The rate of convergence of a CI calculation on the ground state of the helium atom is rigorously derived under suitable assumptions on the regularity of the exact wavefunction. For bases consisting of all partial waves with angular momentum less than or equal to L, the large L asymptotic energies are found to obey the well-known formula EL − E = CL−3 + o(L−3), where C is an explicit constant de...

This paper investigates the issue of the internal stability of nonlinear delay systems controlled with a feedback law that performs exact input–output, linearization and delay cancellation. In previous works the authors showed that, unlike with the case of systems without state delays, when the relative degree is equal to the number of state variables and the output is forced to be identically ...

This work is a numerical perspective to highly dispersive dark optical solitons by using Laplace-Adomian decomposition method. The results are reported this scheme with precise accuracy and the error measure stunningly low. surface plots, density plots exhibited for different parameter choices. simulations almost an exact replica of such that analytically arise from governing system. suggested ...

In the papers [1] and [2] some higher analogs of the nonlinear evolutionary equation of Korteweg– de Vries are considered. Some NEEs of the higher order are represented in handbook [3]. In the present paper we have constructed new types of NEEs of higher order. For their construction the methods of factorization and exact linearization were used (see [4–8]). In Section 2 the summary of results ...

We show that the linearization of all exact solutions of classical chiral gravity around the AdS3 vacuum have positive energy. Non-chiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only ...

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both...

We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical WignerSeitz cells that yields Debye-Hückel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature) limit. Both the canonical (fixed number of microions) as well as the semi-grand-canonical (in contact with an infinite salt reservoir) cases are considered and discu...

This paper is a numerical simulation of highly dispersive optical solitons in birefringent fibers with polynomial nonlinear form, which achieved for the first time. The algorithmic approach applied usage Laplace–Adomian decomposition scheme. Dark and bright soliton simulations are presented. error measure has very low count, thus, almost an exact replica such that analytically arise from govern...