Diophantinc approximation by linear forms on manifolds

The following Khintchine-type theorem is proved for manifoldsM embedded in ℝ ^k which satisfy some mild curvature conditions. The inequality |q·x| <Ψ(|q|) whereΨ(r) → 0 asr → ∞ has finitely or infinitely many solutionsqεℤ ^k for almost all (in induced measure) points x onM according as the sum Σ _r ^{= 1/∞} Ψ(r)r ^k−2 converges or diverges (the divergent case requires a slightly stronger curvature condition than the convergent case). Also, the Hausdorff dimension is obtained for the set (of induced measure 0) of point inM satisfying the inequality infinitely often whenψ(r) =r ^−t . τ >k − 1.     

p-Laplacian problems with jumping nonlinearities

We consider the p-Laplacian boundary value problem

(1)     

An Innovative Hydrogen Peroxide-Sensing Scaffold and Insight Towards its Potential as an ROS-Activated Persulfide Donor

Reactive sulfur species, such as hydrogen sulfide, persulfides, and polysulfides, have recently emerged as key signaling molecules and important physiological mediators within mammalian systems. To better assess the therapeutic potential of their exogenous administration, we report on the development of a unique hydrogen peroxide (H₂O₂)-sensing motif and its capacity for providing cellular protection against oxidative stress while serving as a reactive oxygen species (ROS)-activated persulfide donor. With the strategic implementation of a gem-dimethyl group to promote both stability and cyclization, we found the initial rate of payload release from this newly derived scaffold to be directly proportional to the concentration of H₂O₂ and to proceed via an unprecedented pathway that avoids the production of electrophilic byproducts, a severe limitation that has plagued the physiological application of previous designs.     

Nonresonance conditions for generalised ?-Laplacian problems with jumping nonlinearities

We consider the boundary value problem

(0.1)     

The well‐posedness of the electric field integral equation for transient scattering from a perfectly conducting body

We consider the scattering of a transient electromagnetic field incident on a body with a smooth, perfectly conducting surface. A standard numerical method for calculating the scattered field is to use a time dependent, surface integral equation (called the electric field integral equation) to calculate the surface currents and charges induced by the incident field—these currents and charges then yield the scattered fields by means of standard integral representations (vector and scalar potentials). In this paper we show that the time‐dependent electric field integral equation is well‐posed in a suitable function space setting. We also investigate the behaviour of the solutions at large time. Copyright © 1999 John Wiley & Sons, Ltd.     

Curves of positive solutions of boundary value problems on time-scales

Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem

(2)

(4)

u(a)=u(b)=0,