New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

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 .     

Yolk‐Shell Porous Microspheres of Calcium Phosphate Prepared by Using Calcium L‐Lactate and Adenosine 5′‐Triphosphate Disodium Salt: Application in Protein/Drug Delivery

A facile and environmentally friendly approach has been developed to prepare yolk‐shell porous microspheres of calcium phosphate by using calcium L ‐lactate pentahydrate (CL) as the calcium source and adenosine 5′‐triphosphate disodium salt (ATP) as the phosphate source through the microwave‐assisted hydrothermal method. The effects of the concentration of CL, the microwave hydrothermal temperature, and the time on the morphology and crystal phase of the product are investigated. The possible formation mechanism of yolk‐shell porous microspheres of calcium phosphate is proposed. Hemoglobin from bovine red cells (Hb) and ibuprofen (IBU) are used to explore the application potential of yolk‐shell porous microspheres of calcium phosphate in protein/drug loading and delivery. The experimental results indicate that the as‐prepared yolk‐shell porous microspheres of calcium phosphate have relatively high protein/drug loading capacity, sustained protein/drug release, favorable pH‐responsive release behavior, and a high biocompatibility in the cytotoxicity test. Therefore, the yolk‐shell porous microspheres of calcium phosphate have promising applications in various biomedical fields such as protein/drug delivery.     

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.     

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.     

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.     

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

Chemistry of Natural Compounds -