In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

The impact of undergraduate research experiences on students' academic development and retention in STEM fields is significant. Students' success in STEM fields is based on developing strong research and critical thinking skills that make it essential for students to engage in research activities throughout their academic programs. This work evaluates the effectiveness of undergraduate research experiences with respect to its influence on student retention and academic development. The cases presented are based on years of experience implementing undergraduate research programs in various STEM fields at Colorado State University Pueblo (CSU Pueblo) funded by HSI STEM Grants. The study seeks to establish a correlation between students' reten

Steganography is a useful technique that helps in securing data in communication using different data carriers like audio, video, image and text. The most popular type of steganography is image steganography. It mostly uses least significant bit (LSB) technique to hide the data but the probability of detecting the hidden data using this technique is high. RGB is a color model which uses LSB to hide the data in three color channels, where each pixel is represented by three bytes to indicate the intensity of red, green and blue in that pixel. In this paper, steganography based RGB image is proposed which depends on genetic algorithm (GA). GA is used to generate random key that represents the best ordering of secret (image/text) blocks to b

Steganography is an important class of security which is widely used in computer and network security nowadays. In this research, a new proposed algorithm was introduced with a new concept of dealing with steganography as an algorithmic secret key technique similar to stream cipher cryptographic system. The proposed algorithm is a secret key system suggested to be used in communications for messages transmission steganography

Science, technology and many other fields are use clustering algorithm widely for many applications, this paper presents a new hybrid algorithm called KDBSCAN that work on improving k-mean algorithm and solve two of its
problems, the first problem is number of cluster, when it`s must be entered by user, this problem solved by using DBSCAN algorithm for estimating number of cluster, and the second problem is randomly initial centroid problem that has been dealt with by choosing the centroid in steady method and removing randomly choosing for a better results, this work used DUC 2002 dataset to obtain the results of KDBSCAN algorithm, it`s work in many application fields such as electronics libraries,

This paper proposes a new structure of the hybrid neural controller based on the identification model for nonlinear systems. The goal of this work is to employ the structure of the Modified Elman Neural Network (MENN) model into the NARMA-L2 structure instead of Multi-Layer Perceptron (MLP) model in order to construct a new hybrid neural structure that can be used as an identifier model and a nonlinear controller for the SISO linear or nonlinear systems. Weight parameters of the hybrid neural structure with its serial-parallel configuration are adapted by using the Back propagation learning algorithm. The ability of the proposed hybrid neural structure for nonlinear system has achieved a fast learning with minimum number

When employing shorter (sub picosecond) laser pulses, in ablation kinetics the features appear which can no longer be described in the context of the conventional thermal model. Meanwhile, the ablation of materials with the aid of ultra-short (sub picosecond) laser pulses is applied for micromechanical processing. Physical mechanisms and theoretical models of laser ablation are discussed. Typical associated phenomena are qualitatively regarded and methods for studying them quantitatively are considered. Calculated results relevant to ablation kinetics for a number of substances are presented and compared with experimental data. Ultra-short laser ablation with two-temperature model was quantitatively investigated. A two-temperature model

The health of Roadway pavement surface is considered as one of the major issues for safe driving. Pavement surface condition is usually referred to micro and macro textures which enhances the friction between the pavement surface and vehicular tires, while it provides a proper drainage for heavy rainfall water. Measurement of the surface texture is not yet standardized, and many different techniques are implemented by various road agencies around the world based on the availability of equipment’s, skilled technicians’ and funds. An attempt has been made in this investigation to model the surface macro texture measured from sand patch method (SPM), and the surface micro texture measured from out flow time (OFT) and British pendul