Let $(\mathbb{D}^2,\mathcal{F},\{0\})$ be a singular holomorphic foliation on the unit bidisc $\mathbb{D}^2$ defined by linear vector field \[ z \,\frac{\partial}{\partial z}+ \lambda \,w w}, \] where $\lambda\in\mathbb{C}^*$. Such has non-degenerate linearized singularity at $0$. $T$ harmonic current directed $\mathcal{F}$ which does not give mass to any of two separatrices $(z=0)$ and $(w=0)$...

We study the existence of harmonic maps and Dirac-harmonic from degenerating surfaces to non-positive curved manifold via scheme Sacks Uhlenbeck. By choosing a suitable sequence $\alpha$-(Dirac-)harmonic closed hyperbolic surface, we get convergence cleaner energy identity under uniformly bounded assumption. In this identity, there is no loss near punctures. As an application, obtain result abo...

Abstract: A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart from the standard coherent states, a further class of solutions is derived with a ...

Perfectly Matched Layers (PMLs) are widely used for the numerical simulation of wave-like problems defined on large or infinite spatial domains. However, for both the time-dependent and the time-harmonic cases, their performance critically depends on the so-called absorption function. This paper deals with the choice of this function when classical numerical methods are used (based on finite di...

the potential function of lippincott and schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. the parameters originally introduced to the potential function by lippincott and schroeder have been determined from the structural parameters such as 0.. .odistance 0-h bond distance, h.. .o distance and hoo angle. thevalidity of harmonic oscillator approxim...

The framework of aane and hyperbolic laminations provides a unifying foundation for many aspects of conformal dynamics and hyperbolic geometry. The central objects of this approach are an aane Riemann surface lamination A and the associated hyperbolic 3-lamination H endowed with an action of a discrete group of iso-morphisms. This action is properly discontinuous on H, which allows one to pass ...