The Kac-Moody correction factor, first studied by Macdonald in the affine case, corrects failure of an identity found finite-dimensional root systems 1972. Subsequntly this factor appeared several formulas or analogue p-adic spherical theory for reductive groups. In article we view inverse as a function, prove convergency and holomorphy function on complexified Tits cone.

In this paper, a  fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.Error ana...

In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing with the well-known l1-minimization. Restricted isometry property (RIP) and restricted isometry constant (RIC) of measurement matrices which ensure the converg...

We have performed a Monte Carlo simulation study of a system of ellipsoidal particles with donor± acceptor sites modelling complementary hydrogen-bonding groups in real molecules. We have considered elongated Gay± Berne particles with terminal interaction sites allowing particles to associate and form dimers. The changes in the phase transitions and in the molecular organization and the interpl...

This paper presents a numerical scheme that avoids iterations to solve the nonlinear partial differential equation system for pricing American puts with constant dividend yields. Upon applying a frontfixing technique to the Black-Scholes partial differential equation, a predictor-corrector finite difference scheme is proposed to numerically solve the discrete nonlinear scheme. In the comparison...

We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, CarrMadan’s FFT method [1] could blow up for certain values of the model parameters even for an European vanilla option. Alternative methods one originally proposed by Lewis, and BlackScholes-wise method are considered th...

in this paper, a  fuzzy numerical procedure for solving fuzzy linear volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.error ana...

In this paper we present a theorem for defining fixed-points in categories of sheaves. This result gives a unifying and general account of most techniques used in computer science in order to ensure convergency of circular definitions, such as (but not limited to) well-founded recursion and contractivity in complete ultra metric spaces. This general fixed-point theorem encompasses also a simila...