有限局部环Z/2\+kZ上斜对称矩阵标准形和伪辛群的阶

设R=Z/2\+kZ(k>1)是\{2\}[TX-]为非单位的有限局部环. 该文首先确定了R上斜对称矩阵标准形. 设G\+m\-p(R,H)={P∈GL\-m(R)|PHP′=H}是由矩阵H确定的伪辛群,其中H=[JB((][HL(2]0[]I\+\{(v)\}\=-I\+\{(v)\}[]0[HL)][JB))]Δ，Δ=[JB((][HL(2]\{2\}[TX-]\+\{k-1\}[]\{1\}[TX-]\=-\{1\}[TX-][]0[HL)][JB))]. 其次,计算了伪辛群G\+m\-P(R,H)的阶|G\+m\-P(R,H)|.     

Spontaneous Surgery on the Borromean Rings

We study the cone-manifolds whose singular sets are obtained by orbifold and spontaneous surgeries on components of the Borromean rings. We establish existence of geometric structures on these manifolds. For manifolds with hyperbolic structure we obtain an integral representation for volumes.     

On Gouvêa's conjecture in the unobstructed case

In this article, for a residual modular representation defined over an arbitrary finite field, Gouvêa's conjecture which says that the universal deformation ring is isomorphic to a certain Hecke algebra is proven in the unobstructed case.     

Study of fiber optic sugar sensor

Over the last two decades, the fiber optic technology has passed through many analytical stages. Some commercially available fiber optic sensors, though in a small way, are being used for automation in mechanical and industrial environments. They are also used for instrumentation and controls. In the present work, an intensity-modulated intrinsic fiber optic sugar sensor is presented. This type of sensor, with slight modification, can be used for on-line determination of the concentration of sugar content in sugarcane juice in sugar industry. In the present set-up, a plastic fiber made of polymethylmethacrylate is used. A portion of the cladding (1 cm, 2 cm, 3 cm) at the mid-point along the length of the fiber is removed. This portion is immersed in sugar solution of known concentration and refractive index. At one end of the fiber an 850 nm source is used and at the other end a power meter is connected. By varying the concentration of sugar solution, the output power is noted. These studies are made due to the change in refractive index of the fluid. The device was found to be very sensitive which is free from EMI and shock hazards, stable and repeatable and they can be remotely interfaced with a computer to give on-line measurements and thus become useful for application in sugar industries.     

Synthesis and characterization of new thermally stable copoly(ester–amide)s from diester–dicarboxylic acids

Three new aromatic diester–dicarboxylic acids containing furan rings, namely, benzofuro[2,3-b]benzofuran-2,9-dicarboxyl-bis-phenyl ester-4,4^′-dicarboxylic acid, benzofuro[2,3-b]benzofuran-2,9-dicarboxyl-bis-phenyl ester-3,3^′-dicarboxylic acid and benzofuro[2,3-b]benzofuran-2,9-dicarboxyl-bis-naphthyl ester-2,2^′-dicarboxylic acid were synthesized by the reaction of benzofuro[2,3-b]benzofuran-2,9-dicarbonyl chloride with 4-hydroxybenzoic acid, 3-hydroxybenzoic acid and 3-hydroxy-naphthalene-2-carboxylic acid, respectively. Diester–dicarboxylic acids were characterized by FT-IR and NMR spectroscopy and elemental analyses. Then, these monomers were converted to aromatic copoly(ester–amide)s by their reaction with various aromatic diamines via the direct polycondensation. These polymers were characterized by viscosity measurements, solubility tests, FT-IR, Ultraviolet and ¹H-NMR spectroscopy and thermogravimetry. The polymers with inherent viscosities in the range of 0.16–0.37 dl/g in dimethyl sulfoxide at 30 °C were obtained in high yield. Most of them dissolved readily at room temperature in polar solvents. The synthesized copoly(ester–amide)s possessed glass-transition temperatures from 210–255 °C. The copoly(ester–amide)s exhibited excellent thermal stabilities and had 10% weight loss at temperature above 295 °C under nitrogen atmosphere.     

A versatile and practical synthesis of bis(indolyl)methanes/bis(indolyl)glycoconjugates catalyzed by trichloro-1,3,5-triazine

A practical and efficient electrophilic substitution reaction of indoles with a variety of aldehydes was carried out using catalytic trichloro-1,3,5-triazine (10 mol %) in acetonitrile to furnish the corresponding bis(indolyl)methanes in excellent yields. Similarly, sugar derived aldehydes gave hitherto unknown bis(indolyl)glycoconjugates in very good yields.     

Microwave-assisted efficient synthesis of spiro-fused heterocycles under solvent-free conditions

Spiro-fused heterocycles were synthesized in good to high yields by a pseudo four-component reaction of an aldehyde, urea and a cyclic β-diester or a β-diamide such as Meldrum’s acid or barbituric acid derivatives using microwave irradiation under solvent-free conditions.     

Facile synthesis of C-aryl glycals from sugar-derived lactones

A general entry to C(1) aryl-substituted glycals from the corresponding sugar lactones is described. This approach features one-pot access to aryl glycals. A variety of aryllithium reagents can be used and the method is compatible with various 2-deoxysugar lactones.