We develop a series solution for the bound-state energy levels of the quantum-mechanical one-dimensional finite square-well potential. We show that this general solution is useful for local approximations of the energy spectrum ~which target a particular energy range of the potential well for high accuracy!, for global approximations of the energy spectrum ~which provide analytic expressions of...

We study a group of new methods to solve an open problem that is the shortest paths problem on a given fix-weighted instance. It is the real significance at a considerable altitude to reach our aim to meet these qualities of generic, efficiency, precision which we generally require to a methodology. Besides our proof to guarantee our measures might work normally, we pay more interest to root ou...

Two particles, in absence of hydrodynamics interactions, are considered such a way to have interaction by a hard-core potential plus an potential hole of depth −V0 and width of δ. The Smoluchowski equation has solved for such a system in the center of mass coordinate. Also, the self diffusion coefficient for N particle system interacting among square well potential up to the first order of conc...

Interest in vanadium chemistry has increased since the recognition of the involvement of vanadium ions in many important biological systems.1 The distinctive preference of the vanadium ion for N/O donor atom types has prompted the synthesis and characterization of many model complexes containing N/O donor ligands, the spectroscopic properties and solution behavior of which have been investigate...

Consider an over-determined linear system Ax ≈ b and an under-determined linear system By = c. Given b = A x̂+h, under what conditions x̂ will minimize the residual ATx− b in `1-norm (i.e., ‖h‖1 = minx ‖ATx− b‖1)? On the other hand, given c = Bh, under what conditions h will be the minimum `1-norm solution of By = c? These two “solution-recovery” problems have been the focus of a number of recent...

We prove the Kato conjecture for elliptic operators on Rn. More precisely, we establish that the domain of the square root of a uniformly complex elliptic operator L = −div (A∇) with bounded measurable coefficients in Rn is the Sobolev space H1(Rn) in any dimension with the estimate ‖ √ Lf‖2 ∼ ‖∇f‖2.

In the framework of the Kompaneets approximation the propagation of a shock front (SF) in inhomogeneous medium with the powerlaw density decrease at the exponent n = 2 is investigated. For this important case corresponding to outer regions of the solar and stellar coronas an unexpectedly simple exact solution clearing a structure of the general solution for an arbitrary monotonic density of med...

The generalized integral transform technique (GITT) is employed to obtain a hybrid numericalanalytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that ...