Value functions,domination cones and proper efficiency in multicriteria optimization

In the absence of a clear objective value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications potential optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.     

Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.     

Rigid aromatic fractal polyamides

The preparation of rigid aromatic, highly branched polyamides is described. Owing to the method of preparation and the chosen ratio of difunctional to trifunctional monomers, these entities are highly porous and not dendrimeric in nature. They better conform with the fractal model and are therefore called fractal polyamides (FPs). The effects of variations in the polymerization procedure, in total monomer concentration, in the ratio of amine to carboxyl groups and in the duration of the polycondensation reaction are investigated. Some characterization was performed and the results are presented and briefly discussed.     

The Worpitzky identity for the groups of signed and even-signed permutations

Journal of Algebraic Combinatorics - The well-known Worpitzky identity $$\begin{aligned} (x+1)^n = \sum \limits _{k=0}^{n-1} A_{n,k} {{x+n-k} \atopwithdelims (){n}} \end{aligned}$$ provides a...     

The diagnonal multivariate natural exponential families and their classification

A natural exponential family (NEF)F in ? ⁿ ,n>1, is said to be diagonal if there existn functions,a ₁,...,a _n , on some intervals of ?, such that the covariance matrixV _F (m) ofF has diagonal (a ₁(m ₁),...,a _n (m _n )), for allm=(m ₁,...,m _n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? ^k and ? ^n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? ⁿ , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? ⁿ , under what conditions is its projectionp(F) in ? ^k , underp(x ₁,...,x _n )∶=(x ₁,...,x _k ),k=1,...,n?1, still an NEF in ? ^k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV _F (m ₁,...,m _n ) does not depend on (m _k+1,...,m _n ).     

Water Solubilization in Nonionic Microemulsions Stabilized by Grafted Siliconic Emulsifiers

Microemulsions containing octanol, decanol, or dodecanol as the oil phase and oligomeric, grafted nonionic amphiphiles based on ethoxylated polymethylsiloxanes (Silwets) have been studied. It was demonstrated that significant amounts of water can be solubilized only when the hydrophobic siliconic backbone is very short (trimers). The water solubilization was evaluated using SAXS, DSC, and conductivity measurements. It was found that up to 40 wt% of water can be solubilized in dodecanol and Silwet L-7607 (MW 1000 and 75 wt% ethylene oxide (EO)). Surprisingly, no free water was detected in the aggregate core. All the solubilized water was confined in the vicinity of the interphasal region and froze at -10 degrees C and below. Up to three molecules of water can be associated with each EO headgroup. Based on SAXS measurements, the structural units of the microemulsions were interpreted to be lamellar-like, a form previously found for the related monomeric microemulsions. Copyright 2001 Academic Press.     

Synthesis and some properties of poly-(2,5-trimethylene benzimidazole) and poly-(2,5-trimethylene benzimidazole hydrochloride)

A polymer, poly(2,5-trimethylene benzimidazole), the first of a new family of nonsymmetrical polymers, was synthesized via an eight-step synthetic route. The polymer, obtained by melt polymerization, is amorphous and in its neutral form behaves as a moderate insulator. It forms 1 : 1 HCl adducts. When cast from formic acid solution, it forms 1 : 1 formic acid adducts. The acid adducts are semiconductors with resistivities in the 10⁶–10⁸ ohm-cm range. Space-charge effects are generated in the adducts as carrier mobility rises.     

Reactions in the presence of organic phosphites,II: Low-temperature amidatior in solvent

Polyamides and related model compounds were prepared from carboxy acids and primary amines by reacting them with triphenylphosphite in an appropriate solvent at 100°C. The reactions proceeded in the absence of organic base but were accelerated by the addition of bases such as pyridine. Nevertheless, even the powerful combination of ¹³C and ³¹P NMR failed to indicate the presence of pyridinium phosphite in the reaction mixture. In the reaction of a primary amine and carboxyl groups a detectable amount of the diphenoxy aminophosphine intermediate was observed. The end products are the amides, phenol, and diphenyl phosphite. When primary amine was not present a slow formation of a phenyl ester of the carboxylic acid was evident. All the intermediate species and the end products were formed with or without added pyridine. A mixed anhydride of carboxylic acid and phosphite was never seen. The results in this article are fundamentally the same as those in the companion article (I) for which the data were obtained at 280°C in the absence of solvent and base. However, because the reaction went quickly to completion at 280°C, the diphenoxy aminophosphine intermediate was not observed. A mechanism for the amidation in which the diphenoxy aminophosphine is an initial reaction intermediate is proposed. This species reacts with the carboxylic acid through an intramolecular substitution to give an amide. This mechanism may be valid for the high-temperature reactions as well. Several minor unclear points are indicated.     

THE 'OPSIN SHIFT' IN BACTERIORHODOPSIN: STUDIES WITH ARTIFICIAL BACTERIORHODOPSINS

Abstract— The difference (in cm⁻¹) in absorption maxima between the protonated Schiff base of retinals and the pigment derived therefrom has been defined as the opsin shift. It represents the influence of the opsin binding site on the chromophore. The analysis of the opsin shifts of a series of dihydrobacteriorhodopsins has led to the external point-charge model, which in addition to a counter anion near the Schiff base ammonium, carries another negative charge in the vicinity of the β-ionone ring. This is in striking contrast to the external point-charge model proposed earlier for the bovine visual pigment. The absorption maxima of rhodopsins formed from bromo- and phenyl retinals support the two models. A retinal carrying a photoaffinity label has yielded a nonbleachable bacteriorhodopsin.