Aspects of continuous and discrete harmonic analysis on the circle are generalized to star graphs, and through spherical coordinates to the two sphere. The resulting function theory is used to analyze trapezoidal rule integration on the two sphere. 2000 Mathematics Subject Classification 65D30, 65T99, 34B45

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.

We introduce a tractable multi-issue model of electoral competition in which candidates are exogenously committed to particular positions on a subset of issues, while they can choose a sequence of binary positions for the remaining issues to maximize their winning probability. A majorityefficient position is defined as one where a candidate cannot make a majority of the electorate better off, t...

AUC is an important parameter in pharmacokinetic studies. There are different ways to calculate AUC. Sometime, the statistician or pharmacokineticist has to choose one particular method to calculate AUC depending on the actual concentration data. Among many pharmacokinetic approaches and modeling analyses, traditional trapezoidal, log-linear trapezoidal, Lagrange polynomial integration, and Pur...

Sources providing information about the value of a variable may not be totally reliable. In such a case, it is common in uncertainty theories to take account of this unreliability by a so-called discounting rule. A few discounting rules have been proposed in the framework of imprecise probability theory, but one of the drawback of those rules is that they do not preserve interesting properties ...

A new class of quadrature rules for the integration of both regular and singular functions is constructed and analyzed. For each rule the quadrature weights are positive and the class includes rules of arbitrarily high-order convergence. The quadratures result from alterations to the trapezoidal rule, in which a small number of nodes and weights at the ends of the integration interval are repla...