In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of reduction of order approximation method for solving singular perturbation problems was established, a new Maple procedure redordproc was established, too. The procedure redordproc give not only the approximate analytic solutions but also the numerical solutions of the kinetics...

Exact inference in Bayesian neural networks is non analytic to compute, approximate methods such as the evidence procedure, Monte-Carlo sampling and varia-tional inference have been proposed. In this paper we present a general overview of the Bayesian approach, with a particular emphasis on the variational procedure. We then present a new approximating distribution based on mixtures of Gaussian...

ABSTRACT. Jeřábek showed that analytic propositional-logic deep-inference proofs can be constructed in quasipolynomial time from nonanalytic proofs. In this work, we improve on that as follows: 1) we significantly simplify the technique; 2) our normalisation procedure is direct, i.e., it is internal to deep inference. The paper is self-contained, and provides a starting point and a good deal of...

BACKGROUND Data-sharing is encouraged to fulfill the ethical responsibility to transform research data into public health knowledge, but data sharing carries risks of improper disclosure and potential harm from release of individually identifiable data. METHODS The study objective was to develop and implement a novel method for scientific collaboration and data sharing which distributes the a...

A “feature preference constellation” is a set of commercial website features similar in appeal to shoppers. That is, the features in a constellation: covary in attractiveness (i.e., correlate), are similar in elevation (mean attractiveness), are treated as intact entities rather than being redefined as the partial reflections of underlying factors or dimensions, and can represent more than a si...

In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all Q > Λ they are shown to be represented in the form of an expansion in inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors nf and for ...

Customer requirements play an important role in securing the competitive advantages of a company’s new product development endeavors. Based on the concept of quality function deployment (QFD), this article presents a novel procedure to effectively link customer requirements with design characteristics for product design. The proposed procedure comprises an analytic hierarchy process (AHP), whic...

A procedure for deriving analytic partial derivatives of the Lambert problem is presented. Using the universal, cosine based Lambert formulation; first order partial derivatives of the velocities with respect to the positions and times are developed. Taking advantage of inherent symmetries and intermediate variables, the derivatives are expressed in a computationally efficient form. The added c...

The convex feasibility problem in general is a problem of finding a point in a convex set that contains a full dimensional ball and is contained in a compact convex set. We assume that the outer set is described by second-order cone inequalities and propose an analytic center cutting plane technique to solve this problem. We discuss primal and dual settings simultaneously. Two complexity result...

We compute the gravitational self-force (or “radiation reaction” force) acting on a particle falling radially into a Schwarzschild black hole. Our calculation is based on the “mode-sum” method, in which one first calculates the individual l-multipole contributions to the self-force (by numerically integrating the decoupled perturbation equations) and then regularizes the sum over modes by apply...