Synthesis of silylene-vinylene oligomers via catalytic polycondensation of divinyldimethylsilane

Acyclic diene polymerization (ADP) of divinyldimethylsilane in the presence of ruthenium RuCl₂(PPh₃)₃ and rhodium [RhCl(cod)]₂ catalysts led predominantly to linear silylene-vinylene oligomers (M_n = 1510 and M_w/M_n = 1.19) if the ruthenium catalyst was used or to mixture of cyclic and linear oligomers if rhodium complex was catalyst. © 1996 John Wiley & Sons, Inc.     

Theoretical studies on the infrared spectrum of the tetrahedral molecules R<Subscript>2</Subscript>MH<Subscript>2</Subscript> (R = D(H), CH<Subscript>3</Subscript>, OH; M = Ti,Zr, Hf)

Using Stuttgart/Dresden effective core potentials MWB28, MWB60, and GTO valence basis sets (8s7p6d)/[6s5p3d], (8s7p6d)/[6s5p3d] for Zr and Hf atoms and 6-311++G(3df,3pd) basis set for C, H, O, and Ti atoms, tight convergence criteria geometry optimizations and harmonic frequency calculations are performed at B3LYP and B3LYP/IEF-PCM levels of theory so as to model the gas phase and argon matrix infrared spectra of the tetrahedral molecules R₂MH₂ (R = D(H), CH₃, OH; M = Ti, Zr, Hf). Influence of the transition metal and/or substituent group on the symmetric and asymmetric stretching frequencies of the MH₂ fragment of the R₂MH₂ molecules is investigated at both the levels of theory. The modelling of the argon matrix effect improves the agreement between the calculated frequencies and the experimental ones. The calculated argon matrix to gas phase frequency shifts is compared reasonably to the experimental argon to neon matrix shifts.     

Nonnormality and stochastic differential equations

A highly nonnormal Jacobian may give rise to large transients. This behaviour has been shown to have implications for (a) the relevance of linearising a nonlinear system and (b) the timestep restrictions required to keep a numerical method stable. Here, we show that nonnormality also manifests itself for stochastic differential equations. We give an example of a family of systems that is stable without noise, but can be made exponentially unstable in mean-square by a noise perturbation that shrinks to zero as the nonnormality increases. We then show via finite-time convergence theory that an Euler approximation shares the same property, giving a discrete analogue of the result. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65C30, 34F05     

The Influence of Different Bleaching Protocols on Dentinal Enzymatic Activity: An In Vitro Study

This study aimed to investigate matrix metalloproteinase (MMP) activity in human dentin using in-situ and gelatin zymography, after at-home and in-office bleaching, related to their clinical exposure times. Dentin specimens (n = 5) were treated with 35% hydrogen peroxide (50 min per session/4 sessions), 10% carbamide peroxide (180 min/21 sessions), or no treatment. All were subjected to in-situ zymography. Dentin slices were, subsequently, obtained, covered with fluorescein-conjugated gelatin, and examined with confocal laser-scanning microscopy. The fluorescence intensity was quantified and statistically analyzed using one-way ANOVA and Bonferroni tests (α = 0.05). Furthermore, gelatin zymography was performed on protein extracts obtained from dentin powder (N = 8 teeth), treated with hydrogen peroxide or carbamide peroxide, with different exposure times (10/50 min for hydrogen peroxide; 252/1260 min for carbamide peroxide). The results of the in-situ zymography showed no statistical differences between the bleached specimens and the control group, with a medium level of gelatinolytic activity expressed in the dentin tubules. The results of gelatin zymography showed an increased expression of pro-MMP-9 in carbamide peroxide groups. The expression of pro-MMP-2 decreased in all the experimental groups. The bleaching treatments performed on the enamel of sound teeth do not influence dentinal enzymatic activity. However, when unprotected dentin tissue is bleached, matrix metalloproteinases are more expressed, particularly when carbamide peroxide is used, proportional to the exposure time.     

A Hybrid Method Using HAVOK Analysis and Machine Learning for Predicting Chaotic Time Series

The prediction of chaotic time series systems has remained a challenging problem in recent decades. A hybrid method using Hankel Alternative View Of Koopman (HAVOK) analysis and machine learning (HAVOK-ML) is developed to predict chaotic time series. HAVOK-ML simulates the time series by reconstructing a closed linear model so as to achieve the purpose of prediction. It decomposes chaotic dynamics into intermittently forced linear systems by HAVOK analysis and estimates the external intermittently forcing term using machine learning. The prediction performance evaluations confirm that the proposed method has superior forecasting skills compared with existing prediction methods.     

The nonidealness index of rank-ideal matrices

A polyhedron is integral if all its extreme points have 0, 1 components and in this case the matrix M is called ideal. When Q has fractional extreme points, there are different ways of classifying how far M is away from being ideal, through the polyhedral structure of Q. In this sense, Argiroffo, Bianchi and Nasini (2006) [1] defined a nonidealness index analogous to an imperfection index due to Gerke and McDiarmid (2001) [10].In this work we determine the nonidealness index of rank-ideal matrices (introduced by the authors (2008)). It is known that evaluating this index is NP-hard for any matrix. We provide a tractable way of evaluating it for most circulant matrices, whose blockers are a particular class of rank-ideal matrices, thereby following similar lines as done for the imperfection ratio of webs due to Coulonges, Pêcher and Wagler (2009) [7].Finally, exploiting the properties of this nonidealness index, we identify the facets of the set covering polyhedron of circulant matrices, having maximum strength with respect to the linear relaxation, according to a measure defined by Goemans (1995) [9].     

Covering and radius-covering arrays: Constructions and classification

The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For some of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays.     

Fast algorithms for placing large entries along the diagonal of a sparse matrix

Solving a sparse system of linear equations Ax=b is one of the most fundamental operations inside any circuit simulator. The equations/rows in the matrix A are often rearranged/permuted before factorization and applying direct or iterative methods to obtain the solution. Permuting the rows of the matrix A so that the entries with large absolute values lie on the diagonal has several advantages like better numerical stability for direct methods (e.g., Gaussian elimination) and faster convergence for indirect methods (such as the Jacobi method). Duff (2009) [3] has formulated this as a weighted bipartite matching problem (the MC64 algorithm). In this paper we improve the performance of the MC64 algorithm with a new labeling technique which improves the asymptotic complexity of updating dual variables from O(|V|+|E|) to O(|V|), where |V| is the order of the matrix A and |E| is the number of non-zeros. Experimental results from using the new algorithm, when benchmarked with both industry benchmarks and UFL sparse matrix collection, are very promising. Our algorithm is more than 60 times faster (than Duff’s algorithm) for sparse matrices with at least a million non-zeros.     

具有时变滞后的随机系统的时滞依赖鲁棒稳定性与H_∞分析

研究具有时变滞后与Markov跳跃的随机系统的鲁棒随机稳定性与H_∞分析.通过引进随机Liapunov-Krasovskii泛函,使用自由权矩阵技术(即何技术),得到时滞依赖鲁棒随机稳定性与H_∞扰动衰减的线性矩阵不等式判据.3个数值例子说明提供的方法是有效的,并且与相关文献中存在的一些结果相比是低保守的.     

单函数(A,Γ)小波的存在性问题

小波分析是除了Fourier分析和Gabor分析以外一种新的时频分析工具．它被应用在信号处理、图像处理以及许多其他领域．小波分析的—个基本问题是什么样的(A,Γ)对,使得存在单函数(A,Γ)小波.本文填补了Ionascu,Yang Wang关于单函数小波存在性问题在二维情形论证中的漏洞.