In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.

It was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.

In order to achieve overall balance in the economy to be achieved in different markets and at one time (market commodity, monetary and labor market and the balance of payments and public budget), did not provide yet a model from which to determine the overall balance in the economy and the difficulty of finding the inter-relationship between all these markets and put them applied in the form of allowing the identification of balance in all markets at once.

One of the best models that have dealt with this subject is a model
(LM-BP-IS), who teaches balance in the commodity market and money market and balance of payments and the importance of this issue This research tries to shed light on the reality

To decrease the dependency of producing high octane number gasoline on the catalytic processes in petroleum refineries and to increase the gasoline pool, the effect of adding a suggested formula of composite blending octane number enhancer to motor gasoline composed of a mixture of oxygenated materials (ethanol and ether) and aromatic materials (toluene and xylene) was investigated by design of experiments made by Mini Tab 15 statistical software. The original gasoline before addition of the octane number blending enhancer has a value of (79) research octane number (RON). The design of experiments which study the optimum volumetric percentages of the four variables, ethanol, toluene, and ether and xylene materials leads

Objective: The study aimed to assess Leucine-rich alpha-2-glycoprotein-1 biomarker serum level in hospitalized COVID-19 patients. Methods: The case control study from multi-centers in Baghdad included 45 adult patients (19 females and 26 males) with COVID-19, diagnosed with a positive real-time reverse transcription polymerase chain reaction and excluded negative RT-PCR for COVID-19 and comorbidity conditions. Second group, was 43 control (20 females and 23 males). Results: This study found a decrease Leucine-rich alpha-2-glycoprotein-1 biomarker serum level in these patients and a significant difference in D. dimer, neutrophil count, lymphocyte count, and the neutrophil-lymphocyte ratio between the patients and controls at a P valu

Transformations of the actor when acting many characters are the product of joint work between the actor and the director through the instructions and the exercises that facilitate the reach for the desired goal.

The method or way has often been used which is Stanislavsky premises in his work with the actor in the role. The first section consists of two parts under the heading of the actor's work with himself. The two parts are preparing the actor in creative suffering (internal), and in coexistence and embodiment (outside). The second section is the book of the actor's work with the role. The current research aims at identifying the mechanism of the acting performance transformations among many characters of the same actor.

    The main goal of this paper is to introduce the higher derivatives multivalent harmonic function class, which is defined by the general linear operator. As a result, geometric properties such as coefficient estimation, convex combination, extreme point, distortion theorem and convolution property are obtained. Finally, we show that this class is invariant under the Bernandi-Libera-Livingston integral for harmonic functions.