Steroidal Alkaloids from Veratrum maackii Regel with Genotoxicity on Brain‐Cell DNA in Mice

Two new steroidal alkaloids, 23‐methoxycyclopamine 3‐O‐β‐D ‐glucopyranoside ( 1 ) and isoecliptalbine ( 2 ), were isolated from the root and rhizoma of Veratrum maackii Regel , together with five known compounds, i.e., verussurine ( 3 ), verabenzoamine ( 4 ), verazine ( 5 ), isoverazine ( 6 ), and verazinine ( 7 ). Their structures were established by extensive analysis of spectroscopic data, as well as by comparison with literature data. Compounds 1 – 7 could cause DNA damage in the cerebellum and cerebral cortex of mice in a dose‐dependent manner by using single‐cell gel electrophoresis (comet assay).     

Strong influence of a small fiber on shear stress in fiber-reinforced composites

In stiff fiber-reinforced composites, it has been known that the shear stress increases at the rate of as the distance ? between adjacent fibers approaches 0. This paper reveals a strong influence of a combination of a triple fiber, as well as the distance between a pair of fibers, on the blow-up so that the stress concentration can be significantly accelerated by adding a small fiber in-between fibers. Specifically, if a fiber F₂ with a small diameter δ is located in-between fibers F₁ and F₃, ?₁=dist(F₁,F₂) and ?₂=dist(F₂,F₃), then the stress blows up at the exact rates of and between F₁ and F₂ and between F₂ and F₃, respectively. This estimate still holds even when a part of F₂ overlaps with F₃. The magnification factor yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods.     

Slow-fast Bogdanov-Takens bifurcations

In this paper we study perturbations from planar vector fields having a line of zeros and representing a singular limit of Bogdanov-Takens (BT) bifurcations. We introduce, among other precise definitions, the notion of slow-fast BT-bifurcation and we provide a complete study of the bifurcation diagram and the related phase portraits. Based on geometric singular perturbation theory, including blow-up, we get results that are valid on a uniform neighborhood both in parameter space and in the phase plane.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? 23" alt="View the MathML source" title="View the MathML source" src="http://ars.sciencedirect.com/content/image/1-s2.0-S0022247X1100062X-si2.gif"> transformation formula.     

Matrix algebras with Multiplicative Decomposition Property

We consider the Multiplicative Decomposition Property (the multiplicative analogue of the Riesz Decomposition Property) for entry-wise ordered matrix algebras over the reals. We characterize for which matrix pairs such a decomposition exists and use this result to present necessary and sufficient conditions for a matrix algebra to enjoy the decomposition property by all its positive matrix pairs. Thus we describe all matrix algebras with the decomposition property.     

On the stability of a domain-wall brane model

We establish stability and nonstability results for a domain-wall brane model arising in classical field theory. In particular, we show the nonexistence of nontrivial bounded solutions on the real line for a coupled pair of parameter dependent linear second order ordinary differential equations for an open set of those parameters. Moreover, we establish the existence of nontrivial solutions for a hypersurface of the parameters. We use Fredholm theory for compact linear operators combined with the Lyapunov-Schmidt method to prove our results. The model is stable, respectively unstable, for those parameters for which the coupled system does not, respectively does, have nontrivial solutions.     

Classification of the centers and their isochronicity for a class of polynomial differential systems of arbitrary degree

In this paper we classify the centers localized at the origin of coordinates, and their isochronicity for the polynomial differential systems in R² of degree d that in complex notation z=x+iy can be written as where j is either 0 or 1. If j=0 then d?5 is an odd integer and n is an even integer satisfying 2?n?(d+1)/2. If j=1 then d?3 is an integer and n is an integer with converse parity with d and satisfying 0<n?[(d+1)/3] where [⋅] denotes the integer part function. Furthermore λ∈R and A,B,C,D∈C. Note that if d=3 and j=0, we are obtaining the generalization of the polynomial differential systems with cubic homogeneous nonlinearities studied in K.E. Malkin (1964) [17], N.I. Vulpe and K.S. Sibirskii (1988) [25], J. Llibre and C. Valls (2009) [15], and if d=2, j=1 and C=0, we are also obtaining as a particular case the quadratic polynomial differential systems studied in N.N. Bautin (1952) [2], H. Zoladek (1994) [26]. So the class of polynomial differential systems here studied is very general having arbitrary degree and containing the two more relevant subclasses in the history of the center problem for polynomial differential equations.     

Spin-Spin Relaxation Process of 23Na-NMR in Na-Loaded NaY

Abstract

Spin-spin relaxation of ²³Na-NMR is observed by the spin echo method at room temperature for Y-type zeolite loaded with Na metal without hydration. For saturated and no levels of loading, the echo decay is well fitted by single exponential function. T ₂ decreases to be 0.25 times smaller by loading. This decrease of T ₂ is explained semiquantitatively with assuming nuclear dipole-dipole interaction between neighboring Na.     

Coupling constants in the direct configuration interaction method

A general algorithm of evaluation of the coefficients of molecular integrals (coupling constants) appearing in the direct configuration interaction method is derived. The configurations are assumed to be spin-adapted antisymmetrized products of orthonormal orbitals. No limitation is imposed either upon the reference state (the number of the singly occupied orbitals may be arbitrary) or upon the excitation multiplicity.     

Multicoloring and Mycielski construction

The generalized Mycielskians of graphs (also known as cones over graphs) are the natural generalization of the Mycielskians of graphs (which were first introduced by Mycielski in 1955). Given a graph G and any integer p?0, one can transform G into a new graph μ_p(G), the p-Mycielskian of G. In this paper, we study the kth chromatic numbers χ_k of Mycielskians and generalized Mycielskians of graphs. We show that χ_k(G)+1?χ_k(μ(G))?χ_k(G)+k, where both upper and lower bounds are attainable. We then investigate the kth chromatic number of Mycielskians of cycles and determine the kth chromatic number of p-Mycielskian of a complete graph K_n for any integers k?1, p?0 and n?2. Finally, we prove that if a graph G is a/b-colorable then the p-Mycielskian of G, μ_p(G), is (at+b^p+1)/bt-colorable, where 23" border="0" style="vertical-align:bottom" width="161" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0012365X0700502X-si12.gif">. And thus obtain graphs G with m(G) grows exponentially with the order of G, where m(G) is the minimal denominator of a a/b-coloring of G with χ_f(G)=a/b.