HERMITE MATRIX POLYNOMIALS AND SECOND ORDER MATRIX DIFFERENTIAL EQUATIONS

In this paper we introduce the class of Hermite's matrix polynomials which appear as finite series solutions of second order matrix differential equations Y'-xAY'+BY=0.An explicit expression for the Hermite matrix polynomials,the orthogonality property and a Rodrigues' formula are given.

On the Caginalp for a Conserve Phase-Field with a Polynomial Potentiel of Order 2<i>p</i>- 1

Our aim in this paper is to study on the Caginalp for a conserved phase-field with a polynomial potentiel of order 2p - 1. In this part, one treats the conservative version of the problem of generalized phase field. We consider a regular potential, more precisely a polynomial term of the order 2p - 1 with edge conditions of Dirichlet type. Existence and uniqueness are analyzed. More precisely, we precisely, we prove the existence and uniqueness of solutions.

Parametric geometry representations for wind turbine blade shapes

Based on the Joukowsky transformation and Theodorsen method, a novel parametric function （shape function） for wind turbine airfoils has been developed. The airfoil design space and shape control equations also have been studied. Results of the analysis of a typical wind turbine airfoil are shown to illustrate the evaluation process and to demonstrate the rate of convergence of the geometric characteristics. The coordinates and aerodynamic performance of approximate airfoils is rapidly close to the baseline airfoil corresponding to increasing orders of polynomial. Comparison of the RFOIL prediction and experimental results for the baseline airfoil generally show good agreement. A universal method for three-dimensional blade integration-＂ Shape function/Distribution function＂ is presented. By changing the parameters of shape function and distribution functions, a three dimensional blade can be designed and then transformed into the physical space in which the actual geometry is defined. Application of this method to a wind turbine blade is presented and the differences of power performance between the represented blade and original one are less than 0. 5%. This method is particularly simple and convenient for bodies of streamline forms.

Deep Neural Artificial Intelligence for IoT Based Tele Health Data Anal

Tele health utilizes information and communication mechanisms to convey medical information for providing clinical and educational assistances.It makes an effort to get the better of issues of health service delivery involving time factor,space and laborious terrains,validating cost-efficiency and finer ingress in both developed and developing countries.Tele health has been categorized into either real-time electronic communication,or store-andforward communication.In recent years,a third-class has been perceived as remote healthcare monitoring or tele health,presuming data obtained via Internet of Things(IOT).Although,tele health data analytics and machine learning have been researched in great depth,there is a dearth of studies that entirely concentrate on the progress of ML-based techniques for tele health data analytics in the IoT healthcare sector.Motivated by this fact,in this work a method called,Weighted Bayesian and Polynomial Taylor Deep Network(WB-PTDN)is proposed to improve health prediction in a computationally efficient and accurate manner.First,the Independent Component Data Arrangement model is designed with the objective of normalizing the data obtained from the Physionet dataset.Next,with the normalized data as input,Weighted Bayesian Feature Extraction is applied to minimize the dimensionality involved and therefore extracting the relevant features for further health risk analysis.Finally,to obtain reliable predictions concerning tele health data analytics,First Order Polynomial Taylor DNN-based Feature Homogenization is proposed that with the aid of First Order Polynomial Taylor function updates the new results based on the result analysis of old values and therefore provides increased transparency in decision making.The comparison of proposed and existing methods indicates that the WB-PTDN method achieves higher accuracy,true positive rate and lesser response time for IoT based tele health data analytics than the traditional methods.

Numerical Issues in the Implementation of High Order Polynomial Multi-Domain Penalty Spectral Galerkin Methods for Hyperbolic Conservation Laws

In this paper,we consider high order multi-domain penalty spectral Galerkin methods for the approximation of hyperbolic conservation laws.This formulation has a penalty parameter which can vary in space and time,allowing for flexibility in the penalty formulation.This flexibility is particularly advantageous for problems with an inhomogeneous mesh.We show that the discontinuous Galerkin method is equivalent to the multi-domain spectral penalty Galerkin method with a particular value of the penalty parameter.The penalty parameter has an effect on both the accuracy and stability of the method.We examine the numerical issues which arise in the implementation of high order multi-domain penalty spectral Galerkin methods.The coefficient truncation method is proposed to prevent the rapid error growth due to round-off errors when high order polynomials are used.Finally,we show that an inconsistent evaluation of the integrals in the penalty method may lead to growth of errors.Numerical examples for linear and nonlinear problems are presented.

Global Attractors for a Nonclassical Diffusion Equation

We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.

Propagation of oblique water waves by an asymmetric trench in the presence of surface tension

An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface.Reflection and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1/6 with suitable weights.The energy identity relation is derived by employing Green’s integral theorem in the fluid region of the problem.Reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying several parameters.The correctness of the present method is confirmed by comparing the results available in the literature.The effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of parameters.It can be observed that surface tension plays a qualitatively relevant role in the present study.