Highly efficient chiral copper Schiff-base catalyst for asymmetric cyclopropanation of 2,5-dimethyl-2,4-hexadiene

A remarkable increase in catalytic activity is found for the asymmetric cyclopropanation of 2,5-dimethyl-2,4-hexadiene with diazoacetate by use of the chiral copper Schiff-base complexes, which are derived from substituted salicylaldehydes, chiral aminoalcohols, and copper acetate monohydrate. Furthermore, a combination of a chiral copper Schiff-base with a Lewis acid showed an increase in yield (up to 90%) and in enantioselectivity (up to 90% ee) for the asymmetric cyclopropanation of the diene with t-butyl diazoacetate at 20 °C.     

Expanders obtained from affine transformations

A bipartite graphG=(U, V, E) is an (n, k, δ, α) expander if |U|=|V|=n, |E|≦kn, and for anyX⊆U with |X|≦αn, |Γ _G (X)|≧(1+δ(1−|X|/n)) |X|, whereΓ _G (X) is the set of nodes inV connected to nodes inX with edges inE. We show, using relatively elementary analysis in linear algebra, that the problem of estimating the coefficientδ of a bipartite graph is reduced to that of estimating the second largest eigenvalue of a matrix related to the graph. In particular, we consider the case where the bipartite graphs are defined from affine transformations, and obtain some general results on estimating the eigenvalues of the matrix by using the discrete Fourier transform. These results are then used to estimate the expanding coefficients of bipartite graphs obtained from two-dimensional affine transformations and those obtained from one-dimensional ones.     

The performance evaluation of a multi-stage JIT production system with stochastic demand and production capacities

This paper discusses a single-item, multi-stage, serial Just-in-Time (JIT) production system with stochastic demand and production capacities. The JIT production system is modeled as a discrete-time, M/G/1-type Markov chain. A necessary and sufficient condition, or a stability condition, under which the system has a steady-state distribution is derived. A performance evaluation algorithm is then developed using the matrix analytic methods. In numerical examples, the optimal numbers of kanbans are determined by the proposed algorithm. The optimal numbers of kanbans are robust for the variations in production capacity distribution and demand distribution.     

Projective varieties admitting an embedding with Gauss map of rank zero

We introduce an intrinsic property for a projective variety as follows: there exists an embedding into some projective space such that the Gauss map is of rank zero, which we call (GMRZ) for short. It turns out that (GMRZ) imposes strong restrictions on rational curves on projective varieties: In fact, using (GMRZ), we show that, contrary to the characteristic zero case, the existence of free rational curves does not imply that of minimal free rational curves in positive characteristic case. We also focus attention on Segre varieties, Grassmann varieties, and hypersurfaces of low degree. In particular, we give a characterisation of Fermat cubic hypersurfaces in terms of (GMRZ), and show that a general hypersurface of low degree does not satisfy (GMRZ).     

Magnetic properties of disordered oxides with iron and manganese ions

Magnetic properties of disordered oxides involving oxide glasses have been investigated. Spin glass-like transition is observed for Fe₂O₃–TeO₂ and MnO–TeO₂ glasses in temperature dependence of dc susceptibility, although magnetic transition does not take place for MnO–TeO₂ glasses with low concentration of manganese ion above 2 K at least. The mechanism of magnetic transition observed for Fe₂O₃–TeO₂ glasses is discussed on the basis of dc susceptibility obtained under conditions of field cooling and zero field cooling, magnetic field dependence of magnetization at low temperatures, and frequency dependence of spin-freezing temperature derived from temperature dependence of ac susceptibility. Magnetic properties of disordered ZnFe₂O₄ thin film prepared by a radio frequency sputtering method have been also studied. The disordered ZnFe₂O₄ thin film exhibits ferrimagnetic behavior with high magnetization even at room temperature. At the same time, the thin film shows spin-freezing at around 320 K. Temperature dependence of nonlinear susceptibility leads to a conclusion that this transition is explainable in terms of superparamagnetism with magnetic interaction among clusters.     

Vertically aligned carbon nanotubes from natural precursors by spray pyrolysis method and their field electron emission properties

Vertically aligned carbon nanotubes have been synthesized from botanical hydrocarbons: Turpentine oil and Eucalyptus oil on Si(100) substrate using Fe catalyst by simple spray pyrolysis method at 700°C and at atmospheric pressure. The as-grown carbon nanotubes were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution TEM (HRTEM), thermogravimetric analysis (TGA), differential thermal analysis (DTA), and Raman spectroscopy. It was observed that nanotubes grown from turpentine oil have better degree of graphitization and field emission performance than eucalyptus oil grown carbon nanotubes. The turpentine oil and eucalyptus oil grown carbon nanotubes indicated that the turn-on field of about 1.7 and 1.93 V/μm, respectively, at 10 μA/cm². The threshold field was observed to be about 2.13 and 2.9 V/μm at 1 mA/cm² of nanotubes grown from turpentine oil and eucalyptus oil respectively. Moreover, turpentine oil grown carbon nanotubes show higher current density in relative to eucalyptus oil grown carbon nanotubes. The maximum current density of 15.3 mA/cm² was obtained for ∼3 V/μm corresponding to the nanotubes grown from turpentine oil. The improved field emission performance was attributed to the enhanced crystallinity, fewer defects, and greater length of turpentine oil grown carbon nanotubes.     

Reduced qKZ Equation and Correlation Functions of the XXZ Model

Correlation functions of the XXZ model in the massive and massless regimes are known to satisfy a system of linear equations. The main relations among them are the difference equations obtained from the qKZ equation by specializing the variables (λ₁, . . . ,λ_2n) as (λ₁, . . . ,λ_n,λ_n+1, . . . ,λ₁+1). We call it the reduced qKZ equation. In this article we construct a special family of solutions to this system. They can be written as linear combinations of products of two transcendental functions ,ω with coefficients being rational functions. We show that correlation functions of the XXZ model in the massive regime are given by these formulas with an appropriate choice of ,ω. We also present a conjectural formula in the massless regime. On leave of absence from the Institute for High Energy Physics, Protvino, 142281, Russia Membre du CNRS     

Form Factors and Action of on ∞-Cycles

Let be a sequence of skew-symmetric polynomials in X₁,,X_l satisfying deg_XjP_n,ln–1, whose coefficients are symmetric Laurent polynomials in z₁,,z_n. We call p an -cycle if holds for all n,l. These objects arise in integral representations for form factors of massive integrable field theory, i.e., the SU(2)-invariant Thirring model and the sine-Gordon model. The variables _a=–logX_a are the integration variables and _j=logz_j are the rapidity variables. To each -cycle there corresponds a form factor of the above models. Conjecturally all form-factors are obtained from the -cycles. In this paper, we define an action of on the space of -cycles. There are two sectors of -cycles depending on whether n is even or odd. Using this action, we show that the character of the space of even (resp. odd) -cycles which are polynomials in z₁,,z_n is equal to the level (–1) irreducible character of with lowest weight –₀ (resp. –₁). We also suggest a possible tensor product structure of the full space of -cycles.     

Quantum 2-spheres and bigq-Jacobi polynomials

Orthogonal bases for the algebras of functions of Podles' quantum 2-spheres are explicitly determined in terms of bigq-Jacobi polynomials. This gives a group-theoretic interpretation of the symmetric bigq-Jacobi polynomials and the symmetricq-Hahn polynomials.