相关论文: Toward a canonical qKdV equation

Enlarging on Parts I and II we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of full dynamic equations, including equations where the medium is moving or otherwise changing…

Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained.

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…

We prove some symmetric $q$-congruences.

We report several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. In addition, we report new ``solution generating'' theorems for the TOV, whereby any given solution can be ``deformed'' to a new…

We give a sufficient condition for quantising integrable systems.

Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the…

We prove that small deformations of canonical singularities are canonical.

In recent work with Bhatt and Morrow, we defined a new integral p-adic cohomology theory interpolating between etale and de Rham cohomology. An unexpected feature of this cohomology is that in coordinates, it can be computed by a…

This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…

A way to add an extra dimension is briefly discussed.

A simple model of the new notion of "Markov up" processes is proposed; its positive recurrence and ergodic properties are shown under the appropriate conditions.

The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the…

As an analog of the quantum TKK algebra, a twisted quantum toroidal algebra of type A_1 is introduced. Explicit realization of the new quantum TKK algebra is constructed with the help of twisted quantum vertex operators over a Fock space.

The past few years have seen remarkable progress in the theory and phenomenology of QCD, bringing perturbative and nonperturbative methods into closer contact with each other and with experiment.

In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.

A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given.

A new generalization of the classical separate algebraicity theorem is suggested and proved.

I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.

Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.