Invariant-point theorems and existence of solutions to optimization-related problems

To consider existence of solutions to various optimization-related problems, we first develop some equivalent versions of invariant-point theorems. Next, they are employed to derive sufficient conditions for the solution existence for two general models of variational relation and inclusion problems. We also prove the equivalence of these conditions with the above-mentioned invariant-point theorems. In applications, we include consequences of these results to a wide range of particular cases, from relatively general inclusion problems to classical results as Ekeland’s variational principle, and practical situations like traffic networks and non-cooperative games, to illustrate application possibilities of our general results. Many examples are provided to explain advantages of the obtained results and also to motivate in detail our problem settings.     

Optimizing a multi-stage production/inventory system by DC programming based approaches

This paper deals with optimizing the cost of set up, transportation and inventory of a multi-stage production system in presence of bottleneck. The considered optimization model is a mixed integer nonlinear program. We propose two methods based on DC (Difference of Convex) programming and DCA (DC Algorithm)—an innovative approach in nonconvex programming framework. The mixed integer nonlinear problem is first reformulated as a DC program and then DCA is developed to solve the resulting problem. In order to globally solve the problem, we combine DCA with a Branch and Bound algorithm (BB-DCA). A convex minorant of the objective function is introduced. DCA is used to compute upper bounds while lower bounds are calculated from a convex relaxation problem. The numerical results compared with those of COUENNE (http://www.coin-or.org/download/binary/Couenne/), a solver for mixed integer nonconvex programming, show the rapidity and the ?-globality of DCA in almost cases, as well as the efficiency of the combined DCA-Branch and Bound algorithm. We also propose a simple heuristic algorithm which is proved by experimental results to be better than an existing heuristic in the literature for this problem.     

The characteristic polynomial of a random permutation matrix at different points

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enable us to study also the wreath product of permutation matrices and diagonal matrices with i.i.d. entries and more general class functions on the symmetric group with a multiplicative structure.     

Capillary electrochromatography with contactless conductivity detection for the determination of some inorganic and organic cations using monolithic octadecylsilica columns

A fast separation of alkali and alkaline earth metal cations and ammonium was carried out by capillary electrochromatography on monolithic octadecylsilica columns of 15 cm length and 100 μm inner diameter using water/methanol mixtures containing acetic acid as mobile phase. On-column contactless conductivity detection was used for quantification of these non-UV-absorbing species. The method was also extended successfully to the determination of small amines as well as of amino acids, and the separation selectivity was optimized by varying the composition of the mobile phase. Detection limits of about 1 μM were possible for the inorganic cations as well as for the small amines, while the amino acids could be quantified down to about 10 μM. The separation of 12 amino acids was achieved in the relatively short time of 10 min.     

An efficient entry to furo[2,3-d]pyrimidines via inverse electron demand Diels–Alder reactions of 2-aminofurans with 1,3,5-triazines

Furo[2,3-d]pyrimidines were readily prepared via an inverse electron demand Diels–Alder (IDA) reaction between 2-aminofurans and 1,3,5-triazines. 2-Aminofurans proved to be productive dienophiles leading to the IDA product in moderate to good yields. This study further expanded the scope of 1,3,5-triazine IDA reactions with five-membered aromatic heterocycles as dienophiles.     

结构规整的高密度两亲性接枝聚合物刷的合成及其自组装研究

大分子单体通过两种可控聚合方法, 即开环易位聚合(ROMP)和原子转移自由基聚合(ATRP)的联用, 合成一种新型两亲性接枝聚合物刷. 具有高环张力的降冰片烯单侧链大分子单体norbornene-graft-poly(ε-caprolactone)/Br (PCL- NBE-Br)首先进行ROMP反应, 生成聚合物主链, 每个单体单元上含有一条PCL链和一个溴官能团; 然后用含溴的ROMP聚合物poly(norbornene)-graft-poly(ε-caprolactone)/Br (PCL-PNBE-Br)作为大分子引发剂引发单体2-(dimethyl- amino)ethyl methacrylate)的ATRP反应, 生成结构明确的高密度两亲性接枝聚合物刷poly(norbornene)-graft-poly(ε- caprolactone)/poly(2-(dimethylamino)ethyl methacrylate) (PCL-PNBE-PDMAEMA), 其主链每个单体单元上均含有一条疏水性PCL接枝链和一条亲水性PDMAEMA接枝链. 最后, 研究此类高密度两亲性接枝聚合物刷的自组装行为, 用动态激光光散射(DLS)研究其在混合溶剂(THF/H2O)中的胶束行为, 考察胶束溶液的浓度以及不同长度的亲水性接枝链对胶束尺寸的影响; 利用透射电镜(TEM)观察胶束为球形, 具有类似线团或草莓状的形态.     

Formation of microporous poly(hydroxybutyric acid) membranes for culture of osteoblast and fibroblast

Microporous membranes of a biodegradable polymer, poly(hydroxybutyric acid) (PHB), were prepared by a phase‐inversion process and their cell compatibility was evaluated in vitro. A ternary system, ethanol/chloroform/PHB, was employed to prepare the membranes, wherein ethanol and chloroform were served as the nonsolvent and solvent for PHB, respectively. In the phase‐inversion process, the polymer dissolution temperature was varied from 80 to 120°C to yield membranes with specific morphologies, such as globular particles, porous channels, etc. Moreover, cell viability was examined on the formed membranes. Two cell lines, osteoblast hFOB1.19 and fibroblast L929, were cultured in vitro. It was found that these two types of cells exhibited different responses on different membranes: the hFOB1.19 cells showed significant increase in cell proliferation with increase in surface roughness, whereas the L929 cells demonstrated an opposite trend, preferring to attach and grow on a flat surface. PHB membranes with different morphologies exhibit different cell compatibilities, which may be useful means for the architectural design of materials for tissue engineering. Copyright © 2009 John Wiley & Sons, Ltd.     

球形微米镍颗粒的液相体系制备及应用

本研究采用液相还原法,选用六水合硫酸镍为镍源,水合肼为还原剂,在封端剂聚乙烯吡咯烷酮的辅助下,制备得到球形微米镍颗粒。所制备的球形微米镍颗粒粒径约为3 μm,粒径分布均匀,表面粗糙度较低。为了获得球形微米镍颗粒的最优工艺方案,分别探究了PVP浓度、氢氧化钠和水合肼用量及反应温度等工艺参数对产物形貌的影响。研究发现,PVP能够有效控制镍原子的排布和沉积,NaOH可调节反应的pH值,确保水合肼持续还原Ni₂₊^,温度会影响体系的还原反应速率。结果表明：当反应体系使用的PVP浓度为0.5 M、NaOH用量为2.5 mL、水合肼用量为5 mL时,在 60 ℃下水浴反应可获得表面粗糙度低的球形微米镍颗粒,其电导率为5×10₅ S.m_-1^,饱和磁化强度为49.34 emu.g_-1^{。通过添加去离子水、异丙醇和羧甲基纤维素的混合溶液},将球形微米镍颗粒配制成25 wt%的导电油墨,并在纸基表面绘制导电线路,经测试该线路的电导率为1.28×10₃ ^S.m_-1^,此电路在弯折条件下,呈现出良好的工作稳定性。     

Stereochemistry as a tool in deciphering the processes of a tandem iminium cyclization and Smiles rearrangement

To understand the detailed mechanism of a recently reported tandem iminium cyclization and Smiles rearrangement, the reaction processes of a chiral substrate were investigated by monitoring its stereochemical courses. Under the tandem reaction conditions, chiral aldehyde 1 derived from l-prolinol led to two surprising results. First, the iminium cyclization gave a diastereomeric mixture with the cis-configured product as the predominant one. Second, Smiles rearrangement of both cis- and trans-2 led to the same product 3a directly derived from the trans isomer. The former was rationalized by the postulation of a Cram's chelate transition state leading to the cis product as kinetically favored. The latter was due to the equilibration between the trans/cis pair involving a carbocation intermediate and the steric hindrance, which prevented the cis isomer from undergoing the intramolecular nucleophilic substitution. This hypothesis was further supported by the results of a competition experiment in which the addition of 1 equiv of p-methoxyaniline in the rearrangement step led to a significant amount of anilinyl-exchanged rearrangement product.     

(S)-2-((S)-2-(4-(3-[18F]fluoropropyl)benzamido)-3-phenylpropanamido)pentanedioic acid labeled with 18F

As degradation product of Antineoplaston A10 in vivo, phenylacetyl glutamine showed antitumor activities. According to literatures, we designed and radiosynthesized a phenylacetyl glutamine derivative, which was achieved under a mild reaction condition. Evaluations in vitro and in vivo were performed on tumor bearing mice. Excitingly, the radiochemical purity of (S)-2-((S)-2-(4-(3-fluoropropyl)benzamido)-3-phenylpropanamido)pentanedioic acid ([¹⁸F]FBPPA) was 98%, and besides the best radiochemical yield was up to 46%. T/Bl (Tumor/Blood) and T/M (Tumor/Muscle) ratios of [¹⁸F]FBPPA at 60 min post injection were 2.33 and 3.51. Meanwhile, it showed satisfied stability in vitro and in vivo, compared with 2-[¹⁸F]fluorodeoxyglucose ([¹⁸F]FDG). Although [¹⁸F]FBPPA deserved further studies to make optimizations on its structure, the results revealed it might become a potential PET imaging agent for detecting tumors.