The set of all (n×n) non-singular matrices over the field F. And this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension  over the field F, denoted by . The determinant of these matrices is a homomorphism from  into F* and the kernel of this homomorphism was the special linear group and denoted by  Thus  is the subgroup of  which contains all matrices of determinant one.

The rationally valued characters of the rational representations are written as a linear combination of the induced characters for the groups discussed in this paper. We find the Artin indicator for this group after studying the rationally valued characters of the rational

Background: Although various imaging modalities are available for evaluating suspicious breast lesions, ultrasound-based Shear-Wave Elastography (SWE) is an advanced, non-invasive technique complementary to grayscale sonography. This technique evaluates the elasticity of a specific tissue by applying sonic pressure to that tissue.

Objective: The aim is to assess the role of SWE in evaluating solid breast masses in correlation to histopathological study results.

Subjects and Methods: This prospective study was done in a tertiary care teaching hospital from September 2019 to August 2020. A study population of 50 women aged 18 years or above with an

A fuzzy logic approach (FLA) application in the process of stud arc welding environment was implemented under the condition of fuzziness input data. This paper is composed of the background of FLA, related research work review and points for developing in stud welding manufacturing. Then, it investigates thecase of developingstud arc welding process on the controversial certaintyof available equipment and human skills.Five parameters (welding time, sheet thickness, type of coating, welding current and stud shape) were studied.A pair of parameter was selected asiteration whichis welding current and welding time and used fo

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                Interest in the topic of prediction has increased in recent years and appeared modern methods such as Artificial Neural Networks models, if these methods are able to learn and adapt self with any model, and does not require assumptions on the nature of the time series. On the other hand, the methods currently used to predict the classic method such as Box-Jenkins may be difficult to diagnose chain and modeling because they assume strict conditions.

In this paper has been building a statistical model of the Saudi financial market using GARCH models that take into account Volatility in prices during periods of circulation, were also study the effect of the type of random error distribution of the time series on the accuracy of the statistical model, as it were studied two types of statistical distributions are normal distribution and the T distribution. and found by application of a measured data that the best model for the Saudi market is GARCH (1,1) model when the random error distributed t. student's .

Buzurgan oil field suffers from the phenomenon of asphaltene precipitation. The serious negatives of this phenomenon are the decrease in production caused by clogging of the pores and decrease in permeability and wettability of the reservoir rocks, in addition to the blockages that occur in the pipeline transporting crude oil. The presence of laboratories in the Iraqi oil companies helped to conduct the necessary experiments, such as gas chromatography (GC) test to identify the components of crude oil and the percentages of each component, These laboratory results consider the main elements in deriving a new equation called modified colloidal instability index (MCII) equation based on a well-known global equation called colloidal instabi

Buzurgan oil field suffers from the phenomenon of asphaltene precipitation. The serious negatives of this phenomenon are the decrease in production caused by clogging of the pores and decrease in permeability and wettability of the reservoir rocks, in addition to the blockages that occur in the pipeline transporting crude oil. The presence of laboratories in the Iraqi oil companies helped to conduct the necessary experiments, such as gas chromatography (GC) test to identify the components of crude oil and the percentages of each component, These laboratory results consider the main elements in deriving a new equation called modified colloidal instability index (MCII) equation based on a well-known global equation called colloidal in

Extracorporeal shock wave lithotripsy (ESWL) is considered a standard treatment for nephrolith or kidney stones measuring less than 20 mm. Anatomical, machine-related, and stone factors play pivotal roles in treatment outcomes, the latter being the leading role. This paper examined the relationship between stone density on native CT scans and ESWL treatment to remove renal stones concerning several treatments. One hundred and twenty patients (64 males and 56 females) were enrolled and completed the study from April 2019 to September 2020. Inclusion criteria were a single renal pelvis stone of 5–20 mm to be treated for the first time in adult patients with no urinary or musculoskeletal anatomical abnormalities. We assessed patients

A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

Traumatic radial nerve injury in humeral shaft fracture is the most common traumatic nerve injury in long-bone fracture, with overall prevalence 2-18%, ranging from traction to complete transection. Spontaneous recovery may reach 88%. The aim of the study is to assess the sensitivity & specificity of the ultrasound to detect the radial nerve injury and to see if this can be used as a diagnostic test. This is a prospective study on 17 adult patients with a closed fracture of the humeral shaft, dividing into two groups, the first group of 7 patients had signs and symptoms of radial nerve palsy at presentation and the second group of 10 patients had intact radial nerve function was considered as a control group. All these patients had at leas