Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

Structural Features of Solid Phases and Topology of Phase Diagrams

The paper considers model phase diagrams of binary and ternary systems involving transformations (transitions) of phase equilibria. The relationship between the type of structural solidstate transformation and the type of phase diagram is shown. Topological series of phase diagrams of systems with continuous and limited types of solid solutions are considered, including phase diagrams with polymorphic transitions between intermediate solid phases of variable composition.     

Pion absorption by16O using realistic interactions—II: Free pion absorption followed by emission of proton

Matrix element of the Gallilean invariant nonrelativistic reduction of the pseudoscalar-pseudovector interaction has been calculated for free pion absorption by a single nucleon inside the nucleus of¹⁶O. The Hartree-Fock wavefunctions obtained with the unitary-model-operator approach starting with the hard-core nucleon-nucleon interaction have been used for the π-capturing nucleon in the initial state. The initial pion distortion in the presence of nuclear field of the absorbing nucleus prior to its absorption together with the Coulomb interaction with the finite nuclear size has been taken into account. The distortion of the emitted proton in the field of the residual nucleus has also been considered. The differential cross-sections have been obtained and calculated results are compared with the previous experimental and theoretical work.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Influence of branch length asymmetry on the electrophoretic mobility of rigid rod-like DNA

The electrophoretic mobility of three-arm asymmetric star DNA molecules, produced by incorporating a short DNA branch at the midpoint of rigid-rod linear DNA fragments, is investigated in polyacrylamide gels. We determine how long the added branch must be to separate asymmetric star DNA from linear DNA with the same total molecular weight. This work focuses on two different geometric progressions of small DNA molecules. First, branches of increasing length were introduced at the center of a linear DNA fragment of constant length. At a given gel concentration, we find that relatively small branch lengths are enough to cause a detectable reduction in electrophoretic mobility. The second geometric progression starts with a small branch on a linear DNA fragment. As the length of this branch is increased, the DNA backbone length is decreased such that the total molar mass of the molecule remains constant. The branch length was then increased until the asymmetric branched molecule becomes a symmetric three-arm star polymer, allowing the effect of molecular topology on mobility to be studied independent of size effects. DNA molecules with very short branches have a mobility smaller than linear DNA of identical molar mass. The reason for this change in mobility when branching is introduced is not known, however, we explore two possible explanations in this article. (i) The branched DNA could have a greater interaction with the gel than linear DNA, causing it to move slower; (ii) the linear DNA could have modes of motion or access to pores that are unavailable to the branched DNA.     

Topological effect on MO energies,IV. The total π-electron energy ofS- andT-isomers

A novel general property of theS- andT-isomers (a concept which has been introduced and elaborated elsewhere^{1, 2}) of alternant hydrocarbons is demonstrated, namely that due to the HMO total -electron energy theS-isomer should always be more stable than theT-isomer. Some other classes of conjugated isomers are also constructed, for which similar inequalities are derived.

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Topologischer Effekt bei MO-Energien, 4. Mitt.: Die -Elektronen-Gesamtenergie vonS- undT-Isomeren

Zusammenfassung Es wird allgemein gezeigt, daß bei einemS-T-Isomerenpaar (beschrieben in^{1, 2}) eines alternierenden Kohlenwasserstoffes infolge der HMO -Elektronen-Gesamtenergie dasS-Isomere stets stabiler sein sollte als dasT-Isomere. Weitere Klassen konjugierter Isomere werden konstruiert und ähnliche Ungleichungen angegeben.

     

用气相色谱法测定轻苯干点

研究用气相色谱法代替蒸馏法测定不含萘的轻苯干点。轻苯中1，3，5－三甲苯、1，2，4－三甲苯和茚的色谱峰高之和与轻苯的干点呈线性关系，回归方程为Y＝0.521X-69.2954，线性范围为130－153℃，相关系数为r=0.9997。该方法的相对标准偏差为3.98%；经F检验和t检验证明，该方法与蒸馏法测定结果无显著性差异。     

The topology of energy hypersurfaces III. The fundamental group of reaction mechanisms on potential energy hypersurfaces

The family of all possible reaction mechanisms on a potential surface has an algebraic structure with potential applications in quantum chemical molecular design and synthesis planning.Transformation properties and equivalence relations of reaction paths on potential energy hypersurfaces lead to a topological definition of reaction mechanisms. The family of all fundamental reaction mechanisms on the hypersurface has a group structure,the fundamental group of an appropriately defined topological space. Isomorphism and homomorphism relations between fundamental groups of reaction mechanisms are used to characterize the chemically important topological properties of various subsets of a hypersurface, or those of different excited state hypersurfaces.     

Three-dimensional quantum dynamics study of vibrational predissociation of HeI_2 van der Waals molecule for low vibrational excitation using the time-dependent wave packet method

Three-dimensional quantum mechanical calculations for vibrational predissociation of HeI2(B) van der Waals molecules are presented using the time-dependent wave packet technique within the golden rule approxima tion.The total and partial decay widths,lifetimes,rates and their dependence on initial vibrational states were obtained for HeI2 at low initial vibrational excited levels.Our calculations show that the calculated tota decay widths,lifetimes and rates agree well with those extrapolated from experimental data available The predicted total decay widths as a function of initial vibrational states exhibit highly nonlinear behavior.The very short propagation time (less.than 1 ps) required in the golden rule wave packet calculation is determined by the duration time of the final state inter-action between the fragments on the vibrationally deexcited adiabatic potential surface.The final state interaction between the fragments is shown to play an important role in determining the final rotational distri