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.

Research on the automated extraction of essential data from an electrocardiography (ECG) recording has been a significant topic for a long time. The main focus of digital processing processes is to measure fiducial points that determine the beginning and end of the P, QRS, and T waves based on their waveform properties. The presence of unavoidable noise during ECG data collection and inherent physiological differences among individuals make it challenging to accurately identify these reference points, resulting in suboptimal performance. This is done through several primary stages that rely on the idea of preliminary processing of the ECG electrical signal through a set of steps (preparing raw data and converting them into files tha

Background: Understanding the morphological characteristics between the floor of the maxillary sinus and the tips of the maxillary posterior roots is crucial in orthodontics involving diagnosis and treatment planning. The aim of this study was to evaluate the distances from the maxillary posterior root apices to the inferior wall of the maxillary sinus, thickness and density of maxillary sinus floor using cone-beam computed tomography images and the relationships between roots and maxillary sinus according to gonial angle and skeletal pattern. Materials and methods: Three-dimensional images of each root were checked, and the distances were measured along the true vertical axis from the apex of the root to the sinus floor, and the thickne

In present study, the technique was used, including nuclear track detector type (CR-39), for appreciative concentrations uranium and radon in soil samples from Baghdad University Campus-AL-Jadiriyah utilizing a prolonged -term with a solid-state nuclear path sensor, a technique for charged particles has been developed., the radon concentrations, effective dose rate and uranium concentrations have measured in soil samples. Eight various venues from soil Baghdad University Campus have appointed. The results indicated variant values about uranium and radon concentrations, the average value for radon gas, effective dose rate and uranium concentrations was found to be 281.59 Bq/cm3, 7.09 mSv/y and 0.01 Bq/mm-2 respectively. All results a

It is commonly known that Euler-Bernoulli’s thin beam theorem is not applicable whenever a nonlinear distribution of strain/stress occurs, such as in deep beams, or the stress distribution is discontinuous. In order to design the members experiencing such distorted stress regions, the Strut-and-Tie Model (STM) could be utilized. In this paper, experimental investigation of STM technique for three identical small-scale deep beams was conducted. The beams were simply supported and loaded statically with a concentrated load at the mid span of the beams. These deep beams had two symmetrical openings near the application point of loading. Both the deep beam, where the stress distribution cannot be assumed linear, and the ex

Motifs template is the input for many bioinformatics systems such codons finding, transcription, transaction, sequential pattern miner, and bioinformatics databases analysis. The size of motifs arranged from one base up to several Mega bases, therefore, the typing errors increase according to the size of motifs. In addition, when the structures motifs are submitted to bioinformatics systems, the specifications of motifs components are required, i.e. the simple motifs, gaps, and the lower bound and upper bound of each gap. The motifs can be of DNA, RNA, or Protein. In this research, a motif parser and visualization module is designed depending on a proposed a context free grammar, CFG, and colors human recognition system. GFC describes the m