The nonhomogeneous higher order linear complex differential equation (HOLCDE) with meromorphic (or entire) functions is considered in this paper. The results are obtained by putting some conditions on the coefficients to prove that the hyper order of any nonzero solution of this equation equals the order of one of its coefficients in case the coefficients are meromorphic functions. In this case, the conditions were put are that the lower order of one of the coefficients dominates the maximum of the convergence exponent of the zeros sequence of it, the lower order of both of the other coefficients and the nonhomogeneous part and that the solution has infinite order. Whiles in case the coefficients are entire functions, any nonzero solutio

Estimations of average crash density as a function of traffic elements and characteristics can be used for making good decisions relating to planning, designing, operating, and maintaining roadway networks. This study describes the relationships between total, collision, turnover, and runover accident densities with factors such as hourly traffic flow and average spot speed on multilane rural highways in Iraq. The study is based on data collected from two sources: police stations and traffic surveys. Three highways are selected in Wassit governorate as a case study to cover the studied locations of the accidents. Three highways are selected in Wassit governorate as a case study to cover the studied locations of the accidents. The selection

Estimations of average crash density as a function of traffic elements and characteristics can be used for making good decisions relating to planning, designing, operating, and maintaining roadway networks. This study describes the relationships between total, collision, turnover, and runover accident densities with factors such as hourly traffic flow and average spot speed on multilane rural highways in Iraq. The study is based on data collected from two sources: police stations and traffic surveys. Three highways are selected in Wassit governorate as a case study to cover the studied locations of the accidents. Three highways are selected in Wassit governorate as a case study to cover the studied locations of the accidents. The se

In this paper, the linear system of Fredholm integral equations is solving using Open Newton-Cotes formula, which we use five different types of Open Newton-Cotes formula to solve this system.  Compare the results of suggested method with the results of another method (closed Newton-Cotes formula)    Finally, at the end of each method, algorithms and programs developed and written in MATLAB (version 7.0) and we give some numerical examples, illustrate suggested method

This paper study two stratified quantile regression models of the marginal and the conditional varieties. We estimate the quantile functions of these models by using two nonparametric methods of smoothing spline (B-spline) and kernel regression (Nadaraya-Watson). The estimates can be obtained by solve nonparametric quantile regression problem which means minimizing the quantile regression objective functions and using the approach of varying coefficient models. The main goal is discussing the comparison between the estimators of the two nonparametric methods and adopting the best one between them

A stochastic process {Xk, k = 1, 2, ...} is a doubly geometric stochastic process if there exists the ratio (a > 0) and the positive function (h(k) > 0), so that {α 1 h-k }; k ak X k = 1, 2, ... is a generalization of a geometric stochastic process. This process is stochastically monotone and can be used to model a point process with multiple trends. In this paper, we use nonparametric methods to investigate statistical inference for doubly geometric stochastic processes. A graphical technique for determining whether a process is in agreement with a doubly geometric stochastic process is proposed. Further, we can estimate the parameters a, b, μ and σ2 of the doubly geometric stochastic process by using the least squares estimate for Xk a

     Foreign Object Debris (FOD) is defined as one of the major problems in the airline maintenance industry, reducing the levels of safety. A foreign object which may result in causing serious damage to an airplane, including engine problems and personal safety risks. Therefore, it is critical to detect FOD in place to guarantee the safety of airplanes flying. FOD detection systems in the past lacked an effective method for automatic material recognition as well as high speed and accuracy in detecting materials. This paper proposes the FOD model using a variety of feature extraction approaches like Gray-level Co-occurrence Matrix (GLCM) and Linear Discriminant Analysis (LDA) to extract features and Deep Learning (DL) for classifi

The approach given in this paper leads to numerical methods to find the approximate solution of volterra integro –diff. equ.1st kind. First, we reduce it from integro VIDEs to integral VIEs of the 2nd kind by using the reducing theory, then we use two types of Non-polynomial spline function (linear, and quadratic). Finally, programs for each method are written in MATLAB language and a comparison between these two types of Non-polynomial spline function is made depending on the least square errors and running time. Some test examples and the exact solution are also given.

This paper introduces a generalization sequence of positive and linear operators of integral type based on two parameters to improve the order of approximation. First, the simultaneous approximation is studied and a Voronovskaja-type asymptotic formula is introduced. Next, an error of the estimation in the simultaneous approximation is found. Finally, a numerical example to approximate a test function and its first derivative of this function is given for some values of the parameters. 

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.