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Quantum Optimal Control (QOC) supports the advance of quantum technologies by tackling its problems at the pulse level: Numerical approaches iteratively work towards a given target by parametrising the applied time-dependent fields with a…
A probabilistic method is derived for solution of ohmic circuit problems. It is compared to the standard approach, which is construction and solution of a set of coupled, linear equations manifesting Kirchhoff's laws. An example is made of…
The quantitative description of the effects of nuclear dynamics on the measured neutrino-nucleus cross sections -- needed to reduce the systematic uncertainty of long baseline neutrino oscillation experiments -- involves severe…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
We address and solve the long-standing gauge-invariance problem of the nucleon spin structure. Explicitly gauge-invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
This paper addresses the problem of tracking control for robotic vehicles equipped with pivoted unidirectional actuators. Starting from a baseline robust controller that assumes unconstrained inputs, we redesign the control law to be…
A projection operator technique for solution of relativistic wave equation on non-compact group has been proposed. This technique was applied to the construction of wave equations for charged vector boson in a potential field. The equations…
We consider the problem of strong existence and uniqueness of a Brownian motion forced to stay in the quadrant by an electrostatic repulsion from the sides that works obliquely. The results are reminiscent of the study of a Brownian motion…
We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
The analysis of the affect of angular velocity on the geometry of the basins of convergence (BoC) linked to the equilibrium points in the restricted three-body problem is illustrated when the primaries are source of radiation. The bivariate…
The torsion loading of a coupled cylinder, comprising distinct upper and lower cylindrical sections potentially made of different materials, is considered. The bottom of the cylinder is fixed in place, and induces the cylinder vibration.…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
The main problem is to understand and to find periodic symmetric orbits in the $n$-body problem, in the sense of finding methods to prove or compute their existence, and more importantly to describe their qualitative and quantitative…
The computation of vibrational spectra of diatomic molecules through the exact diagonalization of algebraically determined matrixes based on powers of Morse coordinates is made substantially more efficient by choosing a properly adapted…
The control approaches generally resort to the tools from the mathematics, but whether and how the mathematics can benefit from the control approaches is unclear. This paper aims to bring the "control design" idea into the mathematics by…