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A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number…
The phenomenological investigation of noncommutative space-time in the laboratory frame are presented. We formulate the apparent time variation of noncommutativity parameter $\theta_{\mu\nu}$ in the laboratory frame due to the earth's…
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
Bifurcations of the $A_{n}$ type in Arnold's classification, in non-autonomous $p$-periodic difference equations generated by parameter depending families with $p$ maps, are studied. It is proved that the conditions of degeneracy,…
The main purpose of this paper is to prove the mean ergodic theorem for nonexpansive mappings and semigroups in locally compact Hadamard spaces, including finite dimensional Hadamard manifolds. The main tool for proving ergodic convergence…
Starting from degree N solutions of a time dependent Schroedinger-like equation for classical orthogonal polynomials, a linear matrix equation describing perturbations around the N zeros of the polynomial is derived. The matrix has…
We study the stationary Wigner equation on a bounded, one-dimensional spatial domain with inflow boundary conditions by using the parity decomposition in (Barletti and weifel, Trans. Theory Stat. Phys., 507--520, 2001). The decomposition…
Let $m\in \mathbb{N}$, $\alpha\in[0,1]$, and $V$ be a 1-periodic complex-valued distribution in the negative Sobolev space $H^{-m\alpha}[0,1]$. The singular non-self-adjoint eigenvalue problem $D^{2m}u+V u=\lambda u$, $D=-i d/dx$, with…
We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the…
We introduce and analyse the first order Enlarged Enhancement Virtual Element Method (E$^2$VEM) for the Poisson problem. The method allows the definition of bilinear forms that do not require a stabilization term, thanks to the exploitation…
We develop a framework for studying quasi-periodic maps and diffeomorphisms on $\mathbb{R}^n$. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on $\mathbb{R}^n$. In…
We derive the analytical expression of the coordinate time $t$ in terms of the eccentric anomaly $u$ at the second post-Newtonian order in General Relativity for a compact binary system moving on eccentric orbits. The parametrization of $t$…
The evolution of the vacuum state in a time-dependent external electric field of arbitrary polarization is investigated within a nonperturbative framework of quantum kinetic equations (QKEs). In our previous work [Phys. Rev. Res. 6, 043009…
We consider the renormalization of massive vector field interacting with charged scalar field in curved spacetime. Starting with the theory minimally coupled to external gravity and using the formulations with and without St\"uckelberg…
In this paper we give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible…
We prove the first unconditional consistency result for superpolynomial circuit lower bounds with a relatively strong theory of bounded arithmetic. Namely, we show that the theory V$^0_2$ is consistent with the conjecture that NEXP…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
A representation of partially spatially coherent and partially polarized stationary electromagnetic fields is given in terms of mutually uncorrelated, transversely shifted, fully coherent and polarized elementary electric-field modes. This…
We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…
A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms…