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.

In this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex. 

The purpose of this study is to investigate the histopathological response of dentinopulpal
response of human teeth to the Er: YAG laser cavity preparation in comparison with the conventional
class I cavity preparation. Thirty five sound human upper and lower first premolar teeth which were
needed to be extracted for orthodontic purposes were used in the study. Regarding to the method of
cavity preparation, the teeth were grouped into three groups; Group1; Control group which consists of
seven sound teeth without cavity preparation, Group2; Conventional cavity preparation group and group
3; Er: YAG laser cavity preparation group. Each of Group2 and3 consists of fourteen teeth that is
subdivided into: A. 7teeth that e

This paper presents a comparison between the electroencephalogram (EEG) channels during scoliosis correction surgeries. Surgeons use many hand tools and electronic devices that directly affect the EEG channels. These noises do not affect the EEG channels uniformly. This research provides a complete system to find the least affected channel by the noise. The presented system consists of five stages: filtering, wavelet decomposing (Level 4), processing the signal bands using four different criteria (mean, energy, entropy and standard deviation), finding the useful channel according to the criteria’s value and, finally, generating a combinational signal from Channels 1 and 2. Experimentally, two channels of EEG data were recorded fro

The assessment of a river water’ quality is an essential procedure of monitor programs and isused to collect basic environmental data. The management of integrated water resources in asustainable method is also necessary to allow future generations to meet their water needs. Themain objective of this research is to assess the effect of the Diyala River on Tigris River waterquality using Geographic Information System (GIS) technique. Water samples have beencollected monthly from November 2017 to April 2018 from four selected locations in Tigris andDiyala Rivers using the grab sampling method. Fourteen parameters were studied which areTurbidity, pH, Dissolved Oxygen, Biological Oxygen Demand, Electrical Conductivity, TotalDissolved Solids,

The harmonic oscillator (HO) and Gaussian (GS) wave functions within the binary cluster model (BCM) have been employ to investigate the ground state neutron, proton and matter densities as well as the elastic form factors of two- neutron 6He and 16C halo nuclei. The long tail is a property that is clearly revealed in the density of the neutrons since it is found in halo orbits. The existence of a long tail in the neutron density distributions of 6He and 16C indicating that these nuclei have a neutron halo structure. Moreover, the matter rms radii and the reaction cross section (𝜎𝑅 ) of these nuclei have been calculated using the Glauber model.

This paper attempts to shed light on the most influential factors in the importance of religious buildings were destroyed because of the recent war due to the control of terrorist gangs of ISIS over the city of Mosul, and to prioritize their reconstruction and their role in reviving the historical center of Mosul.

The research’s problem emerged in the lack of knowledge about the identifying the most influential factors in the importance of religious buildings and utilizing them to prioritize their reconstruction. This study aims to analyze the factors influencing the importance of religious buildings using the Expert Choice software through the Analytic Hierarchy Process (AHP) to reach an analysis of their weights and propose p

This study involves the investigation of the effect of nitrogen laser with 337.1 nm wavelength on the sensitivity of Staphylococcus aureus bacteria by using local therapeutic due to burns. Thirty six isolate of Staphylococcus aureus bacteria were isolated from 25 patients suffering from sever burns, each isolate of bacteria was irradiated with nitrogen laser at (5, 10, 15 and 30) pulses/second repetition rates for 1, 5, 10, 20 and 30 minutes for each repetition rate. The effects of nitrogen laser on the local therapeutics sensitivity of bacteria were obtained using Kirby Baur method. Changes in the sensitivity of bacteria to local therapeutics (Tetracyclin, Chloramphenicol, Flumizin and Fucidin) occur at high repetition rate(30 pulses/seco

This paper investigated the treatment of textile wastewater polluted with aniline blue (AB) by electrocoagulation process using stainless steel mesh electrodes with a horizontal arrangement. The experimental design involved the application of the response surface methodology (RSM) to find the mathematical model, by adjusting the current density (4-20 mA/cm2), distance between electrodes (0.5-3 cm), salt concentration (50-600 mg/l), initial dye concentration (50-250 mg/l), pH value (2-12 ) and experimental time (5-20 min). The results showed that time is the most important parameter affecting the performance of the electrocoagulation system. Maximum removal efficiency (96 %) was obtained at a current density of 20 mA/cm2, distance be