New fatty acid derivatives based on barbiturates and other cyclic β-dicarbonyl compounds and an acyl migration

The use of DCC, triethylamine and 4-dimethylaminopyridine in dichloromethane provides a general and standard one-pot procedure for the O-acylation of cyclic β-dicarbonyl compound derivatives (1) with palmitic and stearic acids which have long hydrocarbon tails, to synthesis of new type of fatty acid derivative in good to excellent yields. Structure elucidation was carried out by FT-IR, ¹H NMR and ¹³C NMR spectroscopy techniques. The acyl migration was also found in results and the corresponding structure was characterized by X-ray crystallography. A proposed mechanism was discussed for the formation of products.     

Regioselective One‐pot Synthesis of New Unsymmetric Spiro Dihydrofurans in the Reaction of Mixed Two Different Cyclic β‐Dicarbonyl Compounds with BrCN and Aldehydes in the Presence of Et3N

Crossed one‐pot reaction of mixed cyclic β‐dicarbonyl with various aldehydes in the presence of cyano gen bromide and triethylamine leads to the selective and efficient formation of crossed new unsymmetri cal spiro dihydrofurans at room temperature. The products were obtained in good to excellent yields. Structure elucidation was carried out by ¹H NMR, ¹³C NMR, FT‐IR spectroscopy, Mass analyses and X‐ray crystallography technique. A proposed mechanism was discussed for the formation of products.     

Preparation and characterization of copper(II) tetrasulfonated phthalocyanine nanoparticles formed by laser ablation in poor solvents

Laser irradiation of copper(II) tetrasulfonated phthalocyanine (CuTsPc) microcrystals in poor organic solvents such as methanol, 2-methyl-2-propanol, ethanol, tetrahydrofuran, and acetone has produced CuTsPc nanoparticles with 15–112 nm in diameter. Field emission scanning electron microscopy (FESEM) images have shown the formation of CuTsPc nanoparticles in poor organic solvents used in this work. The mean diameters of CuTsPc nanoparticles obtained from transmission electron microscopy (TEM) images in methanol, 2-methyl-2-propanol, ethanol, tetrahydrofuran, and acetone were determined to be 26, 36, 35, 86, and 78 nm, respectively. A correlation between the size of CuTsPc nanoparticles and a solvent polarity could be found in this work.     

Self-Concordant Barriers for Convex Approximations of Structured Convex Sets

We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems.     

多自由度Maxwell阻尼器减震结构(Ⅱ)——等效阻尼

对多自由度带支撑Maxwell阻尼器减震结构的等效阻尼比进行了系统研究。构建了耗能结构一般微分和积分混合地震响应方程组;基于与多自由度随机平均法分析完全相同的等效准则,建立了耗能结构各振型等效阻尼比的一般解析计算式。与一些典型问题的模态应变能法的计算精度进行对比分析,结果显示:本文方法的计算结果在特定条件下与精确解完全相同;在一个二自由度系统中相对位移响应方差的误差分别为0.99%和0.45%,优于应变能法的8%和5.4%,表明了本文方法的有效性。从而为建立此类耗能结构等效阻尼分析的完备解析解法、直接应用反应谱法进行实际工程设计提供了依据。     

Clustering via minimum volume ellipsoids

We propose minimum volume ellipsoids (MVE) clustering as an alternative clustering technique to k-means for data clusters with ellipsoidal shapes and explore its value and practicality. MVE clustering allocates data points into clusters in a way that minimizes the geometric mean of the volumes of each cluster’s covering ellipsoids. Motivations for this approach include its scale-invariance, its ability to handle asymmetric and unequal clusters, and our ability to formulate it as a mixed-integer semidefinite programming problem that can be solved to global optimality. We present some preliminary empirical results that illustrate MVE clustering as an appropriate method for clustering data from mixtures of “ellipsoidal” distributions and compare its performance with the k-means clustering algorithm as well as the MCLUST algorithm (which is based on a maximum likelihood EM algorithm) available in the statistical package R. Research of the first author was supported in part by a Discovery Grant from NSERC and a research grant from Faculty of Mathematics, University of Waterloo. Research of the second author was supported in part by a Discovery Grant from NSERC and a PREA from Ontario, Canada.     

An axiomatic duality framework for the theta body and related convex corners

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the corresponding antiblocking duality relations. Our framework describes several semidefinite and polyhedral relaxations of the stable set polytope of a graph as generalized theta bodies. As a by-product of our approach, we introduce the notion of “Schur Lifting” of cones which is dual to PSD Lifting (more commonly used in SDP relaxations of combinatorial optimization problems) in our axiomatic generalization. We also generalize the notion of complements of graphs to diagonally scaling-invariant polyhedral cones. Finally, we provide a weighted generalization of the copositive formulation of the fractional chromatic number by Dukanovic and Rendl from 2010.     

Growth and characterization of c-plane AlGaN on γ-LiAlO2

This study demonstrates a pure c-plane AlGaN epilayer grown on a γ-LiAlO₂ (1 0 0) (LAO) substrate with an AlN nucleation layer grown at a relatively low temperature (LT-AlN) by metal-organic chemical vapor deposition (MOCVD). The AlGaN film forms polycrystalline film with m- and c-plane when the nucleation layer grows at a temperature ranging from 660 to 680 °C. However, a pure c-plane AlGaN film with an Al content of approximately 20% can be obtained by increasing the LT-AlN nucleation layer growth temperature to 700 °C. This is because the nuclei density of AlN increases as the growth temperature increases, and a higher nuclei density of AlN deposited on LAO substrate helps prevent the deposition of m-plane AlGaN. Therefore, high-quality and crack-free AlGaN films can be obtained with a (0 0 0 2) ω-rocking curve FWHM of 547 arcsec and surface roughness of 0.79 nm (root-mean-square) using a 700-°C-grown LT-AlN nucleation layer.     

The stable set problem and the lift-and-project ranks of graphs

We study the lift-and-project procedures for solving combinatorial optimization problems, as described by Lovász and Schrijver, in the context of the stable set problem on graphs. We investigate how the procedures' performances change as we apply fundamental graph operations. We show that the odd subdivision of an edge and the subdivision of a star operations (as well as their common generalization, the stretching of a vertex operation) cannot decrease the N₀-, N-, or N₊-rank of the graph. We also provide graph classes (which contain the complete graphs) where these operations do not increase the N₀- or the N-rank. Hence we obtain the ranks for these graphs, and we also present some graph-minor like characterizations for them. Despite these properties we give examples showing that in general most of these operations can increase these ranks. Finally, we provide improved bounds for N₊-ranks of graphs in terms of the number of nodes in the graph and prove that the subdivision of an edge or cloning a vertex can increase the N₊-rank of a graph.Research of these authors was supported in part by a PREA from Ontario, Canada and research grants from NSERC.Mathematics Subject Classification (2000): 0C10, 90C22, 90C27, 47D20