Erdös conjectured that the Diophantine equation x + y = z has infinitely many solutions in pairwise coprime 3-powerful integers, i.e., positive integers n for which p | n implies p3 | n. This was recently proved by Nitaj who, however, was unable to verify the further conjecture that this could be done infinitely often with integers x, y and z none of which is a perfect cube. This is now demonst...

ALEŠ BEZDĚK, DAVID KRÁL & FRANTIŠEK X. J. SLÁDEČEK 1Biology Centre CAS, Institute of Entomology, Branišovská 31, CZ-370 05 České Budějovice, Czech Republic. E-mail: [email protected] 2Charles University in Prague, Faculty of Science, Department of Zoology, Viničná 7, CZ-128 43 Praha 2, Czech Republic. E-mail: [email protected] 3Faculty of Science, University of South Bohemia, Branišovská 31, ...

In this study, a novel mesoporous silica nanoparticles drug carrier contributes to improving the solubility, dissolution, and the oral bioavailability of apigenin (AP). The apigenin of solid dispersion of mesoporous silica nanoparticles (AP-MSN) was prepared by physical absorption method and also, in-vitro drug release and in-vivo bioavailability performance were evaluated. Based on its solubil...

We consider the Banach space X = (R, ‖ · ‖) with a normalized, absolute norm. Our aim in this paper is to calculate the modified NeumannJordan constant C ′ NJ(X) and the Zbăganu constant CZ(X).

Building on previous work of Di Nasso and Luperi Baglini, we provide general necessary conditions for a Diophantine equation to be partition regular. These are inspired by Rado's characterization regular linear homogeneous equations. We conjecture that these also sufficient regularity, at least equations whose corresponding monovariate polynomial is linear. This would natural generalization the...

This study addressed the possibility of forming of co-amorphous systems between clozapine (CZ) and various carboxylic acid plasticizers (CAPs). The aim was to improve the solubility and oral bioavailability of clozapine. Co-amorphous dispersions were prepared using modified solvent evaporation methodology at drug/plasticizer stoichiometric ratios of 1:1, 1:1.5 and 1:2. Solid state characterizat...

The advancements in nanoscience have brought attention to the potential of utilizing nanoparticles as carriers for oral insulin administration. This study aims investigate effectiveness synthesized polymeric mesoporous silica (MSN) and their interactions with IR through in-silico docking. Diabetic rats were treated various MSN samples, including pure MSN, Amin-grafted MSN/PEG/Insulin (AMPI), Al...

Several nanocomposites based on Mesoporous Silica Nanoparticles (MSN), aluminum ions, and Polyethyleneimine (PEI) were synthesized by the combination of sol-gel post-synthesis methods. These mainly composed MSN with leading Al PEI species alone or in combination. The Al-MSN, MSN-PEI, Al-MSN/PEI samples characterized using FT-IR, XRD, SEM, EDX, zeta potential, nitrogen physisorption techniques. ...

Abstract Background A low pH environment is created due to the production of acids by oral biofilms that further leads dissolution hydroxyapatite crystal in tooth structure significantly altering equilibrium. Although overall bacterial counts may not be eradicated from cavity, however, synthesis engineered anti-bacterial materials are warranted reduce pathogenic impact biofilms. The purpose thi...