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In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz and CPT violating QED. Essentially, we control the breaking terms by using a suitable set of…
We analyze the performance of a variant of Newton method with quadratic regularization for solving composite convex minimization problems. At each step of our method, we choose regularization parameter proportional to a certain power of the…
We discuss the approach suggested by Deffayet et al. (DPSV) to analysing the linearized perturbations in Horndeski theory in the case of a static, spherically symmetric background. In $\mathcal{L}_3$ subclass of Horndeski theories we prove…
In this paper, an approach is developed to solve the three body problem involving masses which posses spherical symmetry. The problem dates back to the times of Poincare, and is undoubtedly one of the oldest of unsolved problems of…
We consider arithmetic three-spheres inequalities to solutions of certain second order quasilinear elliptic differential equations and inequalities with a Riccati-type drift term.
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree…
In this paper, we propose a third-order Newton's method which in each iteration solves a semidefinite program as a subproblem. Our approach is based on moving to the local minimum of the third-order Taylor expansion at each iteration,…
We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The…
This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods. This paper establishes the stability and a priori error…
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
We compare the usual operator modulus with two symmetrized variants, the arithmetic symmetric modulus and the quadratic symmetric modulus. For every unitarily invariant norm, we determine sharp equivalence constants among these three…
We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak…
In previous publications, we illustrated the effectiveness of the method of the inhomogeneous differential equation in calculating the electric polarizability in the one-dimensional problem. In this paper we extend our effort to apply the…
Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.
The fundamental solution of the classical approximation of a three waves kinetic equation that happens in the kinetic theory of a condensed gas of bosons near the critical temperature is obtained. It is also proved to be unique in a…
We address the Poincar\'e-Perron's classical problem of approximation for high order linear differential equations in the class of almost periodic type functions, extending the results for a second order linear differential equation in…
Spherical caps play a crucial role in establishing a criterion for the existence of solutions to the Yamabe problem on a compact Riemannian manifold with boundary, similar to the role played by the standard sphere in the problem on a closed…
We analyze a recent application of homotopy perturbation method to some heat-like and wave-like models and show that its main results are merely the Taylor expansions of exponential and hyperbolic functions. Besides, the authors require…