Quantitative and qualitative analysis of the Averaging methods for the parabolic partial differential equation appears as an exciting field of the investigation. In this paper, we generalize some known results due to Krol on the averaging methods and use them to solve the parabolic partial differential equation.

This paper studies the problem of finite-time stabilization of a class of switched linear time-varying delay systems. An event-triggered sampling mechanism and an event-triggered state feedback control are proposed. Based on Lyapunov-like function method, linear matrix inequality technique and averaged dwell time method, sufficient conditions for switched delay systems under event-triggered state feedback control are given to ensure the finite-time stabilization of the switched delay systems. Finally, a numerical example is given to verify the validity of the proposed results.

Let d: Cp?Cp be normal, then the linear map ( ) attains a local minimum at Cp if and only if z Cp such that ( ) ( ( )=0. Also let Cp, and let ( ) have the polar decomposition ( ) ( ) then the map attains local minimum on Cp at T if and only if ( ). Regarding orthogonality, let S Cp and let N(S) have the polar decomposition N(S) = U|N(S)|, then ( ) ( ) for X Cp if ( ). Moreover, the map has a local minimum at if and only if ( )( ( )) fory . In this paper, we give some results on local minimum and orthogonality of normal derivations in Cp-Classes. We employ some techniques for normal derivations due to Mecheri, Hacene, Bounkhel and Anderson.

Principal component analysis (PCA) is one of the successful dimensionality reduction approaches for color face recognition. For various PCA methods, the experiments show that the contribution of eigenvectors is different and different weights of eigenvectors can cause different effects. Based on this, a modified and simplified color two-dimensional quaternion principal component analysis (M2D-QPCA) method is proposed along the framework of the color two-dimensional quaternion principal component analysis (2D-QPCA) method and the improved two-dimensional quaternion principal component analysis (2D-GQPCA) method. The shortcomings of 2D-QPCA are corrected and the CPU time of 2D-GQPCA is reduced. The experiments on two real face data sets show that the accuracy of M2D-QPCA is better than that of 2D-QPCA and other PCA-like methods and the CPU time of M2D-QPCA is less than that of 2D-GQPCA.

In this paper a three-step two hybrid block method with two offgrid hybrid points chosen within interval [Xn,Xn+1] and [Xn+1,Xn+2] was developed to solve second Order Ordinary Differential Equations directly, using the power series as the basic function to approximate and generate some continuous schemes. The basic properties of the method was investigated and was found to converge. Numerical Solution of our method was tested on some stiff equations and was found to give better approximation than the existing method.

Today, the new coronavirus disease (COVID-19) is a global epidemic that spreads rapidly among individuals in most countries around the world and, therefore, becomes the greatest worldwide threat. The aim of this study is to find the best predictive models for the confirmation of daily situations in countries with a large number of confirmed cases. The study was conducted on the countries that recorded the highest infection rate, namely China, Italy and the United States of America. The second goal is using predictive models to get more prepared in terms of health care systems. In this study, predictions were made through statistical prediction models using the ARIMA and exponential growth model. The results indicate that the exponential growth model is better than ARIMA models for forecasting the COVID-19 cases.

This paper introduces a new generalization of moment exponential (or length biased) distribution. The new model is referred to as generalized transmuted moment exponential distribution. This model contains some new existing distributions. Structural properties of the suggested distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi entropy are derived. Maximum likelihood estimation is employed to obtain the parameter estimators of the new distribution. We illustrate the importance of the new model by means of three applications to real data sets.

Rayleigh-Taylor instability of a composite medium with variable density and viscosity is considered by taking into account the frictional effect of collisions of ionized with neutral atoms in the presence of a variable horizontal magnetic field. The criteria determining stability and instability are independent of the effects of viscosity and collisional effects. The magnetic field stabilizes the system which is otherwise unstable in the absence of the magnetic field. The viscosity of the medium has stabilizing as well as destabilizing effect on the growth rates. The collisional frequency has stabilizing effect on the growth rates, but has also destabilizing effect in some region.

Using the Lorentz model and Hamiltonian systems without dissipation as an example, spectral methods for analyzing the dynamics of systems with chaotic behavior are considered. The insufficiency of the traditional approach to the study of perturbation dynamics based on an analysis of the roots of the classical spectral equation is discussed. It is proposed to study nonlinear systems using the method of constructing spectral equations with different eigenvalues, which allows one to take into account the randomness and multiplicity of states. The spectral features of instability and chaos for systems without dissipation are shown by the example of short-wave perturbations of a flow of a weakly ionized plasma gas.

In this paper, we employ variational iterative method (VIM) to develop a suitable Algorithm for the numerical solution of systems of Volterra integro-differential equations. The formulated algorithm is used to solve first and second order linear and nonlinear system of Volterra integrodifferential equations which demonstrated a good numerical approach to overcome lengthen computational and integral simplification involves. Moreover, the comparison of the exact solution with the approximated solutions are made and approximate solutions p(x) q(t) proved to converge to the exact solutions p(x) q(t) respectively. The results reveal that the formulated algorithm are simple, effective and faster than analytical approach of solving Volterra integro-differential equations.

In this paper, we employ variational iterative method (VIM) to develop a suitable Algorithm for the numerical solution of systems of Volterra integro-differential equations. The formulated algorithm is used to solve first and second order linear and nonlinear system of Volterra integrodifferential equations which demonstrated a good numerical approach to overcome lengthen computational and integral simplification involves. Moreover, the comparison of the exact solution with the approximated solutions are made and approximate solutions p(x) q(t) proved to converge to the exact solutions p(x) q(t) respectively. The results reveal that the formulated algorithm are simple, effective and faster than analytical approach of solving Volterra integro-differential equations.

This article concerns with the method of determining different solutions in integers to by reducing it to through employing transformations. A special case has been illustrated along with the corresponding properties. Also, given an integer solution, a process of obtaining sequence of integer solutions based on its given solution is exhibited.

The binary quadratic equation (Equation) representing the hyperbola is studied for its non-zero distinct integer solutions. A few interesting properties among the solutions are presented. Employing the integer solutions of the equation under consideration, integer solutions for special straight lines, hyperbolas and parabolas are exhibited.

The binary quadratic equation (Equation) representing the hyperbola is studied for its non-zero distinct integer solutions. A few interesting properties among the solutions are presented. Employing the integer solutions of the equation under consideration, integer solutions for special straight lines, hyperbolas and parabolas are exhibited.

In this study, we introduce a new generalization of the Pell numbers which is called bi-periodic Pell sequences. We then proceed to find the Binet formula as well as the generating function for this sequence. The well-known Cassini, Catalan and the D’ocagne’s identities as well as some related binomial summation and sum formulas are also given. The convergence properties of the consecutive terms of this sequence is also examined.

In high porosity medium and revolving system the effects of ion-slip and Hall currents are studied on MHD heat and mass transfer flow. The non-linear coupled partial differential equations are determined using byl transformations and solve these equations employing finite difference method. Velocity, temperature as well as concentration profiles are studied for the concerned physical parameters and results are presented graphically. Due to the Hall and ion-slip parameters, Eckert number, and porosity parameter the velocity profiles are pronounced while it is declined for the effects of magnetic parameter, Prandtl number. Also the magnetic parameter enhances the temperature profiles. On the other hand, the temperature (concentration) profile decreases (increases) for the increasing effect of Prandtl number (Soret number). The rate of changes of velocity, temperature and concentration profiles are also presented graphically.

In this paper, we developed a mathematical model for blood flow in the human circulatory system. This model presumes blood to be a couple stress fluid, its flow to be pulsatile, and the artery an elastic circular pipe whose radius is assumed to vary with transmural pressure. The governing differential equation for the flow velocity is time-dependent and has been solved using the homotopy perturbation method. This velocity has been used to estimate the elastic modulus E of the artery, which is a measure of its stiffness and an important metric used by clinical practitioners to understand the state of the cardiovascular system. In this work, the radial artery has been considered and a limited set of experimental data, available for four cases, has been taken from the published literature to validate the model. While the experimental values of elastic modulus reported in literature lie in the range 2.68 1.81 MPa.s, those estimated through the proposed model range from 3.05 to 5.98 MPa.s, appearing to be in close agreement.

Graphical method and mathematical formula are the two approaches for estimating measures of location. Understanding of many instructors of introductory statistics classes are: mean cannot be graphically determined and numerical (formula) approach is more precise than geometrical technique. Contrary to their understanding, this study estimate mean of a dataset geometrically (from histogram) by determining the centroid of histogram drawn from such data set. In addition, we also make known that mathematical formulas for mean, median and mode were derived geometrically (either from ogive or histogram). Finally, the research illustrated the two techniques with a survey data and established that the two approaches produce same results.

A one-dimensional convective-diffusion problem is considered. To improve the quality of difference schemes, the method of moving nodes is used in combination with Richardson interpolation. Approximate analytical solutions and improved schemes are obtained. Numerical experiments carried out.

The explosive growth in internet coupled with advancement in Information and Communication Technology (ICT) has made business transactions much easier than it used to be in the past. For example, e-commerce has particularly benefited from the introduction of GSM system. One of the major challenges, however, is how to isolate fraudulent transactions from genuine businesses. This becomes more imperative as the advancement in ICT has brought with it fraud and related scams. In this work, we examined different types of e-commerce as well as the challenges being encountered in the course of daily transactions. We took advantage of the current trends in mobile communication networks, particularly GSM and proposed a system based on Response Triggered Architecture for electronic transaction. Our proposed system is platform independent which means only little modification is needed when switching from one platform to another. We used Visual.basic.net and knowledge in fraud for our system prototype and presented the results in the body of this work.

The non- homogeneous ternary quadratic diophantine equation is analyzed for its patterns of non-zero distinct integral solutions. Various interesting relations between the solutions and special numbers namely polygonal, Pronic and Gnomonic numbers are exhibited.

Different forms of discriminant functions and the essence of their appearances were considered in this study. Various forms of classification problems were also considered, and in each of the cases mentioned, classification from simple functions of the observational vector rather than complicated regions in the higher-dimensional space of the original vector were made. Violation of condition of equal variance covariance matrix for Linear Discriminant Function (LDF) results to Quadratic Discriminant Function (QDF). The relationships among the classification statistics examined were established: The Anderson’s (W) and Rao’s (R) statistics are equivalent when the two sample sizes are equal, and when a constant is equal to 1, W, R and John-Kudo’s (Z) classification statistics are asymptotically comparable. A linear relationship is also established between W and Z classification statistics.

Nowadays the new universal disease of the coronavirus that is called the epidemic COVID-19 is spread as geometric progression among the people around the world, so, such pathogen considered the most dangerous threat facing humanity. This study aimed to derive the best forecasting models for the close future cases of infected, recovered, and deaths in the four provinces of Kurdistan Region-Iraq to avoid more loss of human lives by applying more health care in certain province. Two forecasting methods were used including Exponential Smoothing and ARIMA models. The results indicate that both ARIMA and Exponential Smoothing models were close to each other for predicting the infected cases of COVID-19 in Kurdistan Region provinces, and the predicting models show that the pandemic might not be under control unless the people apply the government instructions for health care and keep social distances.

Whenever a discriminant function is constructed, the attention of a researcher is often focused on classification. The underlined interest is how well does a discriminant function perform in classifying future observations correctly. In order to assess the performance of any classification rule, probabilities of misclassification of a discriminant function serves as a basis for the procedure. Different forms of probabilities of misclassification and their associated properties were considered in this study. The misclassification probabilities were defined in terms of probability density functions (pdf) and classification regions. Apparent probability of misclassification is expressed as the proportion of observations in the initial sample which are misclassified by the sample discriminant function. Different methods of estimating probabilities of misclassification were related to each other using their individual shortcomings. The status of degrees of uncertainties associated with probabilities of misclassification and their implications were also specified.

This paper has reviewed two important problems in regression analysis (outliers and missing data), as well as some handling methods for these problems. Moreover, two applications have been introduced to understand and study these methods by R-codes. Practical evidence was provided to researchers to deal with those problems in regression modeling with R. Finally, we created a Monte Carlo simulation study to compare different handling methods of missing data in the regression model. Simulation results indicate that, under our simulation factors, the k-nearest neighbors method is the best method to estimate the missing values in regression models.