Existence of solutions to some classes of partial fractional differential equations

In this paper we obtain the existence of solutions to some classes of partial fractional differential equations. Applications include the existence of solutions to a fractional heat-like equation.     

Existence and uniqueness of pseudo-almost periodic solutions to some classes of partial evolution equations

Some sufficient conditions for the existence and uniqueness of pseudo-almost periodic (mild) solutions to some classes of partial evolution equations are given. We then make use of our abstract results to discuss the existence of pseudo-almost periodic solutions to some partial differential equations.     

Analytical solution to the problem of heat interaction of fluid flow and solid filling

The results of analytical solution to the problem of thermal interaction of a fluid stream with a media of solid particles found on the basis of the ODTPM model [1] are presented. A non-stationary behaviour of the volume-averaged temperature of solid filling, being a measure of the efficiency from heat transfer between fluid and solid phases, and of the heat-carrier temperature at the exit of the layer is studied. Time dependences computed according to the obtained relationships are in good agreement with the results of numerical calculations [1] for different sets of the problem parameters. The found solution expands the possibilities to analyze the efficiency of the “fluid-solid phase” systems and can be a basis to develop methods of experimental evaluation of different parameters of the system.     

The existence of a weighted mean for almost periodic functions

In a recent paper by Liang et al. (2010) [1], the original question which is that of the existence of a weighted mean for almost periodic functions was raised. In particular, they showed through an example that there exist weights for which a weighted mean for almost periodic functions may or may not exist. In this note we give some sufficient conditions which do guarantee the existence of a weighted mean for almost periodic functions, which will then coincide with the classical Bohr mean. Moreover, we will show that under those conditions, the corresponding weighted Bohr transform exists.     

Computational studies on G-quadruplex DNA-stabilizing property of novel Wittig-based Schiff-Base ligands and their copper(II) complexes

A series of mono imine (C=N) group that contained Wittig-based Schiff-Base ligands was optimized using the DFT-based computational method and Gaussian 09 program package. These optimized molecules were docked with Quadruplex DNA (PDB ID: 1KF1) and duplex DNA (PDB ID: 1BNA) using AutoDock Vina program along with the reference molecules. Schiff-Base ligands derived from fused aromatic rings contained amines and precursor aldehyde (PA-5 both Z and E isomers) showed lower binding energy for G-quadruplex DNA among all and N-5 category both Z and E isomer Schiff-Base ligands have shown high selectivity for G-quadruplex DNA over duplex DNA which is a very important phenomenon to develop the G-quadruplex DNA stabilizers. For a few Schiff-Base molecules like Ligand-6 (1-{[2-Hydroxy-5-(2-pyren-1-yl-vinyl)-benzylidene]-amino}-naphthalen-2-ol) of N-5 category both Z and E isomers with groove binding and end stacking modes, molecular dynamic calculations were carried out. The study revealed that Ligand-6 of N-5 category E isomer with groove binding mode has higher stabilizing effect on G-quadruplex DNA in spite of having the higher binding energy value. Among Schiff-Base copper(II) complexes, Complex-3 (E-(1-{[2-Hydroxy-5-(2-pyren-1-yl-vinyl)-benzylidene]-amino}-naphthalen-2-ol)Cu) is having high binding affinity for G-quadruplex DNA as compared to others.

     

Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations

The paper revisits the concept of S^p$S^p$-pseudo-almost periodicity recently introduced by the author. In particular, we study the existence of pseudo-almost periodic solutions to some nonautonomous differential equations in the case when the semilinear forcing term is both continuous and S^p$S^p$-pseudo-almost periodic for p>1$p>1$. Applications include the existence of pseudo-almost periodic solutions to the heat equation with a forcing term, which is S^p$S^p$-pseudo-almost periodic and jointly continuous.     

Population models in almost periodic environments

We establish the basic theory of almost periodic sequences on ?₊. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.     

Existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations

In this paper, under Acquistapace-Terreni conditions, we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations. Applications include the existence of weighted pseudo-almost periodic solutions to a nonautonomous heat equation with gradient coefficients.     

Existence of asymptotically almost periodic solutions for some second-order hyperbolic integrodifferential equations

Semigroup Forum - In this paper we study and obtain the existence of asymptotically almost periodic solutions to some classes of second-order hyperbolic integrodifferential equations of...