Barrier method in nonsmooth convex optimization without convex representation

In this article we want to demonstrate that under mild conditions the barrier method is an effective solution approach for convex optimization problems whose objective is nonsmooth and whose feasible set is described by smooth inequality constraints in which all the constraint functions need not be convex.     

Quantitative stability of full random two-stage stochastic programs with recourse

In this paper, we consider quantitative stability analysis for two-stage stochastic linear programs when recourse costs, the technology matrix, the recourse matrix and the right-hand side vector are all random. For this purpose, we first investigate continuity properties of parametric linear programs. After deriving an explicit expression for the upper bound of its feasible solutions, we establish locally Lipschitz continuity of the feasible solution sets of parametric linear programs. These results are then applied to prove continuity of the generalized objective function derived from the full random second-stage recourse problem, from which we derive new forms of quantitative stability results of the optimal value function and the optimal solution set with respect to the Fortet–Mourier probability metric. The obtained results are finally applied to establish asymptotic behavior of an empirical approximation algorithm for full random two-stage stochastic programs.     

On a convex set with nondifferentiable metric projection

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with \(C^{1,1}\) boundary which possesses the same property.     

Ragnar Frisch and interior-point methods

The distinguished econometrician Ragnar Frisch (1895–1973) also played an important role in optimization theory. In fact, he was a pioneer of interior-point methods. This note reconsiders his contribution, relating it to history and modern developments.     

Highly Regioselective Ring Opening of Epoxides with Thiols Catalyzed by SbCl3 Under Solvent-Free Conditions

The ring-opening reaction of epoxides with thiols by SbCl ₃ supported on Kieselguhr under solvent-free conditions, afforded high yields of β-hydroxy sulfides. Nucleophilic attack of the thiols occurs regioselectively at the less hindered side of the epoxides.     

Synthesis and In Vitro Anti-HIV Activity of Some New Schiff Base Ligands Derived from 5-Amino-4-phenyl-4H-1,2,4-triazole-3-thiol and Their Metal Complexes

New Schiff base ligands (6–9) derived from 5-amino-4-phenyl-4H-1,2,4-triazole-3-thiol 1 and substituted benzaldehydes (2–5) as well as their metal complexes with Cu(II), Fe(II), Au(III), and Mn(II) (12–17) have been synthesized. A new benzothiazole derivative (11) was prepared from coupling of 7 with N-(benzothiazol-2-yl)-2-chloroacetamide 10. Their spectral properties were investigated. The newly designed and synthesized Schiff base ligands and the metal complexes were assayed for anti-HIV-1 and HIV-2 activity by examination of their inhibition of HIV-induced cytopathogenicity in MT-4 cells. Compounds 11 and 16 were found to be the most active inhibitors in cell culture (EC₅₀ = 12.2 μg/mL (SI = 4) and > 2.11 μg/mL (SI = > 1), respectively) against HIV-1, whereas 11 showed inhibition against HIV-2 of EC₅₀ > 10.2 μg/mL with SI = 9, which provided a good lead for further optimization.     

Synthesis and anticancer activity of some novel diethyl {(chromonyl/pyrazolyl) [(4-oxo-2-phenyl-quinazolin-3(4H)-yl)amino]methyl}phosphonates

Abstract

The synthesis of some novel chromonyl and pyrazolyl α-aminophosphonates containing a quinazolinone ring was carried out by applying Pudovik and Kabachnik-Fields reactions under solvent- and catalyst-free conditions. The anticancer activities of these compounds were evaluated against five cancer cell lines. 3-{[(3-Phenyl/1,3-diphenyl-1H-pyrazol-4-yl)methylidene]amino}-2-phenyl-quinazolin-4(3H)-ones (3d,e) and diethyl {[3-phenyl/1,3-diphenyl-1H-pyrazol-4-yl][(4-oxo-2-phenyl-quinazolin-3(4H) yl)amino] methyl}phosphonates (4d,e) displayed the potent anticancer activities against HCT116, MCF-7 and HepG2 cell lines in comparison with the standard drug.     

Characterization of Electron Transfer Dissociation in the Orbitrap Velos HCD Cell

Electron transfer dissociation (ETD) is commonly employed in ion traps utilizing rf fields that facilitate efficient electron transfer reactions. Here, we explore performing ETD in the HCD collision cell on an Orbitrap Velos instrument by applying a static DC gradient axially to the rods. This gradient enables simultaneous three dimensional, charge sign independent, trapping of cations and anions, initiating electron transfer reactions in the center of the HCD cell where oppositely charged ions clouds overlap. Here, we evaluate this mode of operation for a number of tryptic peptide populations and the top-down sequence analysis of ubiquitin. Our preliminary data show that performing ETD in the HCD cell provides similar fragmentation as ion trap-ETD but requires further optimization to match performance of ion trap-ETD.      

Random Copolymers of 1,5-Dioxepan-2-one

ABSTRACT

Copolymers of 1,5-dioxepan-2-one (DXO) and e-caprolactone (?-CL), δ-valerolactone (δ-VL) or L-lactide (LLA) have been synthesized and characterized. High molecular weight copolymers were obtained using stannous-2-ethyl hexanoate as catalyst in bulk. Reactivity ratios for the copolymerization of DXO and δ-VL were determined at 110°C as r_VL=0.5 and r_DXO=2.3. At high conversion, depolymerization of δ-VL occurred, resulting in lower molecular weight and variations in the copolymer composition.

Physical properties, such as crystallinity and melting temperature of the DXO-copolymers proved to be strongly dependent on the choice of comonomer and on the molar composition of the copolymers. DXO appears to be incorporated into the poly-?-caprolactone (PCL) crystals and to some extent into the poly-δ-valerolactone (PVL) crystals, resulting in a more gradual decrease in crystallinity with increasing amount of DXO.