Vibrational Distributions of N2 (A3∑+u) in the nitrogen afterglow

Absolute populations of the lowest six vibrational levels of N₂ (A³∑⁺_u) have been measured under various conditions in the Lewis-Rayleigh afterglow of nitrogen for the first time. These vibrational distributions are interpreted in terms of a simple kinetic model which permits the evaluation of rate constants for vibrational relaxation of the A-state levels by V-V energy transfer to ground state nitrogen molecules.     

Performance Analysis of Cyclical Simulated Annealing Algorithms

Generalized hill climbing (GHC) algorithms provide a framework for modeling local search algorithms for addressing intractable discrete optimization problems. Measures for assessing the finite-time performance of GHC algorithms have been developed using this framework, including the expected number of iterations to visit a predetermined objective function value level. This paper analyzes how the expected number of iterations to visit a predetermined objective function value level can be estimated for cyclical simulated annealing. Cyclical simulated annealing uses a cooling schedule that cycles through a set of temperature values. Computational results with traveling salesman problem instances taken from TSPLIB show how the expected number of iterations to visit solutions with predetermined objective function levels can be estimated for cyclical simulated annealing.AMS 2000 Subject Classification 90-08 Computational Methods: Local Search, 90C59 Heuristics: Simulated Annealing     

Spatial photorelease of oligonucleotides, using a safety-catch photolabile linker

[reaction: see text] We report the development of a safety-catch photolabile linker that allows the light-directed synthesis and spatially selective photorelease of oligonucleotides from microarrays. The linker remains stable to light during DNA synthesis, and is activated for photorelease after acidic hydrolysis. We demonstrate that the photoreleased oligonucleotides can be amplified by PCR to produce double stranded DNA. The advantages offered by this linker could aid the development of an automated gene synthesis platform.     

Some congruences modulo 5 and 25 for overpartitions

We present two new Ramanujan-type congruences modulo 5 for overpartitions. We also give an affirmative answer to a conjecture of Dou and Lin, which includes four congruences modulo 25 for overpartition.     

Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions

A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.     

A set oriented definition of finite-time Lyapunov exponents and coherent sets

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron–Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron–Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.     

Central Sets and Radii of the Zero-Divisor Graphs of Commutative Rings

For a commutative ring R with identity, the zero-divisor graph, Γ(R), is the graph with vertices the nonzero zero-divisors of R and edges between distinct vertices x and y whenever xy = 0. This article gives a proof that the radius of Γ(R) is 0, 1, or 2 if R is Noetherian. The center union {0} is shown to be a union of annihilator ideals if R is Artinian. The diameter of Γ(R) can be determined once the center is identified. If R is finite, then the median is shown to be a subset of the center. A dominating set of Γ(R) is constructed using elements of the center when R is Artinian. It is shown that for a finite ring R ? ?₂ × F for some finite field F, the domination number of Γ(R) is equal to the number of distinct maximal ideals of R. Other results on the structure of Γ(R) are also presented.     

Additive‐dependent iptycene incorporation in polyanilines: Insights into the pentiptycene clipping effect and the polymerization mechanism

Despite the long history of polyaniline chemistry, backbone‐substituted polyanilines are limited. Here, we report the synthesis of pentiptycene‐incorporated polyanilines through acidic aniline oxidative polymerization with three pentiptycene derivatives, TA, DA, and TP, as nucleate additives. The reactivity of TA > DA ? TP, as evidenced by structural and property analysis of the corresponding polyaniline products, demonstrates a radical coupling mechanism and the formation of Dewar π‐complex intermediates for the chain propagation. In addition, the iptycene substituent effect on enhancing the electrochemical stability and charge storage capability of polyaniline are discussed with a clip model, namely, the threading of neighboring polyaniline chains through the U‐ and V‐shaped cavities of pentiptycene restricts lateral motions of the polymer chains and promotes interchain conductivity. Density function theory (DFT) calculations suggest a larger clipping effect for the U versus V cavities. Both the conclusion of a terminal planar p‐phenylenediamine (ppda) group being the key component of an effective nucleate and the concept of interchain clipping for enhanced electrochemical performance should facilitate the design and synthesis of novel polyanilines for electronic applications.     

Raising the bar on-bead: Efficient on-resin synthesis of α-conotoxin LvIA

α4/7-Conotoxin LvIA is an isoform-selective inhibitor of the α3β2 nicotinic acetylcholine receptor. An efficient strategy for the synthesis of this toxin is critical to advancing its utility as a probe for receptor function and as a potential pharmaceutical lead target. On-resin methods for peptide synthesis offer potential synthetic advantages; however, strategies for on-resin formation of multiple disulfides have historically been low-yielding. Here, we harness the reactivity of the Allocam protecting group and employ a 3-amino acid spacer strategy to synthesize α4/7-conotoxin LvIA via three different on-resin strategies, each of which results in an isolated yield higher than previous fully on-resin approaches.