Phase behaviour of polyethylene knotted ring chains

The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations. In this paper, we focus on the collapse of the polyethylene knotted ring chain, and also present the results of linear and ring chains for comparison. At high temperatures, a fully extensive knot structure is observed. The mean-square radius of gyration per bond （S2）/（Nb2） and the shape factor （（δ＊） depend on not only the chain length but also the knot type. With temperature decreasing, chain collapse is observed, and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity Cv, and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse, which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.

On Left A-Injective Rings

The main results of this paper are following theorems: (1)A left A-injective ring satisfying the ascending chain condition on right annihilator is QF ring. (2)A left A-injective ring satisfying the ascending hain condition on left annihilator is QF ring. (3)If R satisfies the following conditions: (ⅰ) r(A∩B)=r(A)+r(B), for each pair of left ils A,B;(ⅱ) rl(I)=I, for every right ideal I. Then R is semiperfect ring and has essential left s. In particular, any right CF left A-injective (or E(_RR) is projective left R-module) is QF ring

Octa-membered Water Ring Chain Based on Sulfonic Group in Ni(II) Complex with 2-[(E)-(2-Oxidophenyl)methyleneamino] Ethanesulfonato and 2,2′-Bipyridinyl

The title compound, [Ni（tssb）（2,2-bipy）2].5（H2O） 1 （tssbH2 =2-[（E）-（2-oxido- phenyl）methyleneamino]ethanesulfonato, 2,2-bipy = 2,2＇-bipyridinyl）, belongs to orthorhombic, space group Pbcn with a = 20.3983（18）, b = 17.6929（15）, c = 17.0897（15） nm, V= 6167.8（9） nm^3, Mr= 688.38, Z = 8, De = 1.481 g.cm^-3, F（000） = 2880,μ = 0.758 mm-1 and S =1.099. Each NiIr atom is six-coordinated by one N and one O atoms from one tssb^2- anion and four N atoms from two 2,2-bipy ligands to give a distorted octahedral geometry. Noticeably, there exists a rare octa-mem- bered water ring which presents a 1D chain by sulfonic group.

CYCLIC CODES OVER FORMAL POWER SERIES RINGS

In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.

Self-Dual Permutation Codes over Finite Chain Rings

Permutation codes over finite chain rings are introduced; by using the character of the finite chain rings and the knowledge of representation of group, some conditions for existence or non-existence of self-dual permutation codes over finite chain rings are obtained. Specially, when the group is a direct product of a 2-group and a T-group, and the group action is transitive, the sufficient and necessary condition of the existence of permutation codes is given.

Spin transport in a chain of polygonal quantum rings with Dresselhaus spin-orbit coupling

Using a transfer matrix method, we investigate spin transport through a chain of polygonal rings with Dresselhaus spin-orbit coupling（DSOC）. The spin conductance is dependent on the number of sides in the polygons. When DSOC is considered in a chain which also has Rashba spin-orbit coupling（RSOC） of the same magnitude, the total conductance is the same as that for the same chain with no SOC. However, when the two types of SOC have different values, there results a unique anisotropic conductance.

Synchronization of N different coupled chaotic systems with ring and chain connections

Synchronization of N different coupled chaotic systems with ring and chain connections is investigated. The New system, the Chen system, the Lii system, the Lorenz system, and the Rossler system are used as examples in verifying effectiveness of the method. Based on the Lyapunov stability theory, the form of the controller is designed and the area of the coupling coefficients is determined. Simulations indicate that global synchronization of the N different chaotic systems can be realized by choosing appropriate coupling coefficients by using the controller.

ON THE CHARACTERIZATION OF CYCLIC CODES OVER TWO CLASSES OF RINGS

Let R be a finite chain ring with maximal ideal （7） and residue field F,and letγ be of nilpotency index t. To every code C of length n over R, a tower of codes C = （C ： γ0） C_ （C： 7） C ... C_ （C： γ2） C_ .-. C_ （C：γ^t-1） can be associated with C, where for any r C R, （C ： r） = {e C Rn I re E C}. Using generator elements of the projection of such a tower of codes to the residue field F, we characterize cyclic codes over R. This characterization turns the condition for codes over R to be cyclic into one for codes over the residue field F. Furthermore, we obtain a characterization of cyclic codes over the formal power series ring of a finite chain ring.

Two New Chlorovanadates:Ba_8Cs_5V_8O_(24)Cl_(13)with[V_8O_(24)]Ring and MgCsV_2O_6Cl with[VO_3]_∞Chain

Two new crystals of chlorovanadates,Ba_8Cs_5V_8O_（24）Cl_（13）（1） and MgCsV_2O_6Cl（2）,were grown in the molten salt media. 1 crystallizes in tetragonal,space group P4/mmm（No. 123）,with a = 14.801（2）,c = 12.341（3） ？,V = 2703.5（8） ？~3,Z = 2,Mr = 3015.56,F（000） = 2640,μ = 11.044 mm-1,Dc = 3.704 g/cm3,the final R = 0.0380 and wR = 0.0937 for 1654 observed reflections with I 〉 2σ（I）. 2 crystallizes in a monoclinic space group C2/c（No. 15） with a = 11.128（2）,b = 10.540（2）,c = 6.9892（14） ？,β = 118.38（3）°,V = 721.2（2） ？~3,Z = 4,M_r = 390.55,F（000） = 712,μ = 7.997 mm-1,D_c = 3.597 g/cm^3,the final R = 0.0537 and w R = 0.1363 for 740 observed reflections with I 〉 2σ（I）. 1 exhibits a novel 8-membered-ring [V_8O_（24）] consisting of 8 corner-shared VO_4 tetrahetra,but in 2,an infinite ladder-like [VO_3]_∞ chain is formed by VO_5 square pyramids through sharing the edges.

CYCLIC AND NEGACYCLIC CODES OF LENGTH 2p^s OVER F_(p^m) + uF_(p^m)

In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m ＋ uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.

A Convenient Synthesis of Pyrazolylpyrazoles Using α-Oxo Ketene S,S- and N,S-Acetals

Substituted pyrazolylpyrazoles were synthesized through the reaction of hydrazine hydrate and α-oxo-(3, 5-dimethyl-1 H-pyrazole-1-ly)ketene S, S- and N,S-Acetals which were obtained from α-oxo-(3,5-dimethyl-1 H-pyrazole-1-yl) acetophenone. Pyrazolylpyrazole was also prepared via α-oxo ketene N,O-acetal by way of ring chain transformation.

The maximal size of 6-and 7-arcs in projective Hjelmslev planes over chain rings of order 9 Dedicated to Professor Feng Keqin on the Occasion of his 70th Birthday

We complete the determination of the maximum sizes of （k,n）-arcs, n ≤ 12, in the projective gjelmslev planes over the two （proper） chain rings Z9 = Z/9Z and S3 = F3[X]/（X2） of order 9 by resolving the hitherto open cases n = 6 and n = 7. Parts of our proofs rely on decidedly geometric properties of the planes such as Desargues＇ theorem and the existence of certain subplanes.

Notes on Linear Codes over Finite Commutative Chain Rings

The properties of the generator matrix are given for linear codes over finite commutative chain rings, and the so-called almost-MDS （AMDS） codes are studied.

Significantly Improved Stereocomplexation Ability in Cyclic Block Copolymers

Stereocomplex crystallization in cyclic polymer blend and cyclic block copolymers was investigated by means of dynamic Monte Carlo simulations.Five polymer systems(linear polymer blend,linear diblock copolymer,cyclic polymer blend,cyclic diblock copolymer and tetrablock copolymer)were established.It was interestingly found that the cyclic polymer blend exhibited the weakest stereocomplexation ability,while the two cyclic block copolymers showed stronger stereocomplexation ability than the linear diblock copolymer.This abnormal improved stereocomplexation ability of the cyclic block copolymers can be attributed to the synergy between the ring chain topology and the block copolymer structure.Compared with the linear block copolymers,the ring chain topology confined segmental motions of cyclic polymer chains to smaller regions,and then the segments belonging to the different blocks in the cyclic block copolymers have more chance to contact with each other.In this way,the cyclic block copolymers had better miscibility between segments belonging to different types of blocks,leading to the stronger stereocomplexation ability.