Facile Synthesis of Alkylidene Phthalides by Rhodium-Catalyzed Domino C−H Acylation/Annulation of Benzamides with Aliphatic Carboxylic Acids

The Rh-catalyzed ortho-C(sp²)−H functionalization of 8-aminoquinoline-derived benzamides with aliphatic acyl fluorides generated in situ from the corresponding acids has been developed. This reaction initiated with 8-aminoquinoline-directed ortho-C(sp²)−H acylation, which was accompanied by subsequent intramolecular nucleophilic acyl substitution of amide group to produce alkylidene phthalides This approach exhibits high stereo-selectivity for Z-isomer products, and tolerates a variety of functional groups as well as aliphatic carboxylic acids with diverse structural scaffolds.     

An attempt to differential Galois theory of second order polynomial system and solvable subgroup of M(o)bius transformations

By introducing the conception "relativistic differential Galois group" for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of M(o)bius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of M(o)bius transformations at the first author's article published in this journal in 1996 are refreshed in this paper.     

群集建筑中大跨裙摆屋盖风荷载特性的数值模拟研究

以苏州太平金融大厦为工程背景,针对其大跨裙摆屋盖的风荷载作用,首先采用RNG k-ε模型模拟分析了其平均风压分布规律,以及风向变化对屋盖表面风荷载体型系数的影响;其次,引入干扰因子IF,探讨了周边建筑对大跨裙摆屋盖风荷载的气动干扰作用。结果表明:0°风向下,走廊上方屋盖两侧区域出现“上吸下顶”的叠加作用;90°风向下屋盖北侧飘带末端区域受到狭道风效应出现正压集中现象;风向变化对大跨裙摆屋盖的风荷载体型系数分布影响较大;且周围建筑物对大跨裙摆屋盖的气动干扰效应明显,主要表现为风压“遮挡效应”,而局部区域表现为风压“放大效应”。     

Explicit formula of holomorphic automorphism group on complex homogeneous bounded domains

We known that the maximal connected holomorphic automorphism group Aut (D)(0) is a semi-direct product of the triangle group T(D) and the maximal connected isotropic subgroup Iso(D)(0) of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F). In this paper, we give the explicit formula of any holomorphic automorphism in T(D(VN, F)) and Iso(D(VN,F))(0), where G(0) is the unit connected component of the Lie group G.     

Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

带隙可调各向同性蛋白石光子晶体的制备与研究

用旋涂法将聚苯乙烯微球组装成光子晶体,研究了此光子晶体的特点,并分析了在单一微球粒径下旋涂参数对光子带隙的影响.结果表明:旋涂法制备的光子晶体具有各向同性特点,其光子带隙由旋涂参数决定.光子晶体的反射波段取决于乳液中微球的质量分数,而反射强度取决于旋涂层数.因此,在设计光子晶体时,可以根据需要,通过微球的质量分数和旋涂...     

1,2‐Dithioquadratato‐ und 1,2‐Dithiooxalatoindate(III)

Indium(III) chloride forms in water with potassium 1,2‐dithiooxalate (dto) and potassium 1,2‐dithiosquarate (dtsq) stable coordination compounds. Due to the higher bridging ability of the 1,2‐dithiooxalate ligand in all cases only thiooxalate bridged binuclear complexes were found. From 1,2‐dithioquadratate with an identical donor atom set mononuclear trischelates could be isolated. Five crystalline complexes, (BzlMe₃N)₄[(dto)₂In(dto)In(dto)₂] ( 1 ), (BzlPh₃P)₄[(dto)₂In(dto)In(dto)₂] ( 2 ), (BzlMe₃N)₃[In(dtsq)₃] ( 3 ), (Bu₄N)₃[In(dtsq)₃] ( 4 ) and (Ph₄P)[In(dtsq)₂(DMF)₂] ( 5 ), have been isolated and characterized by X‐ray analyses. Due to the type of the complex and the cations involved these compounds crystallize in different space groups with the following parameters: 1 , monoclinic in P2₁/c with a = 14.4035(5) Å, b = 10.8141(5) Å, c = 23.3698(9) Å, β = 124.664(2)°, and Z = 2; 2 , triclinic in P with a = 11.3872(7) Å, b = 13.6669(9) Å, c = 17.4296(10) Å, α = 88.883(5)°, β = 96.763(1)°, γ = 74.587(5)°, and Z = 1; 3 , hexagonal in R3 with a = 20.6501(16) Å, b = 20.6501(16) Å, c = 19.0706(13) Å and Z = 6; 4 , monoclinic in P2₁/c with a = 22.7650(15) Å, b = 20.4656(10) Å, c = 14.4770(9) Å, β = 101.095(5)°, and Z = 4; 5 , triclinic in P with a = 9.2227(6) Å, b = 15.3876(9) Å, c = 15.5298(9) Å, α = 110.526(1)°, β = 100.138(1)°, γ = 101.003(1)°, and Z = 2.     

On circle diffeomorphisms with discontinuous derivatives and quasi-invariance subgroups of Malliavin-Shavgulidze measures

This note is devoted to construction of the domain of the regular representation of Diff₊(S¹). We consider a subgroup of diffeomorphism group such that the Malliavin-Shavgulidze measure is quasi-invariant with respect to the left action of the subgroup. The measure appears to be quasi-invariant with respect to the left action of diffeomorphisms with discontinuous second derivative. We derive an expression for quasi-invariance density and obtain an additional PSL(2,R) symmetry breaking term.