The paper is devoted to theoretic and numeric investigation of a nonlinear integral equation with an unknown function in the upper limit of integration. This equation appears in optimal replacement problems of engineering and production economics. Its solution is essential for finding the optimal policy of equipment replacement under technological advances. Solvability and qualitative dynamics ...

We address multivariate integration and extrapolation techniques for the computation of Feynman loop integrals. Loop integrals are required for perturbation calculations in high energy physics, as they contribute corrections to the scattering amplitude and the cross section for the collision of elementary particles. We use iterated integration to calculate the multivariate integrals. The combin...

We know we can solve this problem: Given any rational function f(x) = p(x)/q(x), where p and q are univariate polynomials over the rationals, compute its indefinite integral, using if necessary, algebraic numbers. But in many circumstances an approximate result is more likely to be of use. Furthermore, it is plausible that it would be more useful to solve the problem to allow definite integrati...

We present Pika, an implemented self-explanatory simulator that is more than 5000 times faster than SimGen Mk2 [ Forbus and Falkenhainer, 1992 ] , the previous state of the art. Like SimGen, Pika automatically prepares and runs a numeric simulation of a physical device speci ed as a particular instantiation of a general domain theory, and it is capable of explaining its reasoning and the simula...

The ever growing repository of data in all fields poses new challenges to the modern analytical systems. Real-world datasets, with mixed numeric and nominal variables, are difficult to analyze and require effective visual exploration that conveys semantic relationships of data. Traditional data mining techniques such as clustering clusters only the numeric data. Little research has been carried...

The length of curves may be measured by numeric integration if the curves are given by analytic formulas. Not all curves can or should be described parametrically. In this report we use the alternative grid topology approach. The shortest polygonal Jordan curve in a simple closed one-dimensional grid continuum is used to estimate a curve's length. An O(n) algorithm for finding the shortest poly...

Cloud services have been widely employed in IT industry and scientific research. By using Cloud services users can move computing tasks and data away from local computers to remote datacenters. By accessing Internet-based services over lightweight and mobile devices, users deploy diversified Cloud applications on powerful machines. The key drivers towards this paradigm for the scientific comput...