Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based data classification problems where they are used to describe the containments as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments.     

Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Fluorescence from the second excited singlet state of [18] annulenes

The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S₂ → S₀ emission. In addition, fluorescence from the S₁ state can be observed in monofluoro [13] annulene by exciting into the S₂ or directly into the S₁ absorption.     

Anionic polymerization of 1,2-butylene oxide

Anionic polymerizations of 1,2-butylene oxide were carried out in vacuum-sealed dilatometers in the range of 30–60°C. Potassium terbutoxide and dimsyl sodium were used as initiators; dimethyl sulfoxide (DMSO) and mixtures of DMSO with tetrahydrofuran were solvents. The polymer products were analyzed by gel permeation chromatography and infrared spectroscopy. The object of the investigation was to obtain information on the mechanism of the reaction and to elucidate some of its kinetic aspects. It has been shown that the polymerizations occur by two different processes, depending on the choice of experimental conditions. One of the processes involves free ions and ion-pairs, the other, ion-pairs alone. In the first case, where dimethyl sulfoxide is used as solvent, the order of the reaction with respect to the initiator concentration far exceeds unity (～1.8), while in the second case, involving mixed solvents, the order of the reaction, for all practical purposes, is one.     

A Perturbation Approach to Vector Optimization Problems: Lagrange and Fenchel–Lagrange Duality

Journal of Optimization Theory and Applications - In this paper, we study a general minimization vector problem which is expressed in terms of a perturbation mapping defined on a product of locally...     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.     

Convenient syntheses of "heavy fluorous" cyclopentadienes and cyclopentadienyl complexes with three to five ponytails

Reactions of (eta5-C5H(5-x)Brx)M(CO)3(M = Re, Mn; x= 1, 3, 4, 5) and IZn(CH2)2R(f8) in the presence of Cl2PdL2 catalysts give the title complexes (eta5)-C5H(5-x)(CH2)2R(f8)x)M(CO3), accompanied in the case of x= 5 by hydride-transfer byproducts. Extremely high fluorophilicities are realized, and the cyclopentadienyl ligands are readily detached (hnu) from the manganese complexes.     

Facile synthesis of O6-alkyl-, O6-aryl-, and diaminopurine nucleosides from 2'-deoxyguanosine

The 3',5'-bis-O-TBDMS derivative of 2'-deoxyguanosine can be converted to its O6-alkyl and O6-aryl ethers as well as to N6-substituted diaminopurine nucleosides in two simple steps. Also described is a novel, nonaqueous, one-step O6-desulfonylation method that leads to deprotection of the carbonyl moiety of 2'-deoxyguanosine.     

Aza-Diels-Alder reaction in fluorinated alcohols. A one-pot synthesis of tetrahydroquinolines

Hexafluoroisopropanol and trifluoroethanol are found to promote imino-Diels-Alder reactions of the N-aryl aldimine 1 with alkyl vinyl ethers to afford the corresponding tetrahydroquinolines in good yields without Lewis acid under mild and neutral conditions. The reaction is also efficient in a three component process from aldehyde, amine and vinyl ethers.     

Synthesis and spectral characterization of some complexes of platinum(II) containing η-methyleugenol

Several complexes of the formula trans-[Pt(Meug)(Am)Cl₂], Meug: methyleugenol (4-allyl-1,2-dimethoxybenzene), a η²-coordinated olefin, and Am: ammine, methylamine, diethylamine, o-toluidine, m-toluidine, p-toluidine, o-anisidine, m-anisidine and p-anisidine have been prepared. UV, IR, Raman, ¹H NMR, ¹³C NMR and 2D NMR spectra of the complexes were recorded and analyzed.