Related papers: Quasi-Pfaffians and applications
We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the non-commutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the…
We present a new fermionic solution of the supersymmetric matrix model. The solution satisfies the commutation and anticommutation relations for noncommutative superspace. Therefore the solution can be considered as an implementation of…
Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of…
We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.
We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that…
We propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization to the existing quasiconformal methods and allows manipulation of the geometry of folding. Moreover, the crucial quantity…
The totally non-negative pfaffian (TNNP) is define for a skew-symmetric matrix such that all the sub-pfaffians are non-negative. It appears in the pfaffian structure of $\tau$-function for the non-singular web solitons of the BKP equation .…
In this paper we will show that monomial summability processes with respect to different monomials are not compatible, except in the (trivial) case of a convergent series. We will apply this fact to the study of solutions of Pfaffian…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate…
We generalize the seminal polynomial partitioning theorems of Guth and Katz to a set of semi-Pfaffian sets. Specifically, given a set $\Gamma \subseteq \mathbb{R}^n$ of $k$-dimensional semi-Pfaffian sets, where each $\gamma \in \Gamma$ is…
Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models,…
In this paper, the author introduces the concept of the quasi-geometrically convex and defines a new identity for fractional integrals. By using of this identity, author obtains new estimates on generalization of Hadamard, Ostrowski and…
In a minimalistic view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind: 1-particle solutions (wavefunctions) of the equation of motion in the presence of an…
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of…
The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived…
A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear…
This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…
It is known that the universal enveloping algebra of the orthogonal Lie algebra of size even has a central element expressed in terms of Pfaffian of a certain matrix alternating along the anti-diagonal (which we call anti-alternating for…