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. 相似文献
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. 相似文献
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. 相似文献
The new cadmium(II) coordination polymer [Cd(bte)2(dca)2]n 1 (bte = 1,2-bis(1,2,4- triazol-1-yl)ethane, dca = dicyanamide) was synthesized and characterized by single-crystal X-ray diffraction. The crystal is of monoclinic, space group P21/n with a = 8.7148(15), b = 8.6142(17), c = 15.204(3) A, β = 92.100(10)o, V = 1140.6(4) A3, Z = 2, Mr = 572.87, Dc = 1.668 g/cm3, F(000) = 572, μ = 1.004 mm-1, the final R = 0.0654 and wR = 0.1429 for 1737 observed reflections (I > 2σ(I)). The cadmium atom is coordinated equatorially by four nitrogen atoms from four bte ligands and axially by two nitrogen atoms from two dca anions to adopt a distorted octahedral geometry. Each bte molecule bridges two cadmium(II) atoms. Two strands of bte molecules are wrapped around each other, and held together by cadmium(II) atoms. 1 Forms a double chain structure containing eighteen-membered Cd2(bte)2 rings. 相似文献
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. 相似文献
The reaction of either Li2PPh or Li2AsPh with the diborane(4) derivative B2(NMe2)2Br2 affords the compounds [PhP(BNMe2)2]2 ( 1 ) or [PhAs(BNMe2)2]2 ( 2 ) in good yield. Both 1 and 2 have cyclic structures featuring non-planar P2B4 or As2B4 six-membered rings which have chair configurations. Although all four borons in each ring have planar coordination, the two phosphorus or arsenic centers have different degrees of pyramidalization. Bond distances within the rings indicate that the B? B, B? P or B? As bonds are single, whereas the exo-B? N bond lengths are consistent with significant π-bonding. The ring structures of 1 and 2 are in sharp contrast to the related boron-nitrogen species (t-BuN)2N4Me4 which has a nido-N2B4 framework. The attempted synthesis of the nitrogen analogue of 1 or 2 by using a similar approach did not result in the isolation of [PhN(BNMe2)2]2, instead the tetramino diborane(4) species [B(NMe2)NHPh]2 ( 3 ), which has a structure similar to other tetramine diborane(4) compounds, was isolated. 相似文献
Formation of Liesegang rings on the growth of BaMoO4 crystals in silica gel by single diffusion is discussed. The rhythmic precipitation is found to be influenced profoundly by (a) the molarity of inner and outerelectrolytes (b) the age of gel and (c) the pH of the gel medium. The time law, spacing law and the law relating diffusion depth and width are verified. A method to estimate the diffusion coefficient of the outer electrolyte in the gel medium is developed and calculated for Ba++ions. 相似文献
A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.
A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.