The Klein-Gordon equation of the hydrogen atom has a low-lying eigenstate, called hydrino state, with square integrable wavefunction. The corresponding spinor solution of Dirac’s equation is not square integrable. For this reason the hydrino state has been rejected in the early days of quantum mechanics as being unphysical. Maybe it is time to change opinion.

We argue that the square of the norm of the Hubbard wave function is proportional to the determinant of a matrix, which is obtained by linearization of the Lieb-Wu equations around a solution. This means that in the vicinity of a solution the Lieb-Wu equations are non-degenerate, if the corresponding wave function is non-zero. We further derive an action that generates the LiebWu equations and ...

A new approach to the construction of mean-square numerical methods for the solution of stochastic differential equations with small noises is proposed. The approach is based on expanding the exact solution of the system with small noises in powers of time increment and small parameter. The theorem on the mean-square estimate of method errors is proved. Various efficient numerical schemes are d...

This talk deals with the construction of reliable numerical solutions of mixed problems for hyperbolic second order partial differential models with random information in the variable coefficients of the differential equation and in the initial data. Using random difference schemes, a random discrete eigenfunctions method is developed in order to construct a discrete approximating stochastic pr...

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic quadratic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are...

In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a BSDE under full information. In particular, we provide a suitable version of the Föllmer-Schweizer d...

In Part I [2], we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We performed a stability analysis and established the notable fact that the network is still able to converge in the mean-square-error sense to the desired solution. Once stable be...

In this paper the authors propose a flexible electronic solution, to improve the energetic efficiency of a thermo plant. This is achieved by replacing the mechanical gear box, placed traditionally between a gas turbine and a synchronous generator; by a power electronic converter. After reminding problematic of gear boxes and interest of a proposed electronic solution in high power plants, the a...

Abstract. A special class of recurrent neural network, termed Zhang neural network (ZNN) depicted in the implicit dynamics, has recently been proposed for online solution of time-varying matrix square roots. Such a ZNN model can be constructed by using monotonically-increasing odd activation functions to obtain the theoretical time-varying matrix square roots in an error-free manner. Different ...

The properties of the solvent affect the behavior of the solution. We propose a model that accounts for the contribution of the solvent free energy to the free energy of globular proteins in solution. For the case of an attractive square-well potential, we obtain an exact mapping of the phase diagram of this model without solvent to the model that includes the solute-solvent contribution. In pa...