Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Derived Brackets

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and of Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of Poisson structures with background'.     

动力系统的稳定化问题

In this paper, we are concerned with the problem of stabilization for autonomous dynamical systems. We use theories in Liapunov stability and Lasalle stability theory and show that system (H) is stabilizable.     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

对NO生理作用的新认识及其电化学实时检测

本文综述了近年来学术界对ＮＯ生理作用的新认识，并介绍了现场实时检测生物活体中释放的ＮＯ浓度的电化学方法．     

X-Ray Investigation of Chiral β-Hydroxyketone Derived From (+)-Isomenthone

X-ray analysis was carried out to study the molecular structure of β-hydroxyketone, which is one of the minor products of selective aldol condensation of (−)-menthone with 4-carbomethoxybenzaldehyde. The cyclohexanone ring of the compound has a practically undistorted chair conformation with an axial orientation of the 1-methyl group and the bulkiest 2-[1′-hydroxy-1′ -(4-carbomethoxyphenyl)]methyl substituent and the equatorial orientation of the isopropyl group in the 4 position. The stereochemical configuration was found to be (1R,2R,4 R, 1′ S), supporting that the compound belongs to the group of (+)-isomenthones; i.e., the starting (-)-menthone undergoes (to a certain extent) epimerization under the reaction conditions used. In crystal, there is intermolecular hydrogen bonding >C=O...HO- (the -O...H- bond length is 2.15 Å). The molecular conformation in hydroxyketone crystals differs from the one which prevails in solutions (according to previous NMR data) and which is characterized by an inverted cyclohexanone ring and intramolecular hydrogen bonding >C=O...HO.Original Russian Text Copyright © 2004 by S. V. Shishkina, T. G. Drushlyak, L. A. Kutulya, N. S. Pivnenko, and O. V. Shishkin__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 933–940, September–October, 2004.     

Gorenstein AC亏范畴*

作者定义了Gorenstein AC导出范畴 D^b_gac(R)并且和导出范畴作了一些比较.作者定义了Gorenstein AC奇点范畴 D^b_gacsg(R),在这个范畴中具有有限Gorenstein AC- 投射维数的模都是零对象.同时, 作者给出了由Gorenstein AC- 投射模构成的稳定范畴到奇点范畴的三角嵌入 F : GAC → D^b_sg(R) .通过作函子 F 的商引入Gorenstein AC亏范畴 D^b_gacd(R),并且给出三角等价 D^b_gacd(R) = D^b_gacsg(R)     

Anti-solvent assisted treatment for improved morphology and efficiency of lead acetate derived perovskite solar cells

An efficient solution-processable route employing Pb(Ac)₂ as lead source and anti-solvent treatment to achieve fully covered and homogenous perovskite films is reported.     

DETERMINATION OF DEGREE OF CRYSTALLINITY OF NYLON 1212 BY WIDE-ANGLE X-RAY DIFFRACTION

Based on the X-ray scattering intensity theory and using the approximate expression for the atomic scattering factor, the correction factors for three crystalline peaks and an amorphous peak of Nylon 1212 were calculated and the formula of degree of crystallinity of Nylon 1212 was derived by a graphic multipeak resolution method. The degree of crystallinity calculated from the WAXD method is compatible with those obtained by density and calorimetry methods.