We develop the theory of Abelian functions defined using a tetragonal curve of genus six, with the specific example of the cyclic curve, y = x + λ4x + λ3x + λ2x + λ1x + λ0 discussed in detail. We define generalisations of the Weierstrass σ and ℘ functions, along with additional classes of Abelian functions. In addition, we present the associated partial differential equations satisfied by the f...

We give a new recursive method to compute the number of cliques and cycles of a graph. This method is related, respectively to the number of disjoint cliques in the complement graph and to the sum of permanent function over all principal minors of the adjacency matrix of the graph. In particular, let G be a graph and let G be its complement, then given the chromatic polynomial of G, we give a r...

We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil (1994). We study the properties of these estimators and compare them with Rosenblatt’s nonrecursive estimator. It turns out that, for pointwise estimation, it is preferable to use the nonrecursive Rosenblatt’s kernel esti...

In order to improve the safety of train operation, a short-term wind speed forecasting method is proposed based on a linear recursive autoregressive integrated moving average (ARIMA) algorithm and a non-linear recursive generalized autoregressive conditionally heteroscedastic (GARCH) algorithm (ARIMA-GARCH). Firstly, the non-stationarity embedded in the original wind speed data is pre-processed...

One approach to a recursive identification of continuous – time systems was implemented in self – tuning control of a system of interconnected tanks. Since derivatives of input and output variables of continuous – time systems can not be directly measured, differential filters and filtered variables are established to substitute primary variables. The filtered variables are then used in a recur...

We consider here the collection of all partitions of an n-set, for fixed n, and we ask: is it possible to arrange these partitions in a list (Gray Code) so that each partition is obtained from its immediate predecessor by changing the class of exactly one element? The answer is affirmative, and we give descriptions of two algorithms which implement the method, the first recursive, the second no...

In functional languages, iterative operations on data collections are naturally expressed using recursive functions on recursive data structures. In this paper, we present a method to extract data parallelism from recursive functions and generate data parallel programs. As the parallel model for object programs, we use polytypic parallel skeletons. This model can express data parallel operation...

background: precise diagnosis of disease risk factors via efficient statistical models is the primary step for reducing the heavy costs of breast cancer, as one of the most highly prevalent cancer throughout the world. therefore, the aim of this study was to present a recently introduced statistical model in order to assess its proficiency for model fitting. methods: the information of 1465 eli...

The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of New-ton's method, but previous researchers have mentioned that some iter...

This paper describes a general and powerful method for dependence analysis in the presence of recursive data constructions. The particular analysis presented is for identifying partially dead recursive data, but the general framework for representing and manipulating recursive substruc-tures applies to all dependence analyses. The method uses projections based on general regular tree grammars e...