Related papers: Generator functions and their applications
The generating functionals (GF) method in Bogolyubov's formulation and its application for particle physics is considered. Effectiveness of the method is illustrated by two examples. So, GF method can be used as the technical trick solving…
Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization…
An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…
We propose a rigorous reformulation of the incompressible Navier Stokes equations, starting from the energy equation and the ideal gas law. This reformulation allows the definition of a functional over the pressure field, which is used to…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…
Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…
In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by…
The aim of this paper is to construct general forms of ordinary generating functions for special numbers and polynomials involving Fibonacci type numbers and polynomials, Lucas numbers and polynomials, Chebyshev polynomials, Sextet…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
A new version of the Hadwiger theorem on convex functions is established and an explicit representation of functional intrinsic volumes is found using new functional Cauchy-Kubota formulas. In addition, connections between functional…
Let $c\geq0$ and denote by $\mathcal{K}(\mathbb{H},c)$ the set of all infinitesimal generators $G:\mathbb{H}\to\mathbb{C}$ on the upper half-plane $\mathbb{H}$ such that $\limsup_{y\to\infty}y\cdot |G(iy)|\leq c.$ This class is related to…
In these lecture notes we discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green…
In [8] it was shown that the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schr\"odinger equation. In this paper we demonstrate a fundamental property of…
The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…
We establish recurrences formulas of the order of the classical groups that allow us to find a generalization of Euler's angles for classical groups and the invariant measures of these groups. We find the generating function for the SU(2)…
A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final…
We put together a general framework to deal with elliptic and parabolic equations associated with (nonlinear) nonlocal (fractional order) operators. Many well-known nonlocal operators enter into our framework, and in addition one may…
The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the…