A remark on a regularity assumption for the mathematical programming problem in Banach spaces

This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualification is the fact that it can be considered as a condition only on theactive part of the constraint. We prove that the studied regularity condition is equivalent to the regularity assumption normally used in the study of the mathematical programming problem in infinite-dimensional vector spaces.     

13C-13C and (15)N-(13)C correlation spectroscopy of membrane-associated and uniformly labeled human immunodeficiency virus and influenza fusion peptides: amino acid-type assignments and evidence for multiple conformations

Many viruses which cause disease including human immunodeficiency virus (HIV) and influenza are "enveloped" by a membrane and infection of a host cell begins with joining or "fusion" of the viral and target cell membranes. Fusion is catalyzed by viral proteins in the viral membrane. For HIV and for the influenza virus, these fusion proteins contain an approximately 20-residue apolar "fusion peptide" that binds to target cell membranes and plays a critical role in fusion. For this study, the HIV fusion peptide (HFP) and influenza virus fusion peptide (IFP) were chemically synthesized with uniform (13)C, (15)N labeling over large contiguous regions of amino acids. Two-dimensional (13)C-(13)C and (15)N-(13)C spectra were obtained for the membrane-bound fusion peptides and an amino acid-type (13)C assignment was obtained for the labeled residues in HFP and IFP. The membrane used for the HFP sample had a lipid headgroup and cholesterol composition comparable to that of host cells of the virus, and the (13)C chemical shifts were more consistent with beta strand conformation than with helical conformation. The membrane used for the IFP sample did not contain cholesterol, and the chemical shifts of the dominant peaks were more consistent with helical conformation than with beta strand conformation. There were additional peaks in the IFP spectrum whose shifts were not consistent with helical conformation. An unambiguous (13)C and (15)N assignment was obtained in an HFP sample with more selective labeling, and two shifts were identified for the Leu-9 CO, Gly-10 N, and Gly-10 Calpha nuclei. These sets of two shifts may indicate two beta strand registries such as parallel and antiparallel. Although most spectra were obtained on a 9.4 T instrument, one (13)C-(13)C correlation spectrum was obtained on a 16.4 T instrument and was better resolved than the comparable 9.4 T spectrum. More selective labeling and higher field may, therefore, be approaches to obtaining unambiguous assignments for membrane-associated fusion peptides.     

Second order optimality conditions for theL 1-minimization problem

In this paper we establish necessary and sufficient second order optimality conditions for theL ₁-problem. The approach is based on optimality criteria in terms of a curved second directional derivative, discussed in [3]. Our conditions generalize conditions for theL ₁-problem given in [6]. An example demonstrates the usefulness of our criteria.This research was supported by NSF Grant No. ECS-8214081 and the Fund for Promotion of Research at the Technion, andDeutsche Forschungsgemeinschaft.     

First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems

First-order and second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by arbitrary closed convex cones. The necessary conditions are immediate generalizations of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as illustrated by a counterexample. Here, to go from finite to infinite dimensions, causes an essential change in the proof-techniques and the results. We present modified sufficient conditions of first-order and of second-order which are based on a strengthening of the usual assumptions on the derivative of the objective function and on the second derivative of the Lagrangian.     

P,Se-Heterocycles From the Quasi-Binary System PhP/Se

Abstract

Contrary to statements in the literature the PhP/Se system does contain a compound with a PhP/Se ratio lower than 1. The reaction of pentaphenyl-cyclopentaphosphane and elemental selenium yields depending on the molar ratio the heterocyclic compounds (PhP)₄Se (1), (PhP)₃Se₃ (2), or (PhP)₂Se₄ (3). 1, 2, and 3 are yellow to orange-red crystalline stable compounds. Their molecular structures, as shown by the ³¹P- and ⁷⁷Se-NMR data as well as by the X-ray crystal structure determination of 2, parallel those of the corresponding sulfur derivatives. Nucleophiles add easily to the phosphorus in 3 splitting the P₂Se₂-ring.