Related papers: Remarks on trigonometric functions after Eisenstei…
We consider orthogonal polynomials on the unit circle associated with certain semi-classical weight functions. This means that the Pearson-type differential equations satisfied by these weight functions involve two polynomials of degree at…
The Leah-Hamiltonian, $H(x,y)=y^2/2+3x^{4/3}/4$, is introduced as a functional equation for $x(t)$ and $y(t)$. By means of a nonlinear transformation to new independent variables, we show that this functional equation has a special class of…
We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…
Assumed that the parameters of a generalized hypergeometric function depend linearly on a small variable $\varepsilon$, the successive derivatives of the function with respect to that small variable are evaluated at $\varepsilon=0$ to…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
Although Feynman integrals in general cannot be expressed as well-studied special functions, they can be calculated systematically and efficiently using the \texttt{AMFlow} method in combination with differential equations in the kinematic…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
In this paper, we introduce and study multiple $\wp$-functions, which generalize the classical Weierstrass $\wp$-function to iterated sums over lattice points, and we establish explicit formulas expressing them in terms of single…
We survey some topics involving the Whitham equations, concentrating on the role of the Baker Akhiezer function in averaging. Some connections to symplectic geometry and Seiberg-Witten theory are indicated.
Using Bellman function approach, we present new proofs of weighted $L^2$ inequalities for square functions, with the optimal dependence on the $A_2$ characteristics of the weight and further explicit constants. We study the estimates both…
The functional potential formalism is used to analyze stationary axisymmetric spaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendre transformation, a ``Hamiltonian''is obtained, which allows to rewrite the dynamical equations…
Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator. Compared to GTFs with…
The structure of square integrable functionals measurable with respect to the $n-$point motion of the Arratia flow is studied. Relying on the change of measure technique, a new construction of multiple stochastic integrals along…
It is shown that in the two-exponential version of Liouville theory the coefficients of the three-point functions of vertex operators can be determined uniquely using the translational invariance of the path integral measure and the…
We analyze the Wigner function constructed on the basis of the discrete rotation and displacement operators labeled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyze the…
Bose-Einstein correlations of two identically charged $Q$-bosons are derived considering these particles to be confined in finite volumes. Boundary effects on single $Q$-boson spectrum are also studied. We illustrate the effects on the…
We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and…
In the article random functions in modules over the octonion algebra and Cayley-Dickson algebras are investigated. For their study transition measures with values in the octonion algebra and Cayley-Dickson algebras are used. Stochastic…
The present article deals with properties of a certain function of the Minkowski type with arguments defined by Engel series. Differential, integral, and other properties of the function were considered.
We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations…