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.     

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 '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.     

Spectroscopic techniques in medicine: The future of diagnostics

Spectroscopic techniques have been finding increasing applications in the field of biomedicine especially in the field of disease diagnosis and monitoring in spite of the rapid emergence of several molecular biology based techniques. The significance of spectroscopy techniques and the possibility of using some of the underutilized regions of the electromagnetic radiations are discussed in this review. While previous reviews have already dealt with the potential of Fourier transform infrared spectroscopy-based (FTIR) techniques for clinical applications, the present review addresses the lacunae of the techniques along with its future trends that may make it a technique routinely applied in clinical settings.     

Periodic solitons in nonlocal nonlinear media

We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.     

Associated primes of graded components of local cohomology modules

The -th local cohomology module of a finitely generated graded module over a standard positively graded commutative Noetherian ring , with respect to the irrelevant ideal , is itself graded; all its graded components are finitely generated modules over , the component of of degree . It is known that the -th component of this local cohomology module is zero for all > 0$">. This paper is concerned with the asymptotic behaviour of as .

The smallest for which such study is interesting is the finiteness dimension of relative to , defined as the least integer for which is not finitely generated. Brodmann and Hellus have shown that is constant for all (that is, in their terminology, is asymptotically stable for ). The first main aim of this paper is to identify the ultimate constant value (under the mild assumption that is a homomorphic image of a regular ring): our answer is precisely the set of contractions to of certain relevant primes of whose existence is confirmed by Grothendieck's Finiteness Theorem for local cohomology.

Brodmann and Hellus raised various questions about such asymptotic behaviour when f$">. They noted that Singh's study of a particular example (in which ) shows that need not be asymptotically stable for . The second main aim of this paper is to determine, for Singh's example, quite precisely for every integer , and, thereby, answer one of the questions raised by Brodmann and Hellus.