It is well-known that Peirce’s Alpha graphs correspond to propositional logic (PL). Nonetheless, Peirce’s calculus for Alpha graphs differs to a large extent to the common calculi for PL. In this paper, some aspects of Peirce’s calculus are exploited. First of all, it is shown that the erasure-rule of Peirce’s calculus, which is the only rule which does not enjoy the finite choice property, is ...

Weitzman’s [13] search model requires that, conditional on stopping, theagent only takes boxes which have already been inspected. We relax thisassumption and allow the agent to take any uninspected box without in-specting its contents when stopping. Thus, each uninspected box is nowa potential outside option. This introduces a new trade-off: every timethe agent inspects a bo...

An adaptive method based on the trapezoidal rule for the numerical solution of Fredholm integral equations of the second kind is developed. The choice of mesh points is made automatically so as to equidistribute both the chauge in the discrete solution and its gradient. Some numerical experiments with this method are presented.

The quadrature error associated with a regular rule for evaluation of layer potential increases rapidly when the point approaches surface and integral becomes nearly singular. Error estimates are needed to determine accuracy is insufficient more costly special method should be utilized. final result this paper such composite Gauss-Legendre global trapezoidal rule, applied evaluate potentials de...

In this chapter, we present several significant improvements to the original numerical implementation of the two-dimensional method introduced in [13], as described in the previous chapter. The numerical solution of the associated approximate integral equation (2.3) consists of two main parts: efficient, high-order numerical quadrature rules and an efficient linear solver. The numerical evaluat...

We derwe and analyze the properties of Euler-Maclaurin expansions for the differences / ~ / s'(log.~) " /(.~. Qilfj is a combination of one-dimensional generalized trapezoidal rule approximations. 1. ~NlKOL)UC110N In this work we are intcrcstcd in deriving Euler-Maclaurin expansions for the singular double integrals where W(X) = x'(Iog x)'. s >-l.s'=O. 1. (1.3) and f(.~,~l) is as many times dif...

Solution of the diffusion equation is usually performed with the finite element discretization for the spatial elliptic part of the equation and the time dependency is integrated via some difference scheme, often the trapezoidal rule (Crank-Nicolson) or the unconditionally stable semi-implicit two-step algorithm of Lees. A common procedure is to use Picard’s iteration with the trapezoidal rule....

tex Sat Dec 05 13:37:58 2015 1 Two notable advances in numerical methods were supported by this grant. First, a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. T hese transforms play a key role in computational problems ranging from medical imaging to partial differential equa...

Multivariate global polynomial approximations – such as polynomial chaos or stochastic collocation methods – are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two ...

A comparison between different numerical methods which are used to solve cross flow model in multicomponent membrane gas separation is studied. Considering cross flow model, numerical methods such as Bogacki-Shampine method, Dormand-Prince method, Adams-Bashforth-Moulton method, numerical differentiation formulas, modified Rosenbrock formula of order 2, Trapezoidal rule with free interpolant an...