相关论文: Comment on: "Development of the perturbation theor…

In this work, we develop a potential-based formalism for Maxwell's equations in isotropic media with weak spatial dispersion within the electric quadrupole-magnetic dipole approximation. We introduce an operator form of the constitutive…

To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…

In this paper within a field-theoretical approach taking into account explicitly a co-solvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann…

We develop a perturbation method that generalizes an approach proposed recently to treat velocity--dependent quantum--mechanical models. In order to test present approach we apply it to some simple trivial and nontrivial examples.

This manuscript is intended as an accompaniment to Guth's "A restriction estimate using polynomial partitioning". We begin by summarizing the core ideas of the proof, elaborating the history and development of the techniques therein. From…

We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…

We consider an application of a general theory for cavities with point-like perturbations for a rectangular shape. Hereby we concentrate on experimental wave patterns obtained for nearly degenerate states. The nodal lines in these patterns…

We discuss two simple variational approaches to quantum wells. The trial harmonic functions analyzed in an earlier paper give reasonable results for all well depths and are particularly suitable for deep wells. On the other hand, the…

I critically discuss two of the potential inconsistencies pointed out in the recent manuscript by Epelbaum, Gasparyan, Gegelia and Meissner, published in Eur. Phys.J. A54, 186 (2018). The potential inconsistencies are: (i) a possible…

We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…

I present an outline of chiral perturbation theory and discuss some recent developments in the field.

The sum-of-squares method can give rigorous lower bounds on the energy of quantum Hamiltonians. Unfortunately, typically using this method requires solving a semidefinite program, which can be computationally expensive. Further, the…

We provide an explicit expression for the second-order perturbative solution of a single trapped-ion interacting with a laser field in the strong excitation regime. From the perturbative analytical solution, based on a matrix method and a…

A recent paper by L.~Zheng [Phys. Plasmas, 30, 042515 (2023)] presented a critical analysis of standard Lie-transform perturbation theory and suggested that its application to the problem of charged-particle motion in a magnetic field…

An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries,…

The interest in complex deep neural networks for computer vision applications is increasing. This leads to the need for improving the interpretable capabilities of these models. Recent explanation methods present visualizations of the…

Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of…

The replica method for a quenched disordered system is considered in a perturbative field theory. Since correction in a finite-order perturbation is given in a polynomial of the replica number $n$, the zero-replica limit $n \to 0$ is…

High accuracy calculations of atomic properties require using long basis sets. In particular, it is necessary to include large number of partial waves and estimate truncation corrections. The convergence in partial waves is known to be…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…