相关论文: Toward a canonical qKdV equation

It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This…

We present an explicit formula for the canonical height of a projective toric variety.

Kapranov Theorem is a well known generalization of Newton-Puiseux theorem for the case of several variables. This theorem is stated mainly in the context of tropical geometry. We present a new, constructive proof, that also characterizes…

We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…

Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.

In this note we improve the parameter $q$ that appears in Theorem 1 obtained by the author in [Math. Ineq. \& appl., Vol 19 (3) (2016), 1013-1030].

This is a survey of select recent results by a number of authors, inspired by the classical configuration theorems of projective geometry.

This paper is devoted to the system of coupled KdV-like equations. It is shown that this apparently non-integrable system possesses an integrable reduction which is closely related to the Volterra chain. This fact is used to construct the…

Recent achievements in the heavy quark theory are critically reviewed. The emphasis is put on those aspects which either did not attract enough attention or cause heated debates in the current literature. Among other topics we discuss (i)…

We prove a new inequality for Gaussian processes, this inequality implies the Gordon-Chevet inequality. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…

We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…

Following some past advances, we reformulate a large class of linear continuum science equations in the format of the extended abstract theory of composites so that we can apply this theory to better understand and efficiently solve those…

I review recent theoretical advances in quantum chromodynamics. Particular emphasis is put on developments related to the precise prediction and interpretation of experimental data from present and future high energy colliders.

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…

A simple new proof of the Harish-Chandra condition, preceded by an expository part on Hermitian symmetric spaces, holomorphic induction, and on some analytic tools.

Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.

We give a simple geometric interpretation of the mapping of the negative KdV equation as proposed by Qiao and Li {arXiv:1101.1605 [math-ph], Europhys. Lett.,94 (2011) 50003} and the Fuchssteiner equation using geometry of projective…

The current status of the derivation of kinetic equations from quantum many-particle dynamics is reviewed.