Locally s-distance transitive graphs and pairwise transitive designs

The study of locally s-distance transitive graphs initiated by the authors in previous work, identified that graphs with a star quotient are of particular interest. This paper shows that the study of locally s-distance transitive graphs with a star quotient is equivalent to the study of a particular family of designs with strong symmetry properties that we call nicely affine and pairwise transitive. We show that a group acting regularly on the points of such a design must be abelian and give general construction for this case.     

A Note on Free Groups in the Ring of Fractions of Skew Polynomial Rings

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t;σ], the skew polynomial ring in t, over L, with automorphism σ. We prove that the multiplicative group D ^× of D contains a free noncyclic subgroup.     

Fully Invariant Subgroups of Abelian p-Groups with Finite Ulm–Kaplansky Invariants

We study primary groups containing proper fully invariant subgroups isomorphie to the group. The admissable sequence of Ulm–Kaplansky invariants for primary groups is introduced. Using these sequences, If-groups are described in the classes of seperable and periodically complete groups.     

On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

利用单参数Lie群组的一种可解性求自治系统首次积分的方法

讨论了自治系统接受的单参数Lie群组具有一种可解性的情况下求系统的一个首次积分的具体方法.对于n阶自治系统,给出相应参数的一组确定取值,求得系统首次积分；对于三阶自治系统,当系统接受的单参数Lie群组可解时,验证求得首次积分的条件一定成立.     

A novel generation of photoactive comb‐shaped polyamides for the photoalignment of liquid crystals

A new approach to the synthesis of photoactive comb‐shaped homo‐ and copolyamides containing azobenzene, cinnamate, and coumarin side groups for photoalignment of liquid crystals was elaborated. Photooptical properties and photoorientational ability of these polymers with respect to liquid crystals were studied. It was shown that polarized UV irradiation of all spin‐coated polyamides leads to orientation of liquid crystalline molecules deposited on the polyamide thin films. The synthesized polymers containing cinnamate and coumarin side groups as well as azobenzene‐containing cyano‐ and nitro‐substituted polymers demonstrated good orientation ability in relation to liquid crystals displaying photoinduced planar orientation with high dichroism values within the range of 0.68–0.72. Contrary to the above‐mentioned polyamides, azobenzene‐containing fluorosubstituted polymers induced a homeotropic orientation of liquid crystals. It was shown that the synthesized photoactive polyamides can be considered as promising photoalignment materials for application in display technology, photonics, and other “smart” optical devices. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4031–4041     

Donor–acceptor (donor) polymers with differently conjugated side groups at the acceptor units for photovoltaics

Four new donor–acceptor (donor) [D–A(D)], PBDT‐PTQ, PBDT‐PTTQ, PBDT‐TQ, and PBDT‐TTQ, bearing the same backbone of alternative benzodithiophene (BDT) and quinoxaline units but with phenylene thienyl, phenylene di‐thienyl, thienyl and di‐thienyl groups (other donors), respectively, at the acceptor quinoxaline units, were designed and synthesized to investigate the impacts of the conjugated side chains at the acceptor units on the photovoltaic properties of polymers. The power conversion efficiencies (PCEs) of the polymer solar cells (PSCs) based on PBDT‐TQ:[6,6]‐phenyl‐C‐70‐butyric acid methyl ester (PC70BM) and PBDT‐PTQ:PC70BM reach to 4.39 and 3.58%, respectively, which are 43 and 17% higher, respectively, than that of a reported alkylphenyl substituted polymer with the same main chain. However, the PCEs based on PBDT‐TTQ and PBDT‐PTTQ, in which an additional thiophene is added at a side chain of PBDT‐TQ and PBDT‐PTQ, respectively, decline. The mechanism how the conjugated side chains affect the performance of the PSCs is also discussed. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Coloring–decoloring behavior of fluoroalkyl end‐capped 2‐acrylamido‐2‐methylpropanesulfonic acid oligomer/acetone composite in methanol

A reddish‐brown fluoroalkyl end‐capped 2‐acrylamido‐2‐methylpropanesulfonic acid (AMPS) oligomer/acetone composite was prepared by heating the white oligomer powder with acetone at 80 °C for 3 h. The color was not observed in the corresponding non‐fluorinated AMPS oligomer/acetone composite, which was prepared under similar conditions. The coloring was probably caused by the formation of acetone polyaldol condensation products in the fluorinated oligomeric gel network cores. The colored R_F‐(AMPS)_n‐R_F/acetone composite powders were stable and did not exhibit any color change after 2 years in natural light at room temperature. The colored composite powders dissolved in methanol to give a reddish‐brown solution at room temperature. However, the retro‐polyaldol condensation decolored the solution after 1 day at room temperature. This is the first example of the retro‐aldol polycondensation of acetone under mild conditions. The decoloration increased by between 38‐ and 70‐fold under UV irradiation, compared with that in dark conditions. The coloring–decoloring behavior was consistent and repeatable; therefore our fluorinated oligomer/acetone composites are promising candidates for new fluorinated coloring materials. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2555–2564     

Backbonding in Thorium(IV) and Uranium(IV) Diarsenido Complexes with tBuNC and CO

The coordination of tBuNC and CO with the diarsenido complexes (C₅Me₅)₂An(η²-As₂Mes₂), An=Th, U, has been investigated. For the first time, a comparison between isostructural complexes of Th^IV and U^IV has been possible with CO; density functional calculations indicated an appreciable amount of π backbonding that originates from charge transfer from an actinide-arsenic sigma bond. The calculated CO stretching frequencies in the Th^IV and U^IV diarsenido complexes are consistent with the experimental measurements, both show large shifts to lower frequency. We demonstrate that the π backbonding is crucial to explaining the red shifts of CO frequency upon An^IV complex formation. Interestingly, this interaction essentially correlates to the parallel orientation of π*(C−O) orbitals relative to the An−As bond.