Related papers: Elementary combinatorics of the HOMFLYPT polynomia…

We prove that the degree of the Hilbert polynomial of the HOMFLYPT homology of a closed braid $B$ is $l-1$, where $l$ is the number of components of $B$. This controls the growth of the HOMFLYPT homology with respect to its polynomial…

In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this paper we consider invariant formulation of nonlinear (Lagrangian…

The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…

In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion (I_0=H,I_1,I_2). Our main result, formulated and…

We construct an invariant of closed oriented $3$-manifolds using a finite dimensional, involutory, unimodular and counimodular Hopf algebra $H$. We use the framework of normal o-graphs introduced by R. Benedetti and C. Petronio, in which…

In a previous paper we solved a countably infinite family of one-dimensional Schr\"odinger equations by showing that they were supersymmetric partner potentials of the standard quantum harmonic oscillator. In this work we extend these…

We propose an algorithm which allows to derive the generalized Alexander polynomial invariants of knots and links with the help of the q,p-numbers, appearing in bosonic two-parameter quantum algebra. These polynomials turn into HOMFLY ones…

We study two-parameter oscillator variations of the classical theorem on harmonic polynomials, associated with noncanonical oscillator representations of sl(n) and o(n). We find the condition when the homogeneous solution spaces of the…

This paper gives an explicit formula for the Ehrhart quasi-polynomial of certain 2-dimensional polyhedra in terms of invariants of surface quotient singularities. Also, a formula for the dimension of the space of quasi-homogeneous…

In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…

Quadratic bosonic Hamiltonians and their associated unitary transformations form a fundamental class of operations in quantum optics, modelling key processes such as squeezing, displacement, and beam-splitting. Their Heisenberg-picture…

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple…

We study first the supersymmetric quantum mechanics (SUSY QM), specially the cases of the harmonic and radial oscillators. Then, we obtain a new Wronskian formula for the confluent SUSY transformation and apply the SUSY QM to the inverted…

First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…

Distortions in a family of conjugated polymers are studied within two complementary approaches, i.e. within a many-body Valence Bond (VB) approach using a transfer matrix technique to treat the Heisenberg model of the systems, and also in…

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials…

Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…

A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…

A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.

We find all Heegaard diagrams with the property "alternating" or "weakly alternating" on a genus two orientable closed surface. Using these diagrams we give infinitely many genus two 3--manifolds, each admits an automorphism whose…