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.

Phthalimide formation of Phthalic anhydride with various amines using microwave or without a method with the difference of the catalyst used in a prepared Phthalimide, either structure general are C6H4CONRCO and used as starting materials in synthesis several compounds derivative phthalimides are an important compounds because spectrum wide biological activities including Antimicrobial activity, anticonvulsant activity, Anti-inflammatory activity,Analgesic activity, Anti- influenza activity and Thromboxane inhibitory activity

this paper give a proof of known conditions for the existence of peridic conincidence points of continuius maps using lindemann theotem on transcendental numbers

In this work, we focused on studying 1,4-naphthoquinones and their derivatives, and knowing the methods of preparing them using different auxiliary agents and forming derivatives containing heterocyclic rings, active groups and saturated rings containing heterogeneous elements . In addition, due to their strong antibacterial, antifungal and anticancer activity, 1,4-naphthoquinone compounds biological importance and are considered a source of various pharmaceutical compounds.

The optimum separators operating pressure is determined by using flash calculations and equilibrium ratios. In this study, the optimum separator size for Jambur field is calculated by using equations introduced by Arnold and Stewart and API12J Specification [1]. Because Jambur field has a high production rate two conditions are taken in the study to determine separator size, first based on production rate 80,000 bbl/day and second based on split the production between two banks A and B (40,000 bbl/day for each bank). The calculation resulted in optimum separator pressure for the first stage of 700 psi, and the second stage of 300 psi, and the third stage of 120 psi. The results show that as the number of stages increased above three-stag

This article investigates the relationship between foot angle and jump stability, focusing on minimizing injury risk. Here are the key points: Importance: Understanding foot angle is crucial for improving jump stability, athletic performance, and reducing jump-related injuries like ankle sprains. Ideal Foot Angle: Research suggests a forward foot angle of around 15 degrees might be ideal for many people during jumps. This angle distributes forces evenly across the foot, lowers the center of gravity, and provides more surface area for pushing off the ground. Factors Affecting Ideal Angle: The optimal angle can vary depending on the type of jump (vertical vs. long jump), fitness level, and personal preference. Incorrect Foot Angles: Landing w

Gold nanoparticles AuNPs have proven to be powerful tools in various nanomedicine applications, because of their photo-optical distinctiveness and biocompatibility. Noble metal gold nanoparticles was prepared by pulsed laser ablation method (1064-Nd: YAG with various Laser power from 200 to 800 mJ and 1 Hz frequency) in distil water. The process was characterized using UV-VIS absorption spectroscopy. Morphology and average size of nanoparticles were estimated using AFM and X-ray diffraction (XRD) analysis which show the nature of gold nanoparticles (AuNPs). Antibacterial activity of gold nanoparticles as a function of particles concentration against gram negative bacterium Escherichia coli and gram positive bacterial Staphylococcus aureu

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

The aim of the present study was to characterize the Iraqi Tribulus terrestris for the presence of biologically active phyto-chemicals using methanolic extracts of the plant (aerial parts) by Gas Chromatography –Mass spectrometry (GC/MS), while the mass spectra of the compounds found in the extract was matched with the National Institute of Standards and Technology (NIST) library , in addition to study the antioxidant activity of plant extract , results confirmed the presence of therapeutically potent compounds in the Iraqi Tribulus terrestris extract predominantly alkaloids, flavonoids, saponins, tannins and terpenoids. Antioxidant potential of Iraqi Tribulus terrestris

Gelatin a promising biomaterial which is useful and interesting natural polymer which offer possibilities of chemical modification through grafted copolymerization with an saturated acid anhydride such as methyl nadic anhydride formatted gelatin –g- methyl nadic anhydride copolymer (A1), then modified to its corresponding polymer (A2) by substituted salbutamol as useful derivative as biomaterial .the prepared drug biopolymer was characterization by FTIR spectroscopy and thermal analysis was studied controlled drug release was measured in different buffer solution at 37C0 .