相关论文: Recursion operators between degenerate Poisson str…
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…
Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a Manin decomposition then gives rise to several Poisson structures on the…
Two independent Poisson streams of jobs flow into a single-server service system having a limited common buffer that can hold at most one job. If a type-i job (i=1,2) finds the server busy, it is blocked and routed to a separate type-i…
The elliptic algebra A_{q,p}(sl(N)_{c}) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W_N algebra, are constructed. The operators t(z)…
For a stochastic process reset at random times, we discuss to what extent the probabilities of some orderings of observables associated with the intervals of time between resetting events are universal, i.e., independent of the choice of…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
The normal ordering formulae for powers of the boson number operator $\hat{n}$ are extended to deformed bosons. It is found that for the `M-type' deformed bosons, which satisfy $a a^{\dagger} - q a^{\dagger} a = 1$, the extension involves a…
We consider here convolution operators, in the Caputo sense, with non-singular kernels. We prove that the solutions to some integro-differential equations with such operators (acting on the space variable) coincide with the transition…
Classical limits of quantum groups give rise to multiplicative Poisson structures such as Poisson-Lie and quasi-Poisson structures. We relate them to the notion of a shifted Poisson structure which gives a conceptual framework for…
New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…
In this paper we give a new example of duality between fragmentation and coagulation operators. Consider the space of partitions of mass (i.e., decreasing sequences of nonnegative real numbers whose sum is 1) and the two-parameter family of…
It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…
Mixing (of all orders) rank-one actions $T$ of Heisenberg group $H_3(\Bbb R)$ are constructed. The restriction of $T$ to the center of $H_3(\Bbb R)$ is simple and commutes only with $T$. Mixing Poisson and mixing Gaussian actions of…
We prove that two polygons $A$ and $B$ have a reversible hinged dissection (a chain hinged dissection that reverses inside and outside boundaries when folding between $A$ and $B$) if and only if $A$ and $B$ are two noncrossing nets of a…
We show that the character variety for a $n$-punctured oriented surface has a natural Poisson structure.
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd. We exhibit in…
Degenerate Dowling and degenerate r-Dowling polynomials were introduced earlier as degenerate versions and further generalizations of Dowling and r-Dowling polynomials. The aim of this paper is to show their connections with Poisson…
The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold $M$, homogeneous with respect to a vector field $\Delta$ on $M$, and first-order polydifferential…
We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…
We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl(n,C) in pole gauge both in the general position and in the presence of reductions. We present the…