Related papers: The recursion operator for a constrained CKP hiera…
A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.
Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating the symmetric Jack polynomials with the…
In this paper we continue our analysis of the stationary flows of $M$ component, coupled KdV (cKdV) hierarchies and their modifications. We describe the general structure of the $t_1$ and $t_2$ flows, using the case $M=3$ as our main…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
We examine the conformal property of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp. We find that it naturallygives a family of nonlocal extended conformal algebras. We give two examples of such…
We develop a unified framework to characterize the power of higher-level algorithms for the constraint satisfaction problem (CSP), such as $k$-consistency, the Sherali-Adams LP hierarchy, and the affine IP hierarchy. As a result,…
This paper provides a new, decidable definition of the higher- order recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability clo- sure, and bound variables are…
In this paper, we consider the reproducing property in Reproducing Kernel Hilbert Spaces (RKHS). We establish a reproducing property for the closure of the class of combinations of composition operators under minimal conditions. This allows…
We present an explicit formula for the transition matrix $\mathcal{C}$ from the type $BC_n$ Koornwinder polynomials $P_{(1^r)}(x|a,b,c,d|q,t)$ with one column diagrams, to the type $BC_n$ monomial symmetric polynomials $m_{(1^{r})}(x)$. The…
A recursion operator is constructed for a hydrodynamic type system admitting dispersionless Lax representation with non-rational Lax function.
In this paper we discuss the concept of cosymmetries and co--recursion operators for difference equations and present a co--recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion…
A KP-mKP hierarchy was introduced recently via pseudo-differential operators containing two derivations. In this paper, for the KP-mKP hierarchy we derive a class of (differential) Fay identities and construct a series of additional…
We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced…
We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we…
Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the $\tau$-function and conformally invariant equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry…
Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of math-ph/0702045, seeing it as a quantization of certain quadratic Lagrangians in $T^*V$ for some vector space $V$. KS topological recursion is a…
We develop classes of one-parameter families (OPF) of operators on $C^\infty_c(\mathbb{C})$ which characterize the behavior of operators associated to the $\bar\partial$-problem in $L^2(\mathbb{C},e^{-2p})$ where $p$ is a subharmonic,…
Under the Neumann constraints, each equation of the KdV hierarchy is decomposed into two finite dimensional systems, including the well-known Neumann model. Like in the case of the Bargmann constraint, the explicit Lax representations are…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
We construct an integrable hierarchy in terms of vertex operators and Hirota Quadratic Equations (HQE shortly) and we show that the equivariant total descendant potential of $\C P^1$ satisfies the HQE. Our prove is based on the quantization…