Related papers: Topological analysis and Boolean functions. II. Ap…

In this thesis I studied the Symanzik's method for the introduction of the boundary in a field theory and, specifically, I applied this method to three Topological Field Theories of the Shwartz type: the non-abelian Chern-Simons model, the…

Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…

This article is a follow up of our submitted paper [11] in which a decomposition of the Richards equation along two soil layers was discussed. A decomposed problem was formulated and a decoupling and linearisation technique was presented to…

Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the $N=2$ superconformal…

New method of analysing the free and heavy symmetric tops using Euler's equations to perform extraction from the body frame to the lab frame. Subsequent to extraction, the lab frame equations are solved by space phasor method.

This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…

We show, in a borderline case which was not covered before, the validity of nonlinear Calder\'on-Zygmund estimates for a class of non-uniformly elliptic problems driven by double phase energies.

The formula of expanding the Abel variety theta function restricted to Abel subvariety into theta functions of this subvariety is obtained. With the help of this formula the solution of differential equations with Jacobi theta functions,…

We propose a non-abelian higher-spin theory in two dimensions for an infinite multiplet of massive scalar fields and infinitely many topological higher-spin gauge fields together with their dilaton-like partners. The spectrum includes local…

In this paper, we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz-Sobolev space. Here, we use the variational methods developed by Szulkin combined with some properties of…

Two phase picture is a simple and effective methodology to capture the nonequilibrium dynamics of polymer associated with tension propagation. When applying it to the driven translocation process, there is a point to be noted, as briefly…

Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one…

This paper considers some physically interesting cosmological dynamical systems in the FRW-scalarfield category which are examined for integrability according to the criterion of Painlev\'e. In the literature these systems have been…

We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider linear evolutionary problems of elliptic, hyperbolic and…

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property but their energy functional is unbounded both lower and…

The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the…

We propose two types of stochastic extensions of nonholonomic constraints for mechanical systems. Our approach relies on a stochastic extension of the Lagrange-d'Alembert framework. We consider in details the case of invariant nonholonomic…

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space $W^1L^{\Phi}([0,T])$. We employ the direct method of calculus of variations and we consider a potential function $F$…