相关论文: Paraconformal Structures and Integrable Systems

String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend…

Eigenstates of the parabose and parafermi creation operators are constructed. In the Dirac contour representation, the parabose eigenstates correspond to the dual vectors of the parabose coherent states. In order $p=2$, conserved-charge…

The main goal is to classify 4-dimensional real Lie algebras $\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore…

We study vector quadrirational Yang-Baxter maps representing the momentum-energy transformation of two particles after elastic relativistic collisions. The collision maps admit Lax representations compatible with an r-matrix Poisson…

In this paper we build a set of parametric quotient Lie group structures on the probabilistic simplex that can be extended to real vector space structures. In particular, we rediscover the main mathematical objects generally used when…

Based on the fractional $q$-integral with the parametric lower limit of integration, we define fractional $q$-derivative of Riemann-Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we…

We introduce a family of order $N\in \mathbb{N}$ Lax matrices that is indexed by the natural number $k\in \{1,\ldots,N-1\}.$ For each value of $k$ they serve as strong Lax matrices of a hierarchy of integrable difference systems in edge…

We investigate a family of integrable Hamiltonian systems on Lie-Poisson spaces $\mathcal{L}_+(5)$ dual to Lie algebras $\mathfrak{so}_{\lambda, \alpha}(5)$ being two-parameter deformations of $\mathfrak{so}(5)$. We integrate corresponding…

We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their…

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…

The well-studied notion of deductive explosion describes the situation where any formula can be deduced from an inconsistent set of formulas. Paraconsistent logic, on the other hand, is the umbrella term for logical systems where the…

Infinitesimal deformations are governed by partition Lie algebras. In characteristic $0$, these higher categorical structures are modelled by differential graded Lie algebras, but in characteristic $p$, they are more subtle. We give…

For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…

Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…

We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry…

The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.

In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimensional systems. We prove that the deformation algorithm…

In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and $R$-matrix of the two-loop SU(2) sector in…

A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability condition corresponds to the Lie-algebra of SL (2,R), O(3), or…

We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…