Ladder pyrrolone structures with anthraquinone recurring units

1,2,4,5-Tetraaminoanthraquinone and 1,4,5,8-naphthalene-tetracarboxylic acid dianhydride react in dimethylacetamide to give a tetrameric prepolymer with balanced endgroups of anhydride and diamine. When this prepolymer is carefully treated with polyphosphoric acid at elevated temperature it is converted to a soluble polypyrrolone type structure with an inherent viscosity of 2.3–2.7. Polymers of this molecular weight can be wet-spun into pliable fibers from methanesulfonic acid. The TGA curve in air shows little weight loss below 550°C. The polymer can also be solubilized by reduction with sodium dithionite in alkaline aqueous dimethyl sulfoxide.     

Conformational Properties of the Phosphate Rings of Neutral Phosphoramidate Derivatives of Ribo- and 2′-Deoxyribonucleoside Cyclic 3′,5′-Monophosphates

Abstract

An investigation of the effects of changing the nature of X, nitrogen base (B), and amino substituent (R₂N) on the equilibrium 1?2 was carried out.

The influence of the above structural changes on the time-averaged coupling constants J_AP and J_BP, determined at 300 MHz, were used to follow changes in K_eq. With constant R₂N, small effects from variation of X and B were found. A large range in K_eq arose from changes in the steric size of R₂N. These results will be related to the question of the ease of chair to twist interconversion of the phosphate ring essential to the biological activities of the naturally occurring diesters, cAMP and cGMP.     

An Asymptotic Ratio in the Complete Binary Tree

Let T _n be the complete binary tree of height n considered as the Hasse-diagram of a poset with its root 1 _n as the maximum element. For a rooted tree T, define two functions counting the embeddings of T into T _n as follows A(n;T)=|{S T _n  : 1 _n ∈S, S≅T}|, and B(n;T)=|{S T _n :1 _n ∉S, S≅T}|. In this paper we investigate the asymptotic behavior of the ratio A(n;T)/B(n;T), and we show that lim  _n→∞[A(n;T)/B(n;T)]=2^ℓ;−1−1, for any tree T with ℓ leaves. This revised version was published online in June 2006 with corrections to the Cover Date.     

Maximum directed cuts in digraphs with degree restriction

For integers m, k≥1, we investigate the maximum size of a directed cut in directed graphs in which there are m edges and each vertex has either indegree at most k or outdegree at most k. © 2009 Wiley Periodicals, Inc. J Graph Theory     

Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.     

Runge–Kutta convolution quadrature for operators arising in wave propagation

An error analysis of Runge–Kutta convolution quadrature is presented for a class of non-sectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ ₀ and a polynomial bound \operatornameO(|s|^m₁){\operatorname{O}(|s|^{\mu_1})} there, the stronger polynomial bound \operatornameO(s^m₂){\operatorname{O}(s^{\mu_2})} in convex sectors of the form |\operatorname*arg s| ￡ p/2-q{|\operatorname*{arg} s| \leq \pi/2-\theta} for θ > 0. The order of convergence of the Runge–Kutta convolution quadrature is determined by μ ₂ and the underlying Runge–Kutta method, but is independent of μ ₁. Time domain boundary integral operators for wave propagation problems have Laplace transforms that satisfy bounds of the above type. Numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour of Runge–Kutta convolution quadrature for this class of applications. Our results show in particular that the full classical order of the Runge–Kutta method is attained away from the scattering boundary.     

Efficient long-time computations of time-domain boundary integrals for 2D and dissipative wave equation

Linear hyperbolic partial differential equations in a homogeneous medium, e.g., the wave equation describing the propagation and scattering of acoustic waves, can be reformulated as time-domain boundary integral equations. We propose an efficient implementation of a numerical discretization of such equations when the strong Huygens’ principle does not hold.For the numerical discretization, we make use of convolution quadrature in time and standard Galerkin boundary element method in space. The quadrature in time results in a discrete convolution of weights W_j with the boundary density evaluated at equally spaced time points. If the strong Huygens’ principle holds, W_j converge to 0 exponentially quickly for large enough j. If the strong Huygens’ principle does not hold, e.g., in even space dimensions or when some damping is present, the weights are never zero, thereby presenting a difficulty for efficient numerical computation.In this paper we prove that the kernels of the convolution weights approximate in a certain sense the time domain fundamental solution and that the same holds if both are differentiated in space. The tails of the fundamental solution being very smooth, this implies that the tails of the weights are smooth and can efficiently be interpolated. Further, we hint on the possibility to apply the fast and oblivious convolution quadrature algorithm of Schädle et al. to further reduce memory requirements for long-time computation. We discuss the efficient implementation of the whole numerical scheme and present numerical experiments.     

Oxygen-isotope labeled titania: Ti(18)O2

(18)O-isotope labelled titania (anatase, rutile) was synthesized. The products were characterized by Raman spectra together with their quantum chemical modelling. The interaction with carbon dioxide was investigated using high-resolution FTIR spectroscopy, and the oxygen isotope exchange at the Ti(18)O(2)/C(16)O(2) interface was elucidated.