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Time reversal symmetry is studied in a space with noncommutativity of coordinates and noncommutativity of momenta of canonical type. The circular motion is examined as an apparent example of time reversal symmetry breaking in the space. On…

It is argued that there exists the only one inverse of the linear response function $\chi$, i.e. $\chi^{-1}$, which depends symmetrically of its spatial-times variables, see M.K. Harbola, and A. Banerjee, Phys. Rev. A {\bf 60}, 5101 (1999).…

The inverse Langevin function is a fundamental part of the statistical chain models used to describe the behavior of polymeric-like materials, appearing also in other fields such as magnetism, molecular dynamics and even biomechanics. In…

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…

Reversible algorithms play a crucial role both in classical and quantum computation. While for a classical bit the only nontrivial reversible operation is the bit-flip, nature is far more versatile in what it allows to do to a quantum bit.…

We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of…

We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…

In the present paper, we construct an algorithm for the evaluation of real Riemann zeta function $\zeta(s)$ for all real $s$, $s>1$, in polynomial time and linear space on Turing machines in Ko-Friedman model. The algorithms is based on a…

One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.

The key tool of this paper is a new Carleman estimate for an arbitrary parabolic operator of the second order for the case of reversed time data. This estimate works on an arbitrary time interval. On the other hand, the previously known…

An invertible matrix is called a Perron similarity if one of its columns and the corresponding row of its inverse are both nonnegative or both nonpositive. Such matrices are of relevance and import in the study of the nonnegative inverse…

After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.

It is shown that the justification of the Boltzman H-theorem needs more than just the assumption of molecular chaos and the picture of time irreversibility related to it should be reinvestigated.

We obtain direct and inverse approximation theorems of $2\pi$-periodic functions by Taylor--Abel--Poisson operators in the integral metric.

A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand-Levitan equation and the Fourier-Legendre series expansion of the transmutation kernel. A linear…

We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…

We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…

In this article, we study a direct and an inverse problem for the bi-wave operator $(\Box^2)$ along with second and lower order time-dependent perturbations. In the direct problem, we prove that the operator is well-posed, given initial and…