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.

A nano manganese dioxide (MnO₂) was electrodeposited galvanostatically onto a carbon fiber (CF) surface using the simple method of anodic electrodeposition. The composite electrode was characterized by field emission scanning electron microscopy (FESEM), and X-ray diffraction (XRD). Very few studies investigated the efficiency of this electrode for heavy metals removal, especially chromium. The electrosorption properties of the nano MnO₂/CF electrode were examined by removing Cr(VI) ions from aqueous solutions. NaCl concentration, pH, and cell voltage were studied and optimized using the Box-Behnken design (BDD) to investigate their effects and interactions on the electrosorption process. The results showed that the

The 17 α-ethinylestradiol (EE2) adsorption from aqueous solution was examined using a novel adsorbent made from rice husk powder coated with CuO nanoparticles (CRH). Advanced analyses of FTIR, XRD, SEM, and EDSwere used to identify the classification parameters of a CRH-like surface morphology, configuration, and functional groups. The rice husk was coated with CuO nanoparticles, allowing it to create large surface area materials with significantly improved textural qualities with regard to functional use and adsorption performance, according to a detailed characterization of the synthesized materials. The adsorption process was applied successfully with elimination effectiveness of 100% which can be kept up to 61.3%. The parameters of ads

In the present work, the pollutants of the municipal wastewater are reduced using Chlorella vulgaris microalgae. The pollutants that were treated are: Total organic carbon (TOC), Chemical oxygen demand (COD), Nitrate (NO₃), and Phosphate (PO₄). Firstly, the treatment was achieved at atmospheric conditions (Temperature = 25^oC), pH 7 with time (1 – 48 h). To study the effect of other microorganisms on the reduction of pollutants, sterilized wastewater and unsterilized wastewater were used for two types of packing (cylindrical plastic and cubic polystyrene) as well as algae's broth (without packing), where the microalgae are grown on the packing then transported to the wastewater for treatment. Th

Bioremoval of chromium from wastewater of tannery factory in Iraq was studied. The bacteria Proteus vulgaris 7E showed an enhanced capability in biosorping chromium when its concentration increased in the solution, reaching a maximum of 476,7 mg/ ml out of 492 mg/ ml under optimum conditions at pH 6 and 50°C at one hour contact time and biomass of 1 mg/ml. The present results showed that dead cells of P. vulgaris 7E biosorbed 87.41 mg/ml of chromium in comparison with91.18 mg/ml of chromium biosorbed by living cells, this indicates the insignificant effect of physiological state of cells. It was found that the above biosorption is physico-chemical process depends upon electrostatic attraction forces. The results has illustrated that the

   A microbubble air flotation technique was used to remove chromium ions from simulated wastewater (e.g. water used for electroplating, textiles, paints and pigments, and tanning leather). Experimental parameters were investigated to analyze the flotation process and determine the removal efficiency. These parameters included the location of the sampling port from the bottom of the column, where the diffuser is located to the top of flotation column (30, 60, and 90 cm), the type of surfactant (anionic, SDS, or cationic, CTAB) and its concentration (5, 10, 15, and 20 mg/L), the pH of the initial solution (3, 5, 7, 9, and 11), the initial contaminant concentration (10, 20, 30, and 40 mg/L), the gas flow rate (0.1, 0.2, 0.3, and 0.5 L/mi

The present work aims to study the possibility of utilization a forward osmosis desalination process as an alternative method to extract water from brine solution rejected from reverse osmosis process.
Experiments conducted in a laboratory–scale forward osmosis (FO) unit in cross flow flat sheet membrane cell yielded water flux ranging from (0.0315 to 0.56 L/m2 .min) when using CTA membrane,and ranging from (0.419 to 2.785 L/m2 .min) for PA membrane under 0.4 bar. Two possible membrane orientations were tested. Sodium chloride with high concentrations was used as draw solution solute. The effect of membrane orientation on internal concentration polarization (ICP) was studied. Two regimes of ICP; dilutive and concentrative were desc

Cladophora and Spirulina algae biomass have been used for the removal of Tetracycline (TC) antibiotic from aqueous solution. Different operation conditions were varied in batch process, such as initial antibiotic concentration, different biomass dosage and type, contact time, agitation speed, and initial pH. The result showed that the maximum removal efficiencies by using 1.25 g/100 ml Cladophora and 0.5 g/100 ml Spirulina algae biomass were 95% and 94% respectively. At the optimum experimental condition of temperature 25°C, initial TC concentration 50 mg/l, contact time 2.5hr, agitation speed 200 rpm and pH 6.5. The characterization of Cladophora and Spirulina biomass by Fourier transform infrared (FTIR) indicates that the presenc