Cyclodextrins as chiral stationary phases in capillary gas chromatography. Part VII: Cyclodextrins with an inverse substitution pattern – synthesis and enantioselectivity

Transferring the site of specific substitution of dipentylated cyclodextrins with methyl or acyl residues from the secondary 3-hydroxyl group to the primary 6-hydroxyl group was expected to provide new information on the mechanism of chiral recognition. The 3-position points towards and the 6-position points away from the cyclodextrin cavity which via inclusion complex formation is supposed to play a major role in chiral separation. The “inverse” 6-O-acyl-2,3-di-O-pentyl-cyclodextrins displayed almost no enantioselectivity but the corresponding 6-O-methyl derivatives are a versatile supplement to the chiral capillary GC phases nowadays available. Among the compounds that could be enantiomerically resolved are alcohols, amino acids, alkyl halides, bicyclic ethers, acetals, olefins, other hydrocarbons and chiral pharmaceuticals.     

Neue Kupferkomplexe mit Phosphaalkenliganden. Molekülstruktur von [Cu{P(Mes*)C(NMe2)2}2]BF4 (Mes* = 2,4,6‐tBu3C6H2)

New Copper Complexes Containing Phosphaalkene Ligands. Molecular Structure of [Cu{P(Mes*)C(NMe₂)₂}₂]BF₄ (Mes* = 2,4,6‐tBu₃C₆H₂) Reaction of equimolar amounts of the inversely polarized phosphaalkene tBuP=C(NMe₂)₂ ( 1a ) and copper(I) bromide or copper(I) iodide, respectively, affords complexes [Cu₃X₃{μ‐P(tBu)C(NMe₂)₂}₃] ( 2 ) (X =Br) and ( 3 ) (X = I) as the formal result of the cyclotrimerization of a 1:1‐adduct. Treatment of 1a with [Cu(L)Cl] (L = PiPr₃; SbiPr₃) leads to the formation of compounds [CuCl(L){P(tBu)C(NMe₂)₂}] ( 4a ) (L = PiPr₃) and ( 4b ) (L = SbiPr₃), respectively. Reaction of [(MeCN)₄Cu]BF₄ with two equivalents of PhP=C(NMe₂)₂ ( 1b ) yields complex [Cu{P(Ph)C(NMe₂)₂}₂]BF₄ ( 5b ). Similarly, compounds [Cu{P(Aryl)C(NMe₂)₂}₂]BF₄ ( 5c (Aryl = Mes and 5d (Aryl = Mes*)) are obtained from ArylP=C(NMe₂)₂ ( 1c : Aryl = Mes; 1d : Mes*) and [(MeCN)₄Cu]BF₄ in the presence of SbiPr₃. Complexes 2 , 3 , 4a , 4b , and 5b‐5d are characterized by means of elemental analyses and spectroscopy (¹H‐, ¹³C{¹H}‐, ³¹P{¹H}‐NMR). The molecular structure of 5d is determined by X‐ray diffraction analysis.     

Study of modified silicas by inverse gas chromatography. Part I: Influence of chain length on grafting ratio

Summary Silica has been modified by an esterification reaction using either n-alcohols or - diols. The grafting ratios were evaluated by elemental analysis of carbon or by the weight loss of the grafted silica heated to 700°C. The grafting ratio can be easily fixed by changing the silica to reactant impregnation ratios. In the case of n-alcohols, the grafting ratios do not vary monotonously with the number of carbon atoms of the grafts and the density of the grafted layer is 25% higher for - diols than for n-alcohols. This observation needs further investigation.     

Inverse relaxation-model and relation to recovery internal friction

Inverse relaxation is studied for hard elastic polypropylene (HEPP), rubber and non-elastic polypropylene. The results show that contractive stress, stress, and internal friction are three essential factors related to the phenomenon. A three-element model in which each element has a definite meaning is proposed to describe this phenomenon. The results also show that, in the first cyclic deformation, relaxation time increases with the increase of recovery for all the materials, which indicates that recovery viscosity increases with the increase of recovery, but the stress rising amplitude (SRA) of inverse relaxation has a maximum in the recovery range. Analysis indicates that SRA equals recovery internal friction (RIF) for ideal material in which stress is solely a function of strain, independent of paths, and approximately equals RIF for non-ideal material at a given strain. From this principle it is found that the order of the work counteracted by RIF for the four materials is the same as that of their second hysteresis loop, and the RIF of HEPP has a sudden increase at the later recovery range.     

Non-ionic amphiphilic block copolymers by RAFT-polymerization and their self-organization

Water-soluble, amphiphilic diblock copolymers were synthesized by reversible addition fragmentation chain transfer polymerization. They consist of poly(butyl acrylate) as hydrophobic block with a low glass transition temperature and three different nonionic water-soluble blocks, namely, the classical hydrophilic block poly(dimethylacrylamide), the strongly hydrophilic poly(acryloyloxyethyl methylsulfoxide), and the thermally sensitive poly(N-acryloylpyrrolidine). Aqueous micellar solutions of the block copolymers were prepared and characterized by static and dynamic light scattering analysis (DLS and SLS). No critical micelle concentration could be detected. The micellization was thermodynamically favored, although kinetically slow, exhibiting a marked dependence on the preparation conditions. The polymers formed micelles with a hydrodynamic diameter from 20 to 100 nm, which were stable upon dilution. The micellar size was correlated with the composition of the block copolymers and their overall molar mass. The micelles formed with the two most hydrophilic blocks were particularly stable upon temperature cycles, whereas the thermally sensitive poly(N-acryloylpyrrolidine) block showed a temperature-induced precipitation. According to combined SLS and DLS analysis, the micelles exhibited an elongated shape such as rods or worms. It should be noted that the block copolymers with the most hydrophilic poly(sulfoxide) block formed inverse micelles in certain organic solvents.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.     

STRUCTURES OF CIRCULANT INVERSE M-MATRICES

In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c（n- 1）] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c（n-k）] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.