Higher-order optimality conditions in set-valued optimization using radial sets and radial derivatives

We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both necessary and sufficient higher-order conditions for weak efficiency in a general set-valued vector optimization problem without any convexity assumptions. Many examples are provided to explain advantages of our results over a number of existing ones in the literature.     

An Armijo-type method for pseudomonotone equilibrium problems and its applications

We present a new algorithm for solving equilibrium problems, where the underlying bifunctions are pseudomonotone and not necessarily Lipschitz-type continuous. The algorithm is based on the auxiliary problem principle and the Armijo-type linesearch techniques. Convergence properties of the algorithms are established, among them the global convergence is proved under few assumptions. Applications to generalized variational inequalities and some numerical results are reported.     

Semicontinuity of the Approximate Solution Sets of Multivalued Quasiequilibrium Problems

We consider two kinds of approximate solutions and approximate solution sets to multivalued quasiequilibrium problems. Sufficient conditions for the lower semicontinuity, Hausdorff lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity, and closedness of these approximate solution sets are established. Applications in approximate quasivariational inequalities, approximate fixed points, and approximate quasioptimization problems are provided.     

Multifractional Markov Processes in Heterogeneous Domains

In this article, we introduce a class of Markov processes whose transition probability densities are defined by multifractional pseudodifferential evolution equations on compact domains with variable local dimension. The infinitesimal generators of these Markov processes are given by the trace of strongly elliptic pseudodifferential operators of variable order on such domains. The results derived provide a pseudomultifractal version of some existing special classes of multifractional Markov processes. In particular, pseudostable processes are defined on domains with variable local dimension in this framework. In the case where the local dimension of the domain and the local Hölder exponents of the transition probability densities are constant, the existing results on fractal versions of Lévy processes are recovered.     

Methoxyflavone Inhibitors of Cytochrome P450

Abstract  Cytochrome P450 enzymes are a superfamily of enzymes involved in the metabolism of endogenous compounds as well as xenobiotics. Due to the large number of reactions catalyzed by these enzymes and their importance in drug metabolism and carcinogenesis, they have been the focus of many studies over the years. Based on the knowledge that flavones are natural substrates of certain P450 enzymes (such as P450 1A2) involved in carcinogenesis, we have synthesized and studied a number of flavonoids as potential inhibitors of these enzymes. These compounds are structurally very similar to the natural flavone substrates of these enzymes but have methoxy substituents at various positions. Here we are reporting the synthesis, structural analysis, X-ray crystal structures, and preliminary inhibition studies of four methoxyflavones from this series. Crystallographic data: 2′-methoxyflavone, P-1, a = 7.2994(8) ?, b = 8.3322(7) ?, c = 10.8240(10) ?, α = 97.905(8)°, β = 92.779(10)°, γ = 111.105(8)°, V = 604.9(1) ?³; 3′-methoxyflavone, P2₁/n, a = 15.1313(16) ?, b = 3.9699(4) ?, c = 19.9454(16) ?, β = 91.673(8)°, V = 1197.6(2) ?³; 4′-methoxyflavone, P2₁/n, a = 16.451(12) ?, b = 3.881(1) ?, c = 19.529(16) ?, β = 106.65(1)°, V = 1195.1(4) ?³; 3′,4′-dimethoxyflavone, C2/c, a = 30.819(5) ?, b = 4.0857(7) ?, c = 26.100(3) ?, β = 124.21(1)°, V = 2717.6(7) ?³. Index Abstract  Methoxyflavone Inhibitors of Cytochrome P450 Michael McKendall, Tasha Smith, Kien Anh, Jamie Ellis, Terri McGee, Maryam Foroozesh, Naijue Zhu and Cheryl L. Klein Stevens* This paper is a report of the synthesis, structural analysis, X-ray crystal structures, and preliminary inhibition studies of 2′-methoxyflavone, 3′-methoxyflavone, 4′-methoxyflavone, and 3′,4′-dimethoxyflavone.

New indications of potential rat intestinal α-glucosidase inhibition by Syzygium zeylanicum (L.) and its hypoglycemic effect in mice

Research on Chemical Intermediates - Natural α-glucosidase inhibitors (aGIs) have been considered effective agents for type 2 diabetes management. In this study, Syzygium zeylanicum (L.)...     

Subcomponent Self-Assembly of a Cyclic Tetranuclear FeII Helicate in a Highly Diastereoselective Self-Sorting Manner

An enantiomerically pure diamine based on the 4,15-difunctionalized [2.2]paracyclophane scaffold and 2-formylpyridine self-assemble into an optically pure cyclic metallosupramolecular Fe₄L₆ helicate upon mixing with iron(II) ions in a diastereoselective subcomponent self-assembly process. The cyclic assembly results from steric strain that prevents the formation of a smaller linear dinuclear triple-stranded helicate, and hence, leads to the larger strain-free assembly that fulfils the maximum occupancy rule. Interestingly, use of the racemic diamine also leads to a racemic mixture of the homochiral cyclic helicates as the major product in a highly diastereoselective narcissistic chiral self-sorting manner given the fact that the assembly contains ten stereogenic elements, which can in principle give rise to 149 different diastereomers. The metallosupramolecular aggregates could be characterized by NMR, UV/Vis and CD spectroscopy, mass spectrometry, and X-ray crystallography.     

External control of a metal-insulator transition in GaMnAs wires

Quantum transport in disordered ferromagnetic (III,Mn)V semiconductors is studied theoretically. Mesoscopic wires exhibit an Anderson disorder-induced metal-insulator transition that can be controlled by a weak external magnetic field. This metal-insulator transition should also occur in other materials with large anisotropic magnetoresistance effects. The transition can be useful for studies of zero-temperature quantum critical phase transitions and fundamental material properties.     

Inhibitory Effects of Cucurbitane-Type Triterpenoids from Momordica charantia Fruit on Lipopolysaccharide-Stimulated Pro-Inflammatory Cytokine Production in Bone Marrow-Derived Dendritic Cells

The bitter melon, Momordica charantia L., was once an important food and medicinal herb. Various studies have focused on the potential treatment of stomach disease with M. charantia and on its anti-diabetic properties. However, very little is known about the specific compounds responsible for its anti-inflammatory activities. In addition, the in vitro inhibitory effect of M. charantia on pro-inflammatory cytokine production by lipopolysaccharide (LPS)-stimulated bone marrow-derived dendritic cells (BMDCs) has not been reported. Phytochemical investigation of M. charantia fruit led to the isolation of 15 compounds (1−15). Their chemical structures were elucidated spectroscopically (one- and two-dimensional nuclear magnetic resonance) and with electrospray ionization mass spectrometry. The anti-inflammatory effects of the isolated compounds were evaluated by measuring the production of the pro-inflammatory cytokines interleukin IL-6, IL-12 p40, and tumor necrosis factor α (TNF-α) in LPS-stimulated BMDCs. The cucurbitanes were potent inhibitors of the cytokines TNF-α, IL-6, and IL-12 p40, indicating promising anti-inflammatory effects. Based on these studies and in silico simulations, we determined that the ligand likely docked in the receptors. These results suggest that cucurbitanes from M. charantia are potential candidates for treating inflammatory diseases.