On division rings with algebraic commutators of bounded degree

We shall answer several questions concerning additive or multiplicative commutators in a division ring which are algebraic of bounded degree over its center.     

A high sensitivity titration calorimeter using pyroelectric sensor

A new sensitive isothermal titration microcalorimeter using polyvinylidene difluoride (PVDF) as detector has been developed. Heat pulses of less than 0.4 μJ can be detected and the baseline noise level (p-p) is 40 nW. The calorimeter is constructed with one reaction cell (0.7 ml) insulated by several radiation shields inside a vacuum chamber. The performance of the instrument was examined by measuring the heat of protonation of Tris with HCl. The enthalpy of reaction was found to be ?49±1 kJ·mol^?1, in good agreement with the reported value of ?47.5 kJ·mol^?1.     

Profile empirical likelihood for parametric and semiparametric models

This paper introduces a profile empirical likelihood and a profile conditionally empirical likelihood to estimate the parameter of interest in the presence of nuisance parameters respectively for the parametric and semiparametric models. It is proven that these methods propose some efficient estimators of parameters of interest in the sense of least-favorable efficiency. Particularly, for the decomposable semiparametric models, an explicit representation for the estimator of parameter of interest is derived from the proposed nonparametric method. These new estimations are different from and more efficient than the existing estimations. Some examples and simulation studies are given to illustrate the theoretical results. The first author is supported by NNSF projects (10371059 and 10171051) of China. The second author is supported by a grant from The Research Grants Council of the Hong Kong Special Administrative Region, China (#HKU7060/04P). The third author is supported by the University Research Committee of the University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU7323/01M).     

Output dynamics and stabilisation of a multi-mode double-clad Yb-doped silica fibre laser

The intensity dynamics of the double-clad Yb fibre laser have been characterised. Stabilisation of the fibre laser intensity by using uniform bi-directional pumping is demonstrated. For the single-end-pumped Yb fibre laser, the output becomes more stable for the shorter fibre length due to the higher threshold of stimulated Brillouin scattering, SBS, and Kerr effects and the reduction of saturated absorber effects caused by any unpumped fibre section. By additional pumping in a double-end-pumped configuration, the output power can be scaled higher before detecting high intensity pulses initiated by SBS in the Yb fibre laser due to the reduction of saturable absorption effect. It is confirmed that uniform pumping enhances the stability of the laser output.     

A multipolymer system for organocatalytic alcohol oxidation

A system involving two polymer-supported reagents for the selective and organocatalytic oxidation of alcohols to aldehydes or ketones has been developed in which both polymeric reagents can be recovered and reused.     

On some contact problems for composite half-spaces PMM vol. 31, no. 6, 1967, pp. 1001–1008

Solutions are presented herein of some contact problems connected with the torsion of a composite half-space. In the general case the problem of the torsion of a composite elastic half-space is examined by means of the rotation of a stiff finite cylinder welded into a vertical recess of this half-space. Moreover, the following particular problems on the torsion of such a half-space are considered.

1. 1) A composite half-space with a vertical elastic infinite core, twisted by means of the rotation of a stiff stamp affixed to the upper endplate of the elastic core.

2. 2) A half-space with a vertical cylindrical infinite hole, twisted by means of the rotation of a stiff finite cylinder welded into the upper part of this hole.

In the general case the solution of the problem reduces to the solution of an integral equation of the second kind on a half-line. The question of the solvability of this fundamental integral equation is investigated, and it is shown that its solution may be constructed by successive approximations.

Let us note that the problem of the torsion of a homogeneous half space and of an elastic layer by means of rotation of a stiff stamp has been considered by Rostovtsev [1], Reissner and Sagoci [2], Ufliand [3], Florence [4], Grilitskii [5] and others.

The problem of the torsion of a circular cylindrical rod and the half-space welded to it which are subject to a torque applied to the free endface of the rod has been considered by Grilitskii and Kizyma[6].

The torsion of an elastic half-space with a vertical cylindrical inclusion of some other material by the rotation of a stiff stamp on the surface of this half-space has been considered in [7], wherein it has been assumed that the stamp is symmetrically disposed relative to the axis of the inclusion and lies simultaneously on both materials.     

Relations on the period mapping giving extensions of mixed hodge structures on compact Riemann surfaces

We consider a period map from Teichmüller space to , which is a real vector bundle over the Siegel upper half space. This map lifts the Torelli map. We study the action of the mapping class group on this period map. We show that the period map from Teichmüller space modulo the Johnson kernel is generically injective. We derive relations that the quadratic periods must satisfy. These identities are generalizations of the symmetry of the Riemann period matrix. Using these higher bilinear relations, we show that the period map factors through a translation of the subbundle and is completely determined by the purely holomorphic quadratic periods. We apply this result to strengthen some theorems in the literature. One application is that the quadratic periods, along with the abelian periods, determine a generic marked compact Riemann surface up to an element of the kernel of Johnson's homomorphism. Another application is that we compute the cocycle that exhibits the mapping class group modulo the Johnson kernel as an extension of the group SP _g () by the group .     

Crystal Structures of Hydrochlorides of 2,3-Pentamethylene-3, 4-dihydroquinazolin-4-one

The crystal structures of hydrate (1) and anhydrate (2) forms of 2,3-pentamethylene-3,4-dihydroquinazolin-4-one hydrochloride have been determined by X-ray structure analysis. Crystal data of 1 are 2(C₁₃H₁₄N₂O)*3(HCl)*4.5 (H₂O), triclinic P?1, Z=2, a=8.004(5), b=13.129(7), c=15.725(7) Å, α=106.45(4), β=92.61(4), γ=97.98(5), R=0.0652 and 2 are C₁₃H₁₄N₂O*HCl, monoclinic C2/c, Z=8, a=21.360(4), b=5.954(1), c=21.263(4), β=117.89(3), R=0.0556. The crystal of the hydrate form 1is unstable. This form collapses easily with evaporation of H₂O and part of HCl molecules from crystals. By recrystallizing destroyed form has been obtained stable crystal form 2.