Krasnoselski-Mann type iterative method for hierarchical fixed point problem and split mixed equilibrium problem

In this paper, we suggest and analyze a Krasnoselski-Mann type iterative method to approximate a common element of solution sets of a hierarchical fixed point problem for nonexpansive mappings and a split mixed equilibrium problem. We prove that sequences generated by the proposed iterative method converge weakly to a common element of solution sets of these problems. Further, we derive some consequences from our main result. Furthermore, we extend the considered iterative method to a split monotone variational inclusion problem and deduce some consequences. Finally, we give a numerical example to justify the main result. The method and results presented in this paper generalize and unify the corresponding known results in this area.     

Armatans A and B,New Antimicrobial Isoflavans from Colutea armata

Chemistry of Natural Compounds - Armatans A (1) and B (2), new isoflavans, have been isolated from the EtOAc-soluble fraction of the MeOH extract of Colutea armata Hemsl. & Lace, along with...     

Synthesis and antimicrobial activity of some novel 2-(substituted fluorobenzoylimino)-3-(substituted fluorophenyl)-4-methyl-1,3-thiazolines

The synthesis of several 2-(substituted fluorobenzoylimino)-3-(substituted fluorophenyl)-4-methyl-1,3-thiazolines (2a-t) was carried out by base-catalyzed cyclization of corresponding 1-(fluorobenzoyl)-3-(fluorophenyl)thioureas (1a-t) with 2-bromoacetone in aqueous medium. The structures of the synthesized compounds were confirmed by spectral and elemental analysis. All synthesized compounds were evaluated for in vitro antibacterial activity using Gram-positive bacteria (Staphylococcus aureus, Bacillus subtilis) and Gram-negative bacteria (Escherichia coli, Pseudomonas aeruginosa). The minimum inhibitory concentration (MIC) was determined for the most active compounds. In vitro antifungal activity was also determined against the five fungal species (Rhizopus oryzae, Fusarium oxysporum, Aspergillus terreus, A. niger and A. fumigatus).     

An integrated solution and analysis of bioluminescence tomography and diffuse optical tomography

While diffuse optical tomography (DOT) has been studied for years, bioluminescence tomography (BLT) is emerging as a promising optical molecular imaging tool. These two modalities have different goals. DOT is for reconstruction of optical parameters of a medium such as a breast from surface measurements induced by external sources. BLT is for reconstruction of a bioluminescent source distribution in a medium such as a mouse from surface measurements induced by internal bioluminescent sources. However, an important pre-requisite for BLT reconstruction is the knowledge on the distribution of optical parameters within the medium, which is the output of DOT. In this paper, we propose a mathematical model integrating BLT and DOT at the fundamental level; that is, performing the two types of reconstructions simultaneously instead of doing them sequentially. The model is introduced through minimizing the difference between predicted quantities and boundary measurements, as well as incorporating regularization terms. Then, we show the solution existence, introduce numerical schemes and prove convergence of the numerical solution. We also present numerical results to illustrate the utility of our approach.     

Direct interaction between an allosteric agonist pepducin and the chemokine receptor CXCR4

Cell surface heptahelical G protein-coupled receptors (GPCRs) mediate critical cellular signaling pathways and are important pharmaceutical drug targets. (1) In addition to traditional small-molecule approaches, lipopeptide-based GPCR-derived pepducins have emerged as a new class of pharmaceutical agents. (2, 3) To better understand how pepducins interact with targeted receptors, we developed a cell-based photo-cross-linking approach to study the interaction between the pepducin agonist ATI-2341 and its target receptor, chemokine C-X-C-type receptor 4 (CXCR4). A pepducin analogue, ATI-2766, formed a specific UV-light-dependent cross-link to CXCR4 and to mutants with truncations of the N-terminus, the known chemokine docking site. These results demonstrate that CXCR4 is the direct binding target of ATI-2341 and suggest a new mechanism for allosteric modulation of GPCR activity. Adaptation and application of our findings should prove useful in further understanding pepducin modulation of GPCRs as well as enable new experimental approaches to better understand GPCR signal transduction.     

Tin(II) Halide Insertion or Halogen Exchange in the Reactions of Dihaloplatinum(II) Complexes with Tin(II) Halide

Reactions of SnCl₂ with the complexes cis‐[PtCl₂(P₂)] (P₂=dppf (1,1′‐bis(diphenylphosphino)ferrocene), dppp (1,3‐bis(diphenylphosphino)propane=1,1′‐(propane‐1,3‐diyl)bis[1,1‐diphenylphosphine]), dppb (1,4‐bis(diphenylphosphino)butane=1,1′‐(butane‐1,4‐diyl)bis[1,1‐diphenylphosphine]), and dpppe (1,5‐bis(diphenylphosphino)pentane=1,1′‐(pentane‐1,5‐diyl)bis[1,1‐diphenylphosphine])) resulted in the insertion of SnCl₂ into the Pt? Cl bond to afford the cis‐[PtCl(SnCl₃)(P₂)] complexes. However, the reaction of the complexes cis‐[PtCl₂(P₂)] (P₂=dppf, dppm (bis(diphenylphosphino)methane=1,1′‐methylenebis[1,1‐diphenylphosphine]), dppe (1,2‐bis(diphenylphosphino)ethane=1,1′‐(ethane‐1,2‐diyl)bis[1,1‐diphenylphosphine]), dppp, dppb, and dpppe; P=Ph₃P and (MeO)₃P) with SnX₂ (X=Br or I) resulted in the halogen exchange to yield the complexes [PtX₂(P₂)]. In contrast, treatment of cis‐[PtBr₂(dppm)] with SnBr₂ resulted in the insertion of SnBr₂ into the Pt? Br bond to form cis‐[Pt(SnBr₃)₂(dppm)], and this product was in equilibrium with the starting complex cis‐[PtBr₂(dppm)]. Moreover, the reaction of cis‐[PtCl₂(dppb)] with a mixture SnCl₂/SnI₂ in a 2 : 1 mol ratio resulted in the formation of cis‐[PtI₂(dppb)] as a consequence of the selective halogen‐exchange reaction. ³¹P‐NMR Data for all complexes are reported, and a correlation between the chemical shifts and the coupling constants was established for mono‐ and bis(trichlorostannyl)platinum complexes. The effect of the alkane chain length of the ligand and Sn^II halide is described.     

Some Remarks On Vector Optimization Problems

We prove the existence of a weak minimum for vector optimization problems by means of a vector variational-like inequality and preinvex mappings.     

A hybrid projective method for solving system of equilibrium problems with demicontractive mappings applicable in image restoration problems

In this paper, we propose a general iterative scheme based on CQ projection method for finding a common solution of system of equilibrium problems and the fixed point set of a finite family of demicontractive mappings. We also prove strong convergence of the scheme to a common element of the two above-described sets. We then give a numerical example to justify our main result. An example is given in an infinite dimensional space for supporting our main result. Moreover, we apply our main result to solve the unconstrained image restoration problems with a finite family of blurring operators. Our results extend and improve some existing results in the literature.     

General auxiliary problem and algorithm for a generalized multi-valued variational-like inequality problem in reflexive Banach spaces

In this article, some generalized multi-valued variational-like inequality problems and their related general auxiliary problems in real reflexive Banach spaces are introduced. An existence theorem for one of the general auxiliary problems is proved. Furthermore, by exploiting this theorem, an algorithm for the corresponding generalized multi-valued variational-like inequality problem is constructed. The theorems of this article generalize, improve and unify many known corresponding results.