Emilia Witkowska, Paweł Ziń, and Mariusz Gajda Institute of Physics, Polish Academy of Sciences, al. Lotników, 02-668 Warsaw, Poland Institute for Theoretical Physics, Warsaw University, ul. Hoża 69, 00-681 Warsaw, Poland Soltan Institute for Nuclear Studies, ul. Hoża 69, 00-681 Warsaw, Poland Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal’s Stefan Wyszyński Universi...

The problem of Lagrangian and Hamiltonian mechanics with Grassmann variables has been discussed previously in works [1, 2, 3] and an examples of solutions for classical systems were presented. In this paper we propose the Hamilton-Jakobi method for the solution of the classical counterpart of Witten‘s model [4]. We assume that the states of mechanical system are described by the set of ordinary...

It is known that Einstein's equations in general relativity provide explicit expressions for the density, pressure and velocity of a perfect gas in terms of the coefficients of the metric (the potentials) and hence in terms of the coordinates. Using orthogonal space-times, the expressions involve four potentials only between which consistency relations hold. It is shown how degeneration of the ...

Recently new equations for vacuum correlators in the φ theory and in gluodynamics were derived via stochastic quantization method [2]. These equations, alternative to the Schwinger–Dyson and Makeenko–Migdal equations, allow one to connect correlators with different number of fields, but, in contrast to the Schwinger–Dyson equations, they are gauge–invariant in the case of gauge theories, and th...

the classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. many processes exhibit a certain degree of correlation and can be treated by autoregressive models among which the autoregressive model of order one (ar (1)) ...

Numerical models based on the finite-difference time-domain (FDTD) method have been developed to simulate thermal noise and spontaneous emission. Both types of noise may have effects on optical systems. Though their origin lies in quantum mechanics, macroscopic systems in which the discreteness of light can be ignored make it possible to simulate the noise using classical numbers. The absorbing...

Synopsis The density matrix renormalization group (DMRG) method is applied to the interaction round a face (IRF) model. When the transfer matrix is asymmetric, singular-value decomposition of the density matrix is required. A trial numerical calculation is performed on the square lattice Ising model, which is a special case of the IRF model.

The matrix method, due to Bibel and Andrews, is a proof procedure designed for automated theorem-proving. We show that underlying this method is a fully structured combinatorial model of conventional classical proof theory.

We study how to reduce the smoothing problem with obstacles to the smoothing problem with weights. A system connecting deviations of the solution from given values and weights is established. An algorithm for solving this equation is proposed and illustrated by examples.