Evaluation of Feasibility of Gamma-Spectrometer NaI PAK-01 and SAS Na M3 Software Application for Regular Radionuclide Analysis of NPP Permissible Wastes

The feasibility of correct NaI gamma-spectrometry activity measurement for each nuclide in 131I, 132I, 133I, 134I, 135I, 133Xe, 135mXe, 135Xe and 222Rn composition is presented. To get this result the special matrix method M3 and SAS Na M3 software were used for spectra processing. SAS Na M3 software was developed for complex NaI gamma-spectra processing. Special algorithms and auxiliary software are used to overcome the problems of the classic spectra processing matrix method. Being used for spectrum processing SAS Na M3 software determines the nuclide composition of the sample, activity of nuclides identified and activities uncertainties. The activity values estimation is made for nuclides not identified in the sample measured but included in SAS Na M3 software nuclides library. The values of minimal detectable activities for NaI ∅3''× 3'' gamma-spectrometer and 1 hour measuring time are ~ 0.6 Bq for 131I, 132I, 133I, 134I and ~ 2 Bq for 135I.

An improved LogNNet classifier for IoT applications

In the age of neural networks and Internet of Things (IoT), the search for new neural network architectures capable of operating on devices with limited computing power and small memory size is becoming an urgent agenda. Designing suitable algorithms for IoT applications is an important task. The paper proposes a feed forward LogNNet neural network, which uses a semi-linear Henon type discrete chaotic map to classify MNIST-10 dataset. The model is composed of reservoir part and trainable classifier. The aim of the reservoir part is transforming the inputs to maximize the classification accuracy using a special matrix filing method and a time series generated by the chaotic map. The parameters of the chaotic map are optimized using particle swarm optimization with random immigrants. As a result, the proposed LogNNet/Henon classifier has higher accuracy and the same RAM usage, compared to the original version of LogNNet, and offers promising opportunities for implementation in IoT devices. In addition, a direct relation between the value of entropy and accuracy of the classification is demonstrated.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms several results are obtained, which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

A novel matrix technique for multi-order pantograph differential equations of fractional order

The main purpose of this article is to investigate a novel set of (orthogonal) basis functions for treating a class of multi-order fractional pantograph differential equations (MOFPDEs) computationally. These polynomials, denoted by S n ( x ) and called special polynomials , were first discovered in a study of a certain family of isotropic turbulence fields. They are expressible in terms of the generalized Laguerre polynomials and are related to the Bessel and Srivastava–Singhal polynomials. Unlike the Laguerre polynomials, all coefficients of the special polynomials are positive. We further introduce the fractional order of the special polynomials and use them along with some suitable collocation points in a special matrix technique to treat fractional-order MOFPDEs. Moreover, the convergence analysis of these polynomials is established. Through five example applications, the utility and efficiency of the present matrix approach are demonstrated and comparisons with some existing numerical schemes have been performed in this class.

On A Matrix Hypergeometric Differential Equation

In this paper we consider a matrix Hypergeometric differential equation, which are special matrix functions and solution of a specific second order linear differential equation. The aim of this work is to extend a well known theorem on Hypergeometric function in the complex plane to a matrix version, and we show that the asymptotic expansions of Hypergeometric function in the complex plane ” that are given in the literature are special members of our main result. Background and motivation are discussed.

Trace of Positive Integer Power of Squared Special Matrix

The rectangle matrix to be discussed in this research is a special matrix where each entry in each line has the same value which is notated by An. The main aim of this paper is to find the general form of the matrix trace An powered positive integer m. To prove whether the general form of the matrix trace of An powered positive integer can be confirmed, mathematics induction and direct proof are used.

A MATRIX PRESENTATION OF HIGHER ORDER DERIVATIVES OF BÉZIER CURVE AND SURFACE

In this study, the Bézier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bézier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bézier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, whose control points are known, its higher order derivatives can be calculated without it's parametric equations. In this study, the Bézier curves and surfaces are presented in a more easily understandable and easy to use format in algebraic form for designers.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels. In this article, we derive the formulas for Fourier cosine transforms and Fourier sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms a number of results are considered which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

The Drazin inverse matrix modification formulae with Peirce corners

Our motivation is to derive the Drazin inverse matrix modification formulae utilizing the Drazin inverses of adequate Peirce corners under some special cases, and the Drazin inverse of a special matrix with an additive perturbation. As applications, several new results for the expressions of the Drazin inverses of modified matrices A ?? CB and A ?? CDdB are obtained, and some well known results in the literature, as the Sherman-Morrison-Woodbury formula and Jacobson?s Lemma, are generalized.