Related papers: A Combinatorial Approach to the Opposite Bi-Free P…
The transformation of the partial fractional derivatives under spatial rotation in $R^2$ are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed…
We present two hierarchies of partial differential equations in $2+1$ dimensions. Since there exist reciprocal transformations that connect these hierarchies to the Calogero-Bogoyavlenski-Schiff equation and its modified version, we can…
This paper deals with classical solutions of the modified chiral model on $R^{2+1}$. Such solutions are shown to correspond to products of various factor which we call time-dependent unitons. Then the problem of solving the system of…
Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
Interactions of noncommutative solitons in a modified U(n) sigma model in 2+1 dimensions can be analyzed exactly. Using an extension of the dressing method, we construct explicit time-dependent solutions of its noncommutative field equation…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
We introduce a shifted version of the binomial theorem, and use it to study some remarkable trigonometric integrals and their explicit rewriting in terms of binomial multiple sums. Motivated by the expressions of area generating functions…
We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
In this brief note we critically examine the process of partial and of total differentiation, showing some of the problems that arise when we relate both concepts. A way to solve all the problems is proposed.
We compute the generating series for the simplest class of bi-free cumulants, beyond free cumulants, the two-bands bi-free cumulants of a pair of a left and a right variable. We also consider two-faced systems with a commutation condition…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We construct examples of variational bivectors that are not Poissonian.
A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots),…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
We discuss in this paper combinatorial aspects of boundary loop models, that is models of self-avoiding loops on a strip where loops get different weights depending on whether they touch the left, the right, both or no boundary. These…
We provide a detailed description of the relationships between the fractional Laplacian of order $2s\in(0,n)$ on $\mathbb{R}^n$ and the $\textit{$s$-polyharmonic}$ extension operator to the upper half space $\mathbb{R}^{n+1}_+$.
In this paper, operator-valued bi-free distributions are investigated. Given a subalgebra $D$ of a unital algebra $B$, it is established that a two-faced family $Z$ is bi-free from $(B, B^{\mathrm{op}})$ over $D$ if and only if certain…