We solve the Killing spinor equations for all near-horizon IIB geometries which preserve at least one supersymmetry. We show that generic horizon sections are 8-dimensional almost Hermitian spin${}_c$ manifolds. Special cases include horizon sections...
Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of elucidating t...
The penetration of transverse magnetic flux into a thin superconducting square film in the flux flow state is considered by numerical simulation. Due to the film self-field, the governing equations are nonlinear, and in combination with the finite vi...
Products formed are; Cu (OH)_2 + HCl -> CuCl_2 + H_2O Since CuCl_2 is soluble in water.. But; Cu (OH)_2 + HCl -> CuCl_2 + H_2O " [Not Balanced]" Balancing the equation..
The growth-fragmentation equation models systems of particles that grow and split as time proceeds. An important question concerns the large time asymptotic of its solutions. Doumic and Escobedo ($2016$) observed that when growth is a linear function...
The growth-fragmentation equation models systems of particles that grow and reproduce as time passes. An important question concerns the asymptotic behaviour of its solutions. Bertoin and Watson ($2018$) developed a probabilistic approach relying on...
A one-electron Schroedinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single- and multi-d...
For a given many-electron molecule, it is possible to define a corresponding one-electron Schrödinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single- and multi-d...
Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of NNs. In th...
In the present work, we use the Adomian Decomposition method to find the approximate solution for some cases of the Newell whitehead segel nonlinear differential equation which was solved previously with exact solution by the Homotopy perturbation an...
We describe the three-body loss coefficient of identical fermions with $p$-wave interactions using a set of rate equations in which three-body recombination happens via an indirect process. Our theoretical treatment explains experimental results just...
Motivated by its application in ecology, we consider an extended Klausmeier model, a singularly perturbed reaction-advection-diffusion equation with spatially varying coefficients. We rigorously establish existence of stationary pulse solutions by bl...
We consider the evolution of multi-pulse patterns in an extended Klausmeier equation with parameters that change in time and/or space. We formally show that the full PDE dynamics of a $N$-pulse configuration can be reduced to a $N$-dimensional dynami...
Using the non-empirical Variational Induced Breathing (VIB) model, the thermal properties of periclase (MgO) under high pressures and temperatures are investigated using molecular dynamics, which includes all anharmonic effects. Equations of state fo...
This article is concerned with the well-posedness of the "filtering equations", due to Zakai and Kushner-Stratonovich, arising in nonlinear stochastic filtering. In general situations, notably in correlated diffusion models and when signal coefficien...
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic filtering an...
The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime is obtaine...
force up and force down relationship of two fluids in equilibrium. The Young–Laplace equation is the force up description of capillary pressure, and the
developed within a liquid droplet/film can be calculated using the Young–Laplace equation (e.g.): Δ p = − γ ∇ ⋅ n ^ = γ ( 1 R 1 + 1 R 2 ) {\displaystyle
mathematician, unified the work of these two scientists to derive the Young–Laplace equation, the formula that describes the capillary pressure difference