The combinatorial game Nofil played on Steiner triple systems

We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions.     

On bandwidth sums of graphs

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Cramér theorem on symmetric spaces of noncompact type

We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant.     

Characterizations of Kadec-Klee properties in symmetric spaces of measurable functions

We present several characterizations of Kadec-Klee properties in symmetric function spaces on the half-line, based on the -functional of J. Peetre. In addition to the usual Kadec-Klee property, we study those symmetric spaces for which sequential convergence in measure (respectively, local convergence in measure) on the unit sphere coincides with norm convergence.

     

Two-Arc Transitive Graphs and Twisted Wreath Products

The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x ^–1 for all x F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given.     

Estimations of subgraph positions in molecular graphs and their common subgraph peculiarities

Some questions emerged from electronic data processing of molecular structures (graphs) and its fragments have been considered in this work. Quantitative estimations of subgraph positions in molecular graphs are presented and some properties of their maximal common subgraphs are described.     

分子轨道图形理论中对称轴定理

本文试图以浅显明确的形式描述对称轴定理，使之能与对称面定理相媲美，并对对称轴定理作一定的扩展，给出分子轨道构造定理。     

Computer generation of chemical structures from known fragments

The interactive generation of chemical structures from given fragments is described and discussed. It is implemented as a part of our expert system CARBON, based on C-13 NMR spectra. As it is designed, this program can also be a useful tool in the structure elucidation process when information on parts of the structure is obtained by other means (IR, mass and other spectrometries, chemical analysis, other relevant information). The topological characteristics of candidate fragments are first chosen interactively and then the elements are connected in all topologically possible ways. In the following step, the topological building blocks are substituted by chemical structural fragments resulting in a set of all chemical structures consistent with the input information.     

The phonon-assisted proton transfer between hydrazinium cations in (N2H5)2HMF6·2H2O (M∈{Ga, Al, Fe}) type compounds. FT IR and quantum theoretical study

FT IR spectra of a series of compounds with a general formula (N₂H₅)₂HMF₆·2H₂O (where M∈{Ga, Al, Fe}) were recorded at variable temperatures (from ∼100 to 300 K, at 10 K intervals). The appearance of the spectral region of ν(N-N) modes due to hydrazinium cations further supports the conclusions regarding the N₂H₅⁺?H⁺?N₂H₅⁺ hydrogen bond potential well based on Raman spectroscopic data [J. Raman Spectrosc. 28 (1997) 315]. The appearance of two bands corresponding to the ν(N-N) modes in the low temperature FT IR spectra that merge into one upon heating is a clear evidence of a symmetric potential well through which a phonon-assisted proton transfer (PAPT) occurs at higher temperatures. Ab initio MP2/6-311++G(2d,p) quantum chemical study of the proton transfer potential within the N₂H₅⁺?H⁺?N₂H₅⁺ cluster confirmed its double-minimum character. The first-order saddle point found on the MP2/6-311++G(2d,p) potential energy hypersurface corresponds to a centrosymmetric structure (C_2h symmetry), with the proton placed at the inversion center. The potential energy curve along the tunnelling coordinate was calculated by the intrinsic reaction coordinate (IRC) methodology, leading to an adiabatic PT barrier height of 3.94 kcal mol⁻¹ and a tunneling rate of 1.98 s⁻¹. The corresponding MP4(SDTQ)/6-311++G(2d,p)//MP2/6-311++G(2d,p) value of the adiabatic PT barrier height is 4.26 kcal mol⁻¹.     

Comparison between the pervaporation and vapor permeation performances of polycarbonate membranes

The pervaporation and vapor permeation performance of symmetrical and asymmetrical polycarbonate membranes, prepared via a dry-phase inversion and wet-phase inversion methods, respectively, were studied by measuring the permeation rate and separation factor. It was found that the polymer concentration effect on the pervaporation performance for the symmetrical polycarbonate membrane was lower than that for the asymmetrical polycarbonate membrane. Compared with pervaporation, vapor permeation has a significantly increased separation factor with a decreased permeation rate for the symmetrical polycarbonate membrane. Water molecules preferentially dissolve into the symmetrical polycarbonate membrane and diffuse easily through the membrane.