Related papers: Fritz John's equation in mechanism design
Feature engineering is a crucial step in the process of predictive modeling. It involves the transformation of given feature space, typically using mathematical functions, with the objective of reducing the modeling error for a given…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage…
The pivotal issue of reliability is one of colossal concern for circuit designers. The driving force is transistor aging, dependent on operating voltage and workload. At the design time, it is difficult to estimate close-to-the-edge…
The claim by Rohrlich that the Abraham-Lorentz-Dirac equation is not the correct equation for a classical point charge is shown to be incorrect and it is pointed out that the equation which he proposes is the equation {\underline{derived}}…
We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality…
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
The well-known problem of classical mechanics considered by Bertrand (1857) and Darboux (1901) is reviewed in the context of Cartan's geometry.
In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order evolutionary equations in the phase space…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
The Fefferman-Stein type inequality for strong maximal operator is verified with compositions of some maximal operators in the heigher dimensions. An elementary proof of the endpoint estimate for the strong maximal operator is also given.
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
The chain of quantum mechanics equations is constructed for wave functions depending on coordinate and time as well as on velocity, acceleration and acceleration of higher orders.
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
This work is devoted to improve the time decay estimates for the solution and some of its derivatives of the linear structurally damped $\sigma$-evolution equations. The Pitt inequality is the main tool provided that the initial data lies…
New formulas for the construction of Pythagorean triples and generalizations to equations of higher powers. Application of formulas to some problems, in particular Fermat's equation with n=4.
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics.…