In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

<span lang="EN-US">In the last years, the self-balancing platform has become one of the most common candidates to use in many applications such as flight, biomedical fields, and industry. In this paper, the physical prototype of a proposed self-balancing platform that described the self-balancing attitude in the (X-axis, Y-axis, or biaxial) under the influence of road disturbance has been introduced. In the physical prototype, the inertial measurement unit (IMU) sensor will sense the disturbance in (X-axis, Y-axis, and biaxial). With the determined error, the corresponding electronic circuit, DC servo motors, and the Arduino software, the platform overcame the tilt angle(disturbance). Optimization of the proportional-integral-

Air pollution is considered one of the major environmental problems that contain many challenges and difficulties facing most countries of the world, including Iraq. The problem has emerged widely with the emergence of the industrial revolution in the world and the tremendous increase in the population and the increase in the number of transportation and its development in addition to excavation, maintenance and work Construction and weather fluctuations, such as dust and sandstorms, pollution resulting from oil refining, extraction, diversion and other processes that cause pollution, and the start of the world using methods that limit the volume of environmental pollution. The most prominent of these methods is the imposition of

 Inflammatory bowel disease includes both Crohn’s disease and ulcerative colitis, is a chronic, progressive relapsing disease of gastrointestinal tract that require long-term treatment or maintenance therapy. Taking patient’s beliefs about the prescribed medication in consideration had been shown to be an important factor that affects compliance of the patient in whom having positive beliefs is a prerequisite for better compliance. The aim of the current study was to investigate and assess beliefs about medicines among a sample of Iraqi patients with inflammatory bowel disease and to determine possible association between these beliefs and some patient-specific factors.

This study is a cross-sectional study carried out o

The purpose of this paper to discriminate between the poetic poems of each poet depending on the characteristics and attribute of the Arabic letters. Four categories used for the Arabic letters, letters frequency have been included in a multidimensional contingency table and each dimension has two or more levels, then contingency coefficient calculated.

The paper sample consists of six poets from different historical ages, and each poet has five poems. The method was programmed using the MATLAB program, the efficiency of the proposed method is 53% for the whole sample, and between 90% and 95% for each poet's poems.

In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i