Minimum energy configurations on a toric lattice as a quadratic assignment problem

We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since the last two bounds were not compared directly before, we prove that the SDP bound is stronger than the CQP bound. We then apply these to improve known bounds on a discrete energy minimization problem, reformulated as a QAP, which aims to minimize the potential energy between repulsive particles on a toric grid. Thus we are able to prove optimality for several configurations of particles and grid sizes, complementing earlier results by Bouman et al. (2013). The semidefinite programs in question are too large to solve without pre-processing, and we use a symmetry reduction method by Permenter and Parrilo (2020) to make computation of the SDP bounds possible.     

Complex homogeneous spaces of real groups with top homology in codimension two

SupposeX=G/H is a connected homogeneous complex manifold, whereG is a Lie group andH is a closed subgroup. Assume (X) and letG/H G/I be the holomorphic reduction ofX. If the top nonvanishing homology group ofX with coefficients in ₂ is in codimension two, then either a complex Lie group acts tansitively onG/I (see [3]) orG/I is biholomorphic to the unit disk.Partially supported by NSERC Grant A3494 and by the Deutsche Forschungsgemeinschaft     

Potential reduction method for harmonically convex programming

In this paper, we introduce a potential reduction method for harmonically convex programming. We show that, if the objective function and them constraint functions are allk-harmonically convex in the feasible set, then the number of iterations needed to find an -optimal solution is bounded by a polynomial inm, k, and log(1/). The method requires either the optimal objective value of the problem or an upper bound of the harmonic constantk as a working parameter. Moreover, we discuss the relation between the harmonic convexity condition used in this paper and some other convexity and smoothness conditions used in the literature.The authors like to thank Dr. Hans Nieuwenhuis for carefully reading this paper and the anonymous referees for the worthy suggestions.     

由水杨醇衍生的二苯并冠醚的合成和构型

将水杨醇在ＤＭＦ中与ＮａＨ和二甘醇或三某醇二对甲苯磺酸酯反，合成了２个新的二苯并冠醚（１和２），其结构由元素分析和波谱分析所表征，１ 射线衍射分析确定为反位构型，提出了合成反应的机理。     

A novel intumescent flame-retardant system containing metal chelates for polyvinyl alcohol

A novel flame retardant containing phosphorous-nitrogen structure, the ammonium salt of 2-hydroxyl-5,5-dimethyl-2,2-oxo-1,3,2-dioxapho sphorinane (PNOH), was synthesized and its structure was characterized by ¹H NMR and FTIR spectra. PNOH was used together with ammonium polyphosphate (APP) to prepare a novel intumescent flame retardant (IFR) for polyvinyl alcohol (PVA). When a few amounts (0.5%) of metal chelates were added, the flame retardancy of the IFR-PVA systems was significantly improved, having a high LOI value of 34.2 in a total IFR loading of 15 wt.%. In order to have an understanding of the resulting flame retardant effects, the thermal degradation behaviors of IFR-PVA systems were investigated by thermogravimetric analysis (TGA), and the morphology and structures of residues generated in different conditions were investigated by scanning electronic microscopy (SEM) and FTIR spectra. The results show that NiSAO can promote the thermal stability of the IFR-PVA; the residual char containing polyphosphoric or phosphoric acid is formed during the combustion; the formation of a continuous and dense char layer could inhibit the transmission of heat during contacting with flame and shows good flame retardancy.     

Electrochemical synthesis of 1,2,3,4,4,5,6-substituted 1,4-dihydropyridines

It has been shown that chemical oxidation of the methyl ester of 3,4,5-trimethoxycarbonyl-1,2,6-trimethyl-1,4-dihydropyridine to the pyridinium salt, requiring forcing experimental conditions, may be replaced by electrochemical oxidation. On electrochemical reduction of 3,4,5-trimethoxycarbonyl-1,2,6-trimethylpyridinium perchlorate in the presence of alkylating agents 1,2,3,4,4,5,6-substituted 1,4-dihydropyridines are obtained. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 226–237, February, 2007.     

高选择性透过二氧化硫气体分离膜的研究 （Ⅳ）不同烃基乙烯基亚砜接枝聚乙烯醇膜的透过性能

研究了不同烃基乙烯基亚砜接枝聚乙烯醇（ＰＶＡ－ＲＶＳＯ，Ｒ＝Ｍｅ，Ｅｔ，ｔ－Ｂｕ，Ｐｈ）膜对纯ＳＯ２、Ｎ２的透过性能以及ＳＯ２／Ｎ２混合气体的分离性能．结果表明上述膜对ＳＯ２具有高的选择性．对不同烃基乙烯基亚砜接枝膜进行了比较．     

A new Monte Carlo simulation for two models of self-avoiding lattice trees in two dimensions

By means of a new Monte Carlo sampling of a grand canonical ensemble, we verify universality for the critical exponents and of two models of lattice trees constrained to be self-avoiding on sites or on bonds. The attrition constants are also obtained. This algorithm, a generalization of that recently proposed by Berretti and Sokal for random walks, appears to optimize the critical slowing down in the scaling region. Systematic and statistical errors are carefully estimated.     

Extensive Studies on the AlEt3/THF-Promoted Diastereoselec-tive Tandem Rearrangement/Reduction of a-Hydroxy (Amino) Heterocyclopropane: An Efficient Approach to 2-Quaternary 1,3-Diheteroatom Units

Introduction Diastereoselective construction of 1,3-diheteroatom units, especially 1,3-amino alcohols and 1,3-diols, has always been in high demands in synthetic organic chemistry, as they are widely present in many natural products and potent drugs, such as nucleoside antibiot-ics and the HIV protease inhibitors.1,2 They have also been used as chiral ligands for asymmetric catalysts and as synthetic intermediates.3 Although several methods for the construction of 1,3-amino alcohols have been…     

Ozonolytic transformations of olefinic derivatives of L-menthol and ricinolic acid

Ozonolysis and reduction of olefinic derivatives of ricinolic acid and L-menthol were studied using hydroxylamine hydrochloride and sodium trisacetoxyborohydride to reduce the peroxide products. __________ Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 515–518, November–December, 2006.