variation of Mappings with Applications to Composition Operators and Multifunctions

We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV (I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV (I;X) GV (I;Y) is Lipschitzian if and only if h(t,x)=h₀(t)+h₁(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation.     

Changes in the Solubility of β-Cyclodextrin on Complex Formation: Guest Enforced Solubility of β-Cyclodextrin Inclusion Complexes

The most common native host molecule, -cyclodextrin (cycloheptaamylose) is able toform inclusion complexes with a large variety of guestmolecules (or ions) of different size and shape. Theproperties of the included guest molecule are highlyinfluenced by the host-guest interaction, and thepractical usefulness of -cyclodextrin isdependent on these effects. These changes are mainlyinvestigated from the point of view of the guest andto a lesser extent from that of the host. In spite ofthis, the kind of guests and that of the host-guestinteractions during the formation of the inclusioncomplex seem to influence the properties of thehydrophilic domain of -cyclodextrin (i.e. thatof the supramolecule itself), too, and this effect canbe well demonstrated by the change of solubility ofdifferent -cyclodextrin inclusion complexes.This change can be best correlated with the solubilityof the guest as if the guest enforced its solubilityon the supramolecule.     

Complex Forming Ability of a Family of Isolated Cyclosophoraoses with Ergosterol and Its Monte Carlo Docking Computational Analysis

Neutral cyclosophoraoses (unbranched cyclic -1,2-d-glucans) produced by the Rhizo-bium meliloti 2011 were prepared by size exclusion and anion-exchange chromatographic techniques. The degree of polymerization (DP) of isolated cyclosophoraoses was determined by matrix associated laser desorption/ionization mass spectrometry (MALDI/MS) techniques. A family of purified neutral cyclosophoraoses (DP 17–27) was used as a host for the inclusion complexation with hardly soluble ergosterol. High performance liquid chromatographic (HPLC) analysis showed that it induced much enhanced solubility of ergosterol compared to -cyclodextrin. In order to understand the molecular basis of the complex forming ability of cyclosophoraoses, a Monte Carlo (MC) docking-minimization method was used for host-guest complex formation of cyclosophoraoses or -cyclodextrin with ergosterol. From the MC simulation we propose the `hand-shake' mechanism for complexation of cyclosophoraoses with ergosterol.     

Photobleaching of γ-Glycidoxypropyltrimethoxysilane-Chelated Metal Alkoxide Gel Films

Thick photosensitive inorganic-organic hybrid gel films are fabricated using a silica–PEO(poly(ethylene oxide)) polymeric network and several chelated metal alkoxides: Ti(OEt)₄, Al(OBu^sec)₃, Zr(OPr ⁿ )₄. The -glycidoxypropyltrimethoxysilane (GPTS) and the metal alkoxides stabilized by -ketoester or -diketone are used as precursors. The chelated metal complex in the gel films are photodecomposed and forms the oxide network by UV exposure. The photodecomposition of the chelate ring and the photobleaching of the UV absorption bands are investigated as a function of UV exposure time. The photobleaching rates with respect to chelating agents, metal alkoxides and photon energy are compared.     

Development of New Modifiers for Titanium Alkoxide-Based Sol-Gel Process

The effects of several hydroxyketones such as acetol, actoin, -ketobutanol themselves and their combinations with monoethanolamine (MEA) or ethylenediamine (ED) on the stabilization of titanium tetraisopropoxide (TTIP) in isopropanol solution are examined. Acetoin itself and the imine derivatives of acetol and acetoin were found to show extraordinarily strong stabilizing effect for the alkoxide. The properties including the crystal modifications and refractive index of TiO₂ films that were dip-coated using each stabilized solution are examined and discussed in comparison with those of the films obtained from the diethanolamine (DEA) systems. The effect of UV-light irradiation to the gel films on the crystallization of TiO₂ is also examined and discussed.     

Quasi-P*-Maps,P(τ, α, β)-Maps,Exceptional Family of Elements,and Complementarity Problems

Quasi-P_*-maps and P(, , )-maps defined in this paper are two large classes of nonlinear mappings which are broad enough to include P_*-maps as special cases. It is of interest that the class of quasi-P_*-maps also encompasses quasimonotone maps (in particular, pseudomonotone maps) as special cases. Under a strict feasibility condition, it is shown that the nonlinear complementarity problem has a solution if the function is a nonlinear quasi-P_*-map or P(, , )-map. This result generalizes a classical Karamardian existence theorem and a recent result concerning quasimonotone maps established by Hadjisawas and Schaible, but restricted to complementarity problems. A new existence result under an exceptional regularity condition is also established. Our method is based on the concept of exceptional family of elements for a continuous function, which is a powerful tool for investigating the solvability of complementarity problems.     

Some Congruences on S (X)

Some congruences on S (X) are investigated in this paper. A unique atom in the sublattice [C(E), C (E)] is determined for some spaces X and S-equivalences E and X.AMS Subject Classification (1991): 20M20 54H15