Breather, lump and other wave profiles for the nonlinear Rosenau equation arising in physical systems.

This work explores the mathematical technique known as the Hirota bilinear transformation to investigate different wave behaviors of the nonlinear Rosenau equation, which is fundamental in the study of wave occurrences in a variety of physical systems such as fluid dynamics, plasma physics, and materials science, where nonlinear dynamics and dispersion offer significant functions. This equation was suggested to describe the dynamic behaviour of dense discrete systems. We use Mathematica to investigate these wave patterns and obtained variety of wave behaviors, such as M-shaped waves, mixed waves, multiple wave forms, periodic lumps, periodic cross kinks, bright and dark breathers, and kinks and anti-kinks.

Identification of a selective pyruvate dehydrogenase kinase 1 (PDHK1) chemical probe by virtual screening.

PDHK1 is a non-canonical Ser/Thr kinase that negatively regulates the pyruvate dehydrogenase complex (PDC), restricting entry of acetyl-CoA into the tricarboxylic acid (TCA) cycle and downregulating oxidative phosphorylation. In many glycolytic tumors, PDHK1 is overexpressed to suppress activity of the PDC and cause a shift in metabolism toward an increased reliance on glycolysis (the Warburg effect). Genetic studies have shown that knockdown or knockout of PDHK1 reverts this phenotype and inhibits tumor growth in vitro and in vivo, but chemical tools to pharmacologically validate and build upon these data are lacking.

Regularity and wave study of an advection-diffusion-reaction equation.

In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended direct algebraic method with traveling wave transformation has been used.

Numerical study of diffusive fish farm system under time noise.

In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties.