An efficient green synthesis and antibacterial activity of 1,3-benzoxazine and 1,3-naphthoxazine using NaCl.SiO2 as solid catalyst in neat condition

A series of 1,3-oxazine derivatives were synthesized by a one-pot three-component (ie, phenol, formaldehyde, amine) method where SiO₂ bonded with NaCl was used as a reusable, more efficient, easily prepared, and available solid catalyst. The reactions were also carried out at room temperature for greener approach. in vitro studies for the synthesized compounds were also done against two gram-positive (Bacillus subtilis and Staphylococcus aureus) and two gram-negative bacteria (Escherichia coli and Klebsiella pneumonia) to check for their applicability as an antibacterial agent where some of the synthesized compounds gives the best antibacterial activity against selected bacterial strains. Streptomycin was used as a standard control for all the microbial test.     

Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations

This paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations. Upon making some suitable assumptions, the existence and uniqueness of a weighted pseudo almost periodic solution is obtained. To illustrate our main result, we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional-differential equations with feedback control.     

Weighted pseudo-almost periodic solutions to a neutral delay integral equation of advanced type

This paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo-almost periodic solutions to a neutral delay integral equation of advanced type introduced by T.A. Burton in the literature. The abstract results are then utilized to characterize weighted pseudo-almost periodic solutions to the well-known logistic equation.     

Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space

In this paper we are concerned with the spectral analysis for some classes of finite rank perturbations of diagonal operators in the form, A = D + F, where D is a diagonal operator and F = u ₁ ? v ₁ + u ₂ ? v ₂ + … + u _m ? v _m is an operator of finite rank in the non-archimedean Hilbert space \(\mathbb{E}_\omega \) . Using the theory of Fredholm operators in the non-archimedean setting and the concept of essential spectrum for linear operators, we compute the spectrum of A. A few examples are given at the end of the paper to illustrate our main results.     

Fluctuation Theory for a Three-Dimensional Model of Maxwellian Molecules

Under suitable assumptions, a functional central limit theorem is obtained for a three-dimensional model of Maxwellian molecules. This model is related to a nonlinear Boltzmann-type equation. It will be proved that the family of the distributions induced by fluctuation processes converges weakly.     

Almost automorphic solutions of evolution equations

This paper is concerned with the existence of almost automorphic mild solutions to equations of the form

where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .

     

Some Remarks on Some Second-order Hyperbolic Differential Equations

We are concerned with the almost automorphic solutions to the second-order hyperbolic differential equations of type ü(s) + 2B ù(s) + Au(s) = f(s) (*), where A, B are densely defined closed linear operators acting in a Hilbert space H, and f : R |—> H is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions, every solution to (*) is almost automorphic.     

Global phenotypic screening for antimalarials

Malaria, a devastating infectious disease caused by Plasmodium spp., leads to roughly 655,000 deaths per year, mostly of African children. To compound the problem, drug resistance has emerged to all classical antimalarials and may be emerging for artemisinin-based combination therapies. To address the need for new antimalarials with novel mechanisms, several groups carried out phenotypic screening campaigns to identify compounds inhibiting growth of the blood stages of Plasmodium falciparum. In this review, we describe the characterization of these compounds, explore currently ongoing strategies to develop lead molecules, and endorse the concept of a "malaria box" of publicly accessible active compounds.     

Almost automorphic solutions to some damped second-order differential equations

In this paper we make extensive use of dichotomy tools and the well-known Schauder fixed point principle to study and obtain the existence of almost automorphic solutions to some nonautonomous damped second-order differential equations. To illustrate our abstract result, we study the existence of almost automorphic solutions to the so-called plate-like equation.