Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Regular conjugated terpolymers comprising two different acceptors and bithiophene donor in repeating group: Effect of strong and weak acceptors on semiconducting properties

Diketopyrrolopyrrole (DPP)‐based terpolymers—P(DPP‐TPyT) and P(DPP‐T3MTT)—bearing bithiophene donating groups and weak accepting units such as pyridine (Py) or methyl thiophene‐3‐carboxylate (3MT), in the polymer backbone, were successfully synthesized. Although the two polymers had similar physical and electrochemical properties, grazing incidence X‐ray diffraction patterns of P(DPP‐TPyT) and P(DPP‐T3MTT) showed mixed and edge‐on orientations, respectively, in thermally annealed films. Accordingly, the P(DPP‐T3MTT) showed twice the hole mobility of P(DPP‐TPyT) in a thin‐film transistor, and a blended film of P(DPP‐T3MTT) and [6,6]‐phenyl‐C71‐butyric acid methyl ester (PC₇₁BM) showed better power conversion efficiency in a polymer solar cell. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1339‐1347     

pH-temperature Responsive Hydrogel-Mediated Delivery of Exendin-4 Encapsulated Chitosan Nanospheres for Sustained Therapeutic Efficacy in Type 2 Diabetes Mellitus

Type 2 Diabetes Mellitus (T2D) is a chronic, obesity-related, and inflammatory disorder characterize by insulin resistance, inadequate insulin secretion, hyperglycemia, and excessive glucagon secretion. Exendin-4 (EX), a clinically established antidiabetic medication that acts as a glucagon-like peptide-1 receptor agonist, is effective in lowering glucose levels and stimulating insulin secretion while significantly reducing hunger. However, the requirement for multiple daily injections due to EX's short half-life is a significant limitation in its clinical application, leading to high treatment costs and patient inconvenience. To address this issue, an injectable hydrogel system is developed that can provide sustained EX release at the injection site, reducing the need for daily injections. In this study, the electrospray technique is examine to form EX@CS nanospheres by electrostatic interaction between cationic chitosan (CS) and negatively charged EX. These nanospheres are uniformly dispersed in a pH-temperature responsive pentablock copolymer, which forms micelles and undergoes sol-to-gel transition at physiological conditions. Following injection, the hydrogel gradually degraded, exhibiting excellent biocompatibility. The EX@CS nanospheres are subsequently released, maintaining therapeutic levels for over 72 h compared to free EX solution. The findings demonstrate that the pH-temperature responsive hydrogel system containing EX@CS nanospheres can be a promising platform for the treatment of T2D.     

A portable microreactor with minimal accessories for polymerase chain reaction: application to the determination of foodborne pathogens

The authors describe a microreactor for performing a multiplexed polymerase chain reaction (PCR) which is operated with minimal accessories such as a single heater for gene amplification and a hand-held syringe for sample actuation. It was fabricated by wrapping a polytetrafluoroethylene (PTFE) tube around a rectangular poly(dimethylsiloxane) (PDMS) block having a predetermined thickness. The resulting portable microreactor was applied to PCR using a single heater because the rectangular PDMS block spatially segregated the upper and lower arrays of the PTFE tube. This warrants the adjustment of distinct temperatures inside the upper and lower tubes. A hand-held plastic syringe was connected to the inlet of the PTFE tube and used as a portable pump to achieve a homogeneous transport of a sample liquid inside the microreactor. The use of gas-impermeable PTFE prevents the formation of bubbles during thermal cycling. The microreactor was successfully applied to the amplification of typical DNA fragments of three foodborne pathogens in less than 30 min. In our perception, this method paves the way to the construction of a truly portable PCR chip that is applicable to rapid clinical diagnosis and the detection of foodborne pathogens.

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Contraction of the proximal mapping and applications to the equilibrium problem

In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.     

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

In this paper, two splitting extragradient-like algorithms for solving strongly pseudomonotone equilibrium problems given by a sum of two bifunctions are proposed. The convergence of the proposed methods is analyzed and the R-linear rate of convergence under suitable assumptions on bifunctions is established. Moreover, a noisy data case, when a part of the bifunction is contaminated by errors, is studied. Finally, some numerical experiments are given to demonstrate the efficiency of our algorithms.     

Secondary Metabolites from the Fruiting Bodies of Coriolopsis aspera in Vietnam and their Bioactivities

Chemistry of Natural Compounds -     

Finite‐size corrections at the hard edge for the Laguerre β ensemble

A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre β ensemble, characterized by the Dyson parameter β, and the Laguerre weight , in the hard edge limit. The latter relates to the eigenvalues in the vicinity of the origin in the scaled variable . Previous work has established the corresponding functional form of various statistical quantities—for example, the distribution of the smallest eigenvalue, provided that . We show, using the theory of multidimensional hypergeometric functions based on Jack polynomials, that with the modified hard edge scaling , the rate of convergence to the limiting distribution is , which is optimal. In the case , general the explicit functional form of the distribution of the smallest eigenvalue at this order can be computed, as it can for and general . An iterative scheme is presented to numerically approximate the functional form for general .