Topological structure of vortex solution in Jackiw-Pi model

By using phi-mapping method, we discuss the topological structure of the self-duality solution in Jackiw-Pi model in terms of gauge potential decomposition. We set up relationship between Chern-Simons vortex solution and topological number, which is determined by Hopf index and Brouwer degree. We also give the quantization of flux in this case. Then, we study the angular momentum of the vortex, which can be expressed in terms of the flux.

Topological constraints on scroll and spiral waves in excitable media

A conservation equation for topological charges of phase singularities (scroll and spiral waves) in excitable media is given. It provides some topological properties of scroll (spiral) waves: for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using phi-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a 6 function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of phi-mapping. In our solution, the flux of this soliton is naturally quantized.

a computational proof of complexity of some restricted counting problems

South Central University

Topological Diversity of Coordination Polymers Containing the Rigid Terephthalate and a Flexible N,N'-Type Ligand: Interpenetration, Polyrotaxane, and Polythreading

Reactions of zinc(II) or cadmium(II) salts with terephthalic acid (H(2)tp) and 1,3-bis(4-pyridyl) propane (bpp) have afforded four coordination polymers at room temperature, [Zn(mu-tp)(mu-bpp)](n)center dot 2nH(2)O (1), [Cd-2(mu-tp)(2)(mu-bpp)(3)](n)center dot 2nH(2)O (2), [Cd(mu-tp)(mu-bpp)(H2O)](n)center dot nH(2)O (3), and [Cd-2(mu-tp)(mu-bpp)(2)(bpp)(2)Br-2](n) (4). Single-crystal X-ray diffraction has revealed interesting topological features for these compounds.

Two new Cu-II coordination polymers: Studies of topological networks and water clusters

Two new Cull coordination polymers, namely [Cu-2(BDC)(2)(L)(4)(H2O)(2)]center dot 14H(2)O (1) and [Cu-1.5(BTC)(L)(1.5)(H2O)(0.5)]center dot 2H(2)O (2), where L = 1,1'-(1,4-butanediyl)bis(imidazole), BDC = 1,4-benzene dicarboxylate, and BTC = 1,3,5-benzenetricarboxylate, have been synthesized at room temperature. Complex 1 exhibits an unusual, square-planar, four-connected 2D (2)(6)4 net, which has been predicated by Wells. Interestingly, three types of water clusters, namely (H2O)(6), (H2O)(8), and (H2O)(10), are observed in the hydrogen-bonded layers constructed by the BDC ligands and water molecules. The BTC anion in compound 2 is coordinated to the Cu" cation as tetradentate ligand to form a (6(6))(2)(4(2)6(4)8(4))(2)(6(4)810) net containing three kinds of nonequivalent points, Thermogravimetric analyses (TGA) and IR spectra for 1 and 2 are also discussed in detail.

Extended topological indices and prediction of activities of chiral compounds

The activities/properties of two molecules with identical formula but different configuration states of the asymmetric atoms are different. Thus, usually the common topological indices are not suitable. In this study, the chiral topological indices were obtained by extending A(mi) indices suggested by our laboratory and molecular connectivity indices. The modified topologial indices have been used for the studies on D2 for dopamine receptor and a receptor activities of fourteen N-alkylated 3-(3-hydroxypyenyl)-piperidines. It has been observed that selected variables possess low correlations. The results obtained by using multiple regression analysis and artificial neural networks are satisfactory.

Computer perception of topological symmetry by all-paths algorithm

During the development of our ESESOC system (Expert System for the Elucidation of the Structures of Organic Compounds), computer perception of topological symmetry is essential in searching for the canonical description of a molecular structure, removing the irredundant connections in the structure generation process, and specifying the number of peaks in C-13- and H-1-NMR spectra in the structure evaluation process. In the present paper, a new path identifier is introduced and an algorithm for detection of topological symmetry from a connection table is developed by the all-paths method. (C) 1999 Elsevier Science B.V. All rights reserved.