Upper Bound to the Expectation Value of the Squared Hamiltonian

An upper bound to the expectation value of the squared Hamiltonian H ² is derived which relies on replacing products of certain operators with products of the matrix representations of said operators to reduce the computational demands of H ². An example is given which shows the strength of the bound and an application with the Temple lower bound is shown.     

双功能催化剂体系作用下乙烯二聚和共聚合的研究

用乙烯为原料在双功能催化剂体系的作用下通过二聚和共聚合反应，直接合成线性低密度聚乙烯（ＬＬＤＰＥ）．所用二聚反应催化剂为钛酸正丁酯（Ｔｉ（ＯＢｕ）_４），共聚催化剂为ＴｉＣｌ_４／ＭｇＣｌ_２（ＺＭ－１催化剂）．研究了二聚反应动力学行为及影响双功能催化剂体系动力学过程的一些因素．结果表明利用这两种催化剂组成双功能催化剂体系能够很方便地制得密度范围在０．９０－０．９３，Ｅｔ／１０００Ｃ在１０－４０的ＬＬＤＰＥ．     

Chiral separation of the four stereoisomers of a novel antianginal agent using a dual cyclodextrin system in capillary electrophoresis

Reported here is an analytical method enabling the stereochemical resolution of a new antianginal compound possessing two stereogenic centers, leading to four stereoisomers. Only one of these isomers is currently under development as a novel antianginal agent and consequently, the other three isomers are considered as unwanted chiral impurities. Therefore, an enantioselective method is required in order to check its enantiomeric purity. This paper presents a method exploiting the high efficiency of capillary electrophoresis and the complexing properties of cyclodextrins to achieve the separation of the four stereoisomers of this weakly basic compound (pKa = 7.4). For this purpose, the combination of a neutral cyclodextrin, hydroxypropyl-gamma-cyclodextrin (HP-gamma-CD), and an anionic cyclodextrin, carboxymethyl-beta-cyclodextrin (CM-beta-CD), was added to the separation buffer running in an uncoated silica capillary. After selection of the suitable cyclodextrin system, satisfactorily separation conditions were as follows: 30 mM phosphate buffer (pH 6.4) containing 10 mM of HP-gamma-CD and 10 mM of CM-beta-CD, running voltage +30 kV. The resulting run time and resolutions were respectively about 17 min and between 1.95 and 2.84. Linearity curves (0.993 < r2 < 0.998) are also shown.     

Sol-gel polyimide-silica composite membrane: gas transport properties

The effect of introduction of silica particles prepared by the sol-gel technique on the gas transport properties of a polyimide film was studied. The sorption and permeation of N₂, O₂, CO₂, H₂ and CH₄ were studied and correlated with morphological changes in the polymer structure. From sorption isotherms, we observed that the composite membrane presents higher solubility coefficients than the polyimide one. The solubility coefficient ratio between the composite and the polyimide is about 1.5–2.0. The isotherms were analyzed in terms of the dual mode sorption. The Henry's coefficient and the Langmuir's affinity and saturation constants were obtained allowing to calculate the Langmuir to Henry concentration ratios as function of the gas pressure. These ratios decrease until zero within a certain pressure range as long as the Langmuir's mode is acting and they are higher for the polyimide membrane when compared with the composite one. This study was completed with calorimetric measurements during the sorption. The gas interaction energy in kJ/mol decreases within the same pressure range as previously described. The measured energies are higher for the polyimide film when compared with the composite one because the polyimide membrane presents a stronger energetic effect caused by a higher Langmuir's contribution. From permeation studies at 3.15⁵ Pa, the composite membrane showed higher permeability coefficients and permselectivities than the polyimide one. All these results were explained, taking into account the difference on the imidization degree of both membranes and the morphological changes which may be induced by the silica nodules in the organic/inorganic interphases.     

Migration behavior and enantioseparation of hydrobenzoin and structurally related compounds in capillary zone electrophoresis with a dual cyclodextrin system consisting of heptakis-(2,3-dihydroxy-6-O-sulfo)-beta-cyclodextrin and beta-cyclodextrin

Migration behavior and enantioseparation of racemic hydrobenzoin and structurally related compounds, including benzoin and benzoin methyl ether, in CZE with a dual CD system consisting of heptakis-(2,3-dihydroxy-6-O-sulfo)-beta-CD (SI-S-beta-CD) and beta-CD as chiral selectors in the presence and absence of borate complexation at pH 9.0 were investigated. The results indicate that enantioseparation of hydrobenzoin is mainly governed by CD complexation of hydrobenzoin-borate complexes with SI-S-beta-CD when SI-S-beta-CD concentration is relatively high. Whereas CD complexation of hydrobenzoin-borate complexes with beta-CD plays a significant role in enantioseparation when SI-S-beta-CD concentration is comparatively low. The (S,S)-enantiomer of the hydrobenzoin-borate complex was found to interact more strongly than the corresponding (R,R)-enantiomer with both SI-S-beta-CD and beta-CD. These two types of CD show the same chiral recognition pattern, but they exhibit opposite effects on the mobility of the enantiomers of hydrobenzoin-borate complexes. Enantiomer migration reversal of hydrobenzoin occurred in the presence of borate complexation when varying the concentration of beta-CD, while keeping SI-S-beta-CD at a relatively low concentration. Binding constants of the enantiomers of benzoin-related compounds to beta-CD and those of hydrobenzoin-borate complexes to SI-beta-CD were evaluated; the mobility contributions of all complex species to the effective mobility of the enantiomers of hydrobenzoin as a function of beta-CD concentration in a borate buffer were analyzed. In addition, comparative studies on the enantioseparation of benzoin-related compounds with SI-S-beta-CD and with randomly sulfate-substituted beta-CD were made.     

7-(2-Methoxycarbonylvinyl)-3-hydroxychromones: new dyes with red shifted dual emission

7-(2-Methoxycarbonylvinyl)-3-hydroxychromones have been synthesized using Heck coupling reaction from the corresponding 7-bromo-3-hydroxychromones. Introduction of the electron acceptor (2-methoxycarbonylvinyl) group at 7-position of 3-hydroxychromone results in a 30-40 nm red shift in absorption and >50 nm red shifts of both bands in emission. This derivatization allowed us to develop dyes with absorption maxima reaching 480 nm and dual emission in the red region of the spectrum. In comparison to the parent dyes, 7-acryl-3-hydroxychromones demonstrate significantly stronger solvatochromism. This is due to the acceptor group at 7-position, which increases the transfer character of the excited state of the dyes. The new dyes are highly prospective for the development of new fluorescent probes in biological research.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Parameterized approximations for the two-sided assortment optimization

We consider the problem faced by an online service platform that matches suppliers with consumers. Unlike traditional matching models, which treat them as passive participants, we allow both sides of the market to exercise their choices. To model this setting, we introduce a two-sided assortment optimization model wherein each participant's choice is modeled using a multinomial logit choice function, and the platform's objective is to maximize its expected revenue. We first show that the problem is NP-hard even when the number of suppliers is limited to two and provide a mixed-integer linear programming formulation. Next, we discuss two simple greedy heuristics and argue that these can lead to arbitrarily bad solutions. We then develop relaxations that provide upper and lower bounds and investigate the tightness of these relaxations by obtaining parametric approximation guarantees. Finally, we present numerical results on synthetic data demonstrating the practical utility of these relaxations.     

Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

Reliability bounds in DFRA class with known mean and variance

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