Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...

Jacobi algebroids (i.e. a ‘Jacobi versions’ of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten’s gauging of exterior derivative) is developed. One cons...

In this paper, we obtain a complete list of inequivalent irreducible representations the compact quantum group [Formula: see text] for nonzero complex deformation parameters text], which are not roots unity. The matrix coefficients these described in terms little text]-Jacobi polynomials. Haar state is shown to be faithful and an orthonormal basis obtained. Thus, have explicit description Peter...

This paper studies finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject into account such total dominates nondecreasing floor process at each intermediate time. The problem formulated to minimize cost of accumulated injection. We first transform original with constraints an unconstrained cont...

This paper describes a numerical implementation in Maple V R. 5 of an algorithm to compute the Legendre–Fenchel conjugate, namely the Linear-time Legendre Transform algorithm. After a brief motivation on the importance of the Legendre–Fenchel transform, we illustrate the information the conjugate gives (how to test for convexity or compacity, and how to smooth a convex function), with several e...

In this article we identify several beautiful properties of Jacobi sums that become evident when these numbers are organized as a matrix and studied via the tools of linear algebra. In the process we reconsider a convention employed in computing Jacobi sum values by illustrating how these properties become less elegant or disappear entirely when the standard definition for Jacobi sums is utiliz...

Ping et al. [Z. Ping, H. Ren, J. Zou, Y. Sheng, and W. Bo, “Generic orthogonal moments: Jacobi–Fourier moments for invariant image description,” Pattern Recognition, vol. 40, no. 4, pp. 1245– 1254, 2007] made a landmark contribution to the theory of two-dimensional orthogonal moments confined to the unit disk by unifying the radial kernels of existing polynomial-based circular orthogonal moment...

Following the theory of idempotent measures of Maslov, a formalism analogous to probability calculus is obtained for optimization by replacing the classical structure of real numbers (R;+; ) by the idempotent semield obtained by endowing the set R [ f+1g with the \min" and \+" operations. To the probability of an event corresponds the cost of a set of decisions. To random variables correspond d...

This paper is concerned with the optimal investment strategy for a defined contribution (DC) pension plan. We assumed that financial market consists of risk-free asset and risky asset, where subject to Ornstein–Uhlenbeck (O-U) process, stochastic income inflation risk were also considered in model. firstly derived Hamilton–Jacobi–Bellman (HJB) equation through control method. Secondly, under lo...