z-Approximations

Triangular approximations of fuzzy number with value and ambiguity functions

An algorithm for approximating nondominated points of convex multiobjective optimization problems

‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

Finite difference operators approximating second derivatives with variable coefficients and satisfying a summation-by-parts rule have been derived for the second-, fourthand sixth-order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivate, which makes the construction of stable approximations t...

Flexible piecewise approximations based on partition of unity

In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are...

Approximations of the Standard Normal Distribution

This paper presents five new formulas for approximation of cumulative standard normal probabilities. Two of these approximations are polynomial based and are only accurate for 1 0 ≤ ≤ z ; the other three formulas are accurate on the interval 4 . 3 4 . 3 ≤ ≤ − z which is the domain often used in normal tables. We recommend the last of these new formulas.

Atomic energies from the large-dimension limit

Analytic approximations to nonrelativistic atomic ground state energies are obtained from the first two terms of the 1/ D expansion for the N-electron atom. These two terms describe the equilibrium structure (D-+ ct) limit) and normal mode oscillations (1/D term) of a completely symmetric N-dimensional configuration of localized particles. The connection between these large-D results and real a...