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.

This paper proposes a new strategy to enhance the performance and accuracy of the Spiral dynamic algorithm (SDA) for use in solving real-world problems by hybridizing the SDA with the Bacterial Foraging optimization algorithm (BFA). The dynamic step size of SDA makes it a useful exploitation approach. However, it has limited exploration throughout the diversification phase, which results in getting trapped at local optima. The optimal initialization position for the SDA algorithm has been determined with the help of the chemotactic strategy of the BFA optimization algorithm, which has been utilized to improve the exploration approach of the SDA. The proposed Hybrid Adaptive Spiral Dynamic Bacterial Foraging (HASDBF)

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. 

An acidic environment causes surface changes of resin composites. Filler particlesize and filler distribution also have a direct effect on these surface changes. This invitro study evaluated the influence of Pepsi Cola drink on the surface roughness ofComposan LCM and Composan Ceram over time. Sixteen disc shaped specimens(10mm diameter, 2mm thickness) of each resin composite were fabricated, therebyforming two groups (n= 8). Surface roughness (Ra) was analyzed after 24 hrs beforeexposure to beverage. The specimens were submitted to a five minutes immersion inPepsi Cola three times daily interrupted by immersion in deionized distilled water (37C˚). Surface roughness measurements were done at 10, 30, and 60 days intervals. Datawere

The varied applications of polystyrene in various fields of life led to examining the cause of radiation influence on some rheological behavior of commercial Polystyrene (PS) solution in the chloroform (CHCl3) solvent. Polystyrene grains shape samples were irradiated using the radioactive element Cesium- 137 with (9 µci) activity for 10, 20, and 30 minutes. The viscosity of the polymer solution depends on the concentration and size (i.e. molecular weight) of the dissolved polymer. Experimental data showed that the radiation dose affected the value of viscosity (shear, relative, specific, and reduced). The viscosity value significantly reduced at 10 min radiation dose and when increasing the dose, the viscosity value increased

In this work dithine complexes prepared from dithiol benzil ligand and central ion to the Ni,Pd,Pt, element the ligand and complexes have been investigated using FTIR spectrophotometer and uv-vis-NIR spectral reigns show higher intensity represents the ?-?* transition in the chromopher cycle .These absorption which appear in visible and near IR spectral regions ,According to the complexes of one group ,the spectral shifting due to the change of central ion has been found to be related to atomic number of central ion .This shifting is increased while decreasing the central ion atom number These complexes have been implemented in Nd+2:YAG cavity because each posses resonant absorption band near Nd+2:YAG, Nd+2:Glass emitting at (106

Simplification of new fashion design methods

Design and construction of video extractor circuit require an understanding of several parameters, which include: Selector circuit, extracting circuit which contains sampling signal and multiplexing. At each radar pulse, the video signal is fed to one of the selector. The fast filter has a pass –band from 190 Hz to 1800 Hz. These frequencies correspond to targets having radial velocities laying between and 10 Kph and 200 Kph.Slow filter: 60 Hz to 230 Hz for radial velocities laying between 3.5 and 13 Kph.The video- extractor is organized in four PCB CG (A-B-C-D) each one having 16 selector. The sampling signal (ADS) (1-2-3-4) control the 4-line-to-16-line decoders. 8 multiplexers of 8 inputs each, are required for the multiplexing of the