Broyden update is one of the one-rank updates which solves the unconstrained optimization problem but this update does not guarantee the positive definite and the symmetric property of Hessian matrix.

In this paper the guarantee of positive definite and symmetric property for the Hessian matrix will be established by updating the vector  which represents the difference between the next gradient and the current gradient of the objective function assumed to be twice continuous and differentiable .Numerical results are reported to compare the proposed method with the Broyden method under standard problems.

Gumbel distribution was dealt with great care by researchers and statisticians. There are traditional methods to estimate two parameters of Gumbel distribution known as Maximum Likelihood, the Method of Moments and recently the method of re-sampling called (Jackknife). However, these methods suffer from some mathematical difficulties in solving them analytically. Accordingly, there are other non-traditional methods, like the principle of the nearest neighbors, used in computer science especially, artificial intelligence algorithms, including the genetic algorithm, the artificial neural network algorithm, and others that may to be classified as meta-heuristic methods. Moreover, this principle of nearest neighbors has useful statistical featu

Background: Although mammography is a powerful screening tool in detection of early breast cancer, it is imperfect, particularly for women with dense breast, which have a higher risk to develop cancer and decrease the sensitivity of mammogram, Automated breast ultrasound is a recently introduced ultrasonography technique, developed with the purpose to standardize breast ultrasonography and overcome some limitations of handheld ultrasound, this study aims to evaluate the diagnostic efficacy of Automated breast ultrasound and compare it with handheld ultrasound in the detection and characterization of breast lesions in women with dense breasts. Objectives: To evaluate the diagnostic efficacy of Automated breast ultrasound and compare

Background: Although mammography is a powerful screening tool in detection of early breast cancer, it is imperfect, particularly for women with dense breast, which have a higher risk to develop cancer and decrease the sensitivity of mammogram, Automated breast ultrasound is a recently introduced ultrasonography technique, developed with the purpose to standardize breast ultrasonography and overcome some limitations of handheld ultrasound, this study aims to evaluate the diagnostic efficacy of Automated breast ultrasound and compare it with handheld ultrasound in the detection and characterization of breast lesions in women with dense breasts.

Objectives:<

Background: Ankylosing spondylitis is a chronic inflammatory disease that mostly involves the spine and sacroiliac joints. It is associated with a decreased quality of life. Biological medicines such as infliximab and its biosimilar are the mainstay treatments for active ankylosing spondylitis.

Objective: The study objective was to conduct a pharmacoeconomic study comparing the cost-effectiveness of the reference infliximab with its biosimilar in ankylosing spondylitis patients visiting public hospitals.

Subjects and Method: This is a two-center pharmacoeconomic study performed at two large teaching governmental hospitals in Baghdad, Iraq, which s

1-[4-(2-Hydroxy-4, 6-dimethyl-phenylazo)-phenol]-ethanone (HL1) and 2-(4-methoxy-phenylazo)-3, 5- dimethyl-phenol (HL2) were produced by combination the diazonium salts of amines with 3, 5- dimethylphenol. The geometry of azo compounds was resolved on the basis of (C.H.N) analyses, 1H and 13CNMR, FT-IR and UV-Vis spectroscopic mechanisms. Complexes of La (III) and Rh (III) have been performed and depicted. The formation of complexes has been identified by using elemental analysis, FTIR and UV-Vis spectroscopic process as well, conductivity molar quantifications. Nature of complexes produced have been studied obeyed mole ratio and continuous alteration ways, Beer's law followed through a concentration scope (1×10-4 - 3×10-4 M). High molar

Background: Mitral regurgitation (MR) is the most commonly encountered valve lesion in modern clinical practice. Severe mitral regurgitation may cause systolic dysfunction. Left ventricular ejection fraction may not be an accurate measurement of LV function in patients with mitral insufficiency. Myocardial performance index (MPI) is a simple non invasive measure of myocardial function. Methods: The study involved 50 patients with valvular mitral regurgitation and 50 healthy subjects as a control group. Transthoracic echocardiography was carried out for all patients and control group. The echocardiographic measurements included left ventricular end diastolic and end systolic dimensions, left atrial diameter, ejection fraction (EF), and myoca