Study of shape isomer yields of ~（240）Am in the framework of a dynamical-statistical model

A dynamical statistical model is used to analyze the experimental shape isomer yields data in the reaction d＋240Pu at E=20–29 MeV.The possibility of determining the nuclear dissipation is discussed.Comparison of the experimental data with the calculations leads to a value of the reduced dissipation coeffcient β=0.45×1021 s-1 for the Am isotopes.     

Equimatchable claw-free graphs

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm.     

Structure and Mechanical Properties of 50/50 NR/SBR Blend/Pristine Clay Nanocomposites

A blend/clay nanocomposites of 50/50 (wt%) NR/SBR was prepared via mixing the latex of a 50/50 NR/SBR blend with an aqueous clay dispersion and co‐coagulating the mixture. The structure of the nanocomposite was characterized by transmission electron microscopy (TEM) and X-ray diffraction (XRD). Nanocomposites containing less than 10 phr clay showed a fully exfoliated structure. After increasing the clay content to 10 phr, both nonexfoliated (stacked layers) and exfoliated structures were observed in the nanocomposites. The results of mechanical tests showed that the nanocomposites presented better mechanical properties than clay‐free NR/SBR blend vulcanizate. Furthermore, tensile strength, tensile strain at break, and hardness (shore A) increased with increasing clay content, up to 6 phr, and then remained almost constant.     

Non-Commuting Graphs of Nilpotent Groups

Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph Γ _G associated to G is the graph whose vertex set is G?Z(G) and two distinct elements x, y are adjacent if and only if xy ≠ yx. We prove that if G and H are non-abelian nilpotent groups with irregular isomorphic non-commuting graphs, then |G| = |H|.     

Positive definite superfunctions and unitary representations of lie supergroups

For a broad class of Fréchet-Lie supergroups $ \mathcal{G} $ , we prove that there exists a correspondence between positive definite smooth (resp., analytic) superfunctions on $ \mathcal{G} $ and matrix coefficients of smooth (resp., analytic) unitary representations of the Harish-Chandra pair (G, $ \mathfrak{g} $ ) associated to $ \mathcal{G} $ . As an application, we prove that a smooth positive definite superfunction on $ \mathcal{G} $ is analytic if and only if it restricts to an analytic function on the underlying manifold of $ \mathcal{G} $ . When the underlying manifold of $ \mathcal{G} $ is 1-connected we obtain a necessary and sufficient condition for a linear functional on the universal enveloping algebra U( $ {{\mathfrak{g}}_{\mathbb{C}}} $ ) to correspond to a matrix coefficient of a unitary representation of (G, $ \mathfrak{g} $ ). The class of Lie supergroups for which the aforementioned results hold is characterised by a condition on the convergence of the Trotter product formula. This condition is strictly weaker than assuming that the underlying Lie group of $ \mathcal{G} $ is a locally exponential Fréchet-Lie group. In particular, our results apply to examples of interest in representation theory such as mapping supergroups and diffeomorphism supergroups.     

A condition on finitely generated soluble groups

In this note we show that if Gis a finitely generated soluble group, then every infinite subset of Gcontains two elements generating a nilpotent group of class at most kif and only if Gis finite by a group in which every two generator subgroup is nilpotent of class at most k.     

Investigation of magnetic field effect on surface and finite-site free energy in one-dimensional Ising model of nanosystems

We investigate a one-dimensional (1-D) Ising model for finite-site systems. The finite-site free energy and the surface free energy are calculated via the transfer matrix method. We show that, at high magnetic fields, the surface free energy has an asymptotic limit. The absolute surface energy increases when the value of f (the ratio of magnetic field to nearest-neighbor interactions) increases, and for f?≥?10 approaches a constant value. For the values of f?≥?0.2, the finite-site free energy also increases, but slowly. The thermodynamic limit in which physical properties approach the bulk value is also explored.