数学物理
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
This study employs the Riesz-Feller fractional derivative to determine Fisher and Shannon parameters for a one-dimensional harmonic oscillator. By deriving the Riesz fractional derivative of the probability density function, we quantify…
In 1986, Zamolodchikov conjectured an exponential structure for the semi-classical limit of conformal blocks on a sphere. This paper provides a rigorous proof of the analog of Zamolodchikov conjecture for Liouville conformal blocks on a…
Within the class of (1+2)-dimensional ultraparabolic linear equations, we distinguish a fine Kolmogorov backward equation with a quadratic diffusivity. Modulo the point equivalence, it is a unique equation within the class whose essential…
We exhaustively classify the Lie reductions of the real dispersionless Nizhnik equation to partial differential equations in two independent variables and to ordinary differential equations. Lie and point symmetries of reduced equations are…
Conjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geometry, two discretizations of principal curvature line…
We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an applicable framework for the complete solution…
We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems.
We study the minimizers of a magnetic 2D non-linear Schr\"odinger energy functional in a quadratic trapping potential, describing a rotating Bose-Einstein condensate. We derive an effective Thomas-Fermi-like model in the rapidly rotating…
We study mesoscopic fluctuations of orthogonal polynomial ensembles on the unit circle. We show that asymptotics of such fluctuations are stable under decaying perturbations of the recurrence coefficients, where the appropriate decay rate…
The paper is continuation of [6] where we have discussed some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. Strictly speaking, we have considered oscillatory dynamical models on…
In this work we would like to point out the possibility of generating a class of exactly solvable convection-diffusion-reaction equation in similarity form with intrinsic supersymmetry, i.e., the solution and the diffusion coefficient of…
The inverse medium problem, inherently ill-posed and nonlinear, presents significant computational challenges. This study introduces a novel approach by integrating a Neumann series structure within a neural network framework to effectively…
We prove the convergence of Araki-Haag detectors in any Haag-Kastler quantum field theory with an upper and lower mass gap. We cover the case of a single Araki-Haag detector on states of bounded energy, which are selected from the…
We draw connections between contact topology and Maxwell fields in vacuo on 3-dimensional closed Riemannian submanifolds in 4-dimensional Lorentzian manifolds. This is accomplished by showing that contact topological methods can be applied…
In this article, we study wormhole spacetimes in the framework of the static spherically symmetric SU(2) Einstein-Yang-Mills theory coupled to a phantom scalar field. We show rigorously the existence of an infinite sequence of symmetric…
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…
Over $\mathbb{C}$, Montgomery superized Herstein's construction of simple Lie algebras from finite-dimensional associative algebras, found obstructions to the procedure and applied it to $\mathbb{Z}/2$-graded associative algebra of…
1) The differential equation considered in terms of exterior differential forms, as \'E.Cartan did, singles out a differential ideal in the supercommutative superalgebra of differential forms, hence an affine supervariety. In view of this…
We study the Fr\"ohlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass $m_{\mathrm{eff}}(\alpha)\geq \alpha^4 m_{\mathrm{LP}}-C\alpha^{4-\epsilon}$, where $m_{\mathrm{LP}}$ is…