Complexity trees of the sequence of some nonahedral graphs generated by triangle.

Calculating the number of spanning trees of a graph is one of the widely studied graph problems since the Pioneer Gustav Kirchhoff (1847). In this work, using knowledge of difference equations we drive the explicit formulas for the number of spanning trees in the sequence of some Nonahedral (nine faced polyhedral) graphs generated by triangle using electrically equivalent transformations and rules of the weighted generating function. Finally, we evaluate the entropy of graphs in this manuscript with different studied graphs with an average degree being 4, 5 and 6.

Exploiting polymer blending approach for fabrication of buccal chitosan-based composite sponges with augmented mucoadhesive characteristics.

In the course of application and modernization of buccal dosage forms, lyophilized sponges for transmucosal drug delivery symbolize one of the most attractive approaches. Chitosan (CS) has been extensively investigated as a forming material of different buccal dosage forms including sponges. However, CS-based buccal delivery systems suffer from many limitations like weak adhesion strength and poor tensile properties.

Laminated chitosan-based composite sponges for transmucosal delivery of novel protamine-decorated tripterine phytosomes: Ex-vivo mucopenetration and in-vivo pharmacokinetic assessments.

In the current study, laminated chitosan (CS):hydroxypropyl methylcellulose (HPMC) composite sponges were exploited as solid matrices for buccal delivery of tripterine phytosomes functionalized with novel mucopenetrating protamine layer (PRT-TRI-PHY). Tripterine (TRI) is a herbal drug widely investigated as a potential anticancer candidate against various types of cancers. However, clinical use of TRI is handicapped by its low oral bioavailability.

On properties of geodesic semilocal E-preinvex functions.

The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E--semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved by using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-preinvex functions, and geodesic quasi-semilocal E-preinvex functions.

Self-assembled phospholipid-based phytosomal nanocarriers as promising platforms for improving oral bioavailability of the anticancer celastrol.

Celastrol (CST) is a promising natural drug of herbal origin that gained a great interest in the recent years by virtue of its wide variety of pharmacological actions. Nowadays, CST is extensively studied as a natural anticancer surrogate with a potential activity against various types of cancers. However, CST suffers from many limitations that handicapped its clinical utility such as limited aqueous solubility and poor gastrointestinal absorption which resulted into its low oral bioavailability.