Components exponential scator holomorphic function

The components exponential scator function, succinctly labeled “cexp,” is a function of scator variable in 1+n dimensional elliptic scator algebra. This function is introduced here, and its elementary properties are studied. In 1+1 dimensions, the cexp function becomes the usual complex exponential function of complex variable. The cexp function is shown to be scator holomorphic in the entire scator set according to the differential quotient criterion. The scator derivative of the cexp function is the cexp function itself. The relationship between the Cartesian and polar forms of the cexp function can be seen as a higher-dimensional extension of Euler formula. The mappings of grids in 1+2 dimensional space exhibit ellipses and Lissajous-like figures in addition to circles and radial lines. A cusphere surface is generated for the isometric condition in the function's image. An interesting application of the cexp function as propagators regarding the quantum measurement problem is outlined.     

The Crank–Nicolson finite spectral element method and numerical simulations for 2D non-stationary Navier–Stokes equations

In this paper, we first build a semi-discretized Crank–Nicolson (CN) model about time for the two-dimensional (2D) non-stationary Navier–Stokes equations about vorticity–stream functions and discuss the existence, stability, and convergence of the time semi-discretized CN solutions. And then, we build a fully discretized finite spectral element CN (FSECN) model based on the bilinear trigonometric basic functions on quadrilateral elements for the 2D non-stationary Navier–Stokes equations about the vorticity–stream functions and discuss the existence, stability, and convergence of the FSECN solutions. Finally, we utilize two sets of numerical experiments to check out the correctness of theoretical consequences.     

The Green polynomials via vertex operators

An iterative formula for the Green polynomial is given using the vertex operator realization of the Hall-Littlewood function. Based on this, (1) a general combinatorial formula of the Green polynomial is given; (2) several compact formulas are given for Green's polynomials associated with upper partitions of length ≤3 and the diagonal lengths ≤3; (3) a Murnaghan-Nakayama type formula for the Green polynomial is obtained; and (4) an iterative formula is derived for the bitrace of the finite general linear group G and the Iwahori-Hecke algebra of type A on the permutation module of G by its Borel subgroup.     

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.     

Contagion-based distortion risk measures

We propose a class of distortion measures based on contagion from an external “scenario” variable. The dependence between the scenario and the variable whose risk is measured is modeled with a copula function with horizontal concave sections. Special cases are the perfect dependence copula, which generates expected shortfall, the Marshall–Olkin family and the Placket family. As an application, we evaluate distortion measures bank liabilities with respect to a country risk scenario in the current European debt crisis.