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The Finite Transfer Method used to solve a system of linear ordinary differential equations is extended by adding the boundary equations involved in the problem. A Runge-Kutta scheme could be chosen, for example, to obtain Finite Transfer expressions. The use of a recurrence strategy in these equations permits one to relate different points in the domain where boundary equations could be defined. A final algebraic system of equations is annotated and solved. The method could be applied to determine the structural behaviour of a spatially curved beam element. An example is given to show the procedure exposed. [ABSTRACT FROM AUTHOR]

Structure- phenomenological hereditary model for prediction of viscoelastic properties of layered polymer composites based on hereditary mechanics and theory of laminated plates relationships was elaborated. Interrelated creep and relaxation constitutive equations of layered composite was derived on the basis of algebra of resolvent operators and matrix algorithms. On example of cross-ply carbon reinforced plastic the prediction of viscoelastic properties was shown. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study how algorithms of optimization affect the parametersestimation of Autoregressive AR(1)Models. In our research we have represented the AR(1) models in linear state space form and applied the Kalman Filters to estimate the different unknown parameters of the model. Many methods have been proposed by researchers for the estimation of the parameters in the case of the linear state space models. In our work we have emphasized on the estimation through the Maximum Likelihood (ML). Statisticians have used many algorithms to optimise the likelihood function and they have proposed many filters; publishing their results in many papers. In spite of the fact that this field is so extended, we have emphasized our study in the financial field. Two quasi-Newton algorithms: Berndt, Hall, Hall, and Hausman (BHHH) and Broyden-Fletcher-Goldfarb-Shanno (BFGS), and the Expectation-Maximization (EM) algorithm have been chosen for this study. A practical study of these algorithms applied to the maximization of likelihood by means of the Kalman Filter have been done. The results are focused on efficiency in time of computation and precision of the unknown parameters estimation. A simulation study has been carried out, using as true values the parameters of this model published in the literature, in order to test the efficiency and precision of our implemented algorithms. [ABSTRACT FROM AUTHOR]

Imputation of missing data is important in many areas, such as reducing non-response bias in surveys and maintaining medical documentation. Nearest neighbour (NN) imputation algorithms replace the missing values within any particular observation by taking copies of the corresponding known values from the most similar observation found in the dataset. However, when NN algorithms are executed against large multivariate datasets the poor performance (program execution speed) of these algorithms can present major practical problems. We argue that these problems have not been sufficiently addressed, and we present a fast NN imputation algorithm that can employ any method for measuring the similarity between observations. The algorithm has been designed for the imputation of missing values in large multivariate datasets that contain many different missingness patterns with large proportions of missing data. The ideas underpinning the algorithm are explained in detail, and experiments are described which show that the algorithm delivers very good performance when it is used for imputation in both segmented and non-segmented datasets containing several million rows. [ABSTRACT FROM AUTHOR]

A form of Gauss-Quadrature rule over [0,1] has been investigated that involves the derivative of the integrand at the pre-assigned left or right end node. This situation arises when the underlying polynomials are orthogonal with respect to the weight function (ω) := 1 - x over [0,1] . Along the lines of Golub's work, the nodes and weights of the quadrature rule are computed from a Jacobi-type matrix with entries related to simple rational sequences. The structure of these sequences is based on some characteristics of the identity-type polynomials recently developed by one of the authors. The devised rule has a slight advantage over that subject to the weight function (ω) := 1. [ABSTRACT FROM AUTHOR]

Chapter 6.5 of the book "Topology and Groupoids" by Ronald Brown is presented. It defined the fundamental groupoid that used homotopies of paths. It also describes the invariance properties of the fundamental groupoid using homotopies of maps. Moreover, it investigates the concept in the algebra of groupoids corresponding to homotopy maps of topological spaces.

The article presents a paper whose main goal is to describe the higher Chow groups of varieties over an algebraically closed field introduced by author S. Bloch to etale cohomology. According to the author, they followed the approach recommended by the author during the Lumini conference on algebraic K-theory in 1987. He mentioned the fact that a priori higher Chow are not defined as singular homology of a sheaf.

The article focuses on the Hartmanean algebra, which refers to valuemetrics' mathematical system. It states that Hartmanean algebra considers proper fractions with one as numerator and n, k, or an aleph as denominator. It adds that the Hartmanean algebra is used for solving valuemetrics problems, which involves the determination of concept combinations' value indexes.

A subject index for the book "ValuemetricsA: The Science of Personal & Professional Ethics" is presented.