We generalize the concept of a Jacobi field to nonholonomic Riemannian geometry, considering both fields, and, more generally, restricted fields. In first case, corresponding equation involves connection and Schouten curvature tensor. second connections tensors arising in construction Wagner also briefly discuss existence

We introduce a two-dimensional sigma model associated with Jacobi manifold. The is generalisation of Poisson providing topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance under diffeomorphisms. reduced phase space finite-dimensional. By introducing metric tensor on target, non-topological obtained, yielding Polyakov ac...

In this paper the number of Fq-isomorphism classes of Jacobi quartic curves, i.e., the number of Jacobi quartic curves with distinct jinvariants, over finite field Fq is enumerated.

We study spectrum inclusion regions for complex Jacobi matrices which are compact perturbations of real periodic Jacobi matrix. The condition sufficient for the lack of discrete spectrum for such matrices is given.

Abstract A joint algebraic interpretation of the biorthogonal Askey polynomials on unit circle and orthogonal Jacobi is offered. It ties their bispectral properties to an algebra called meta-Jacobi $m\mathfrak {J}$ .

This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as points and derived differentiation matrices for derivatives. With matrices, were transformed into linear systems, which are easier solve. Two types of numerical simulations, results demo...

Let Hω be a self-adjoint Jacobi operator with a potential sequence {ω(n)}n of independently distributed random variables with continuous probability distributions and let μωφ be the corresponding spectral measure generated by Hω and the vector φ. We consider sets A(ω) which are independent of two consecutive given entries of ω and prove that μωφ(A(ω)) = 0 for almost every ω. This is applied to ...