Among a variety of approaches introduced in the literature to establish duality theory, Fenchel duality was of great importance in convex analysis and optimization. In this paper we establish some conditions to obtain classical strong Fenchel duality for evenly convex optimization problems defined in infinite dimensional spaces. The objective function of the primal problem is a family of (possible) infinite even convex functions. The strong duality conditions we present are based on the consideration of the epigraphs of the c-conjugate of the dual objective functions and the ε-c-subdifferential of the primal objective functions.

Gaslift reactors are employed in several bioapplications due to their characteristics of cost-effectiveness and high efficiency. However, the nutrient and thermal gradient is one of the obstacles that stand in the way of its widespread use in biological applications. The diagnosis, analysis, and tracking of fluid paths in external draft tube gaslift bioreactor-type are the main topics of the current study. Several parameters were considered to assess the mixing efficiency such as downcomer-to-rizer diameter ratio (Ded/Dr), the position of the diffuser to the height of bioreactor ratio (Pd/Lr), and gas bubble size (Db). The multiple regression of liquid velocity indicates the optimal setting: Ded/Dr is (0.5), Pd/Lr is (0.02), and Db

The extraction of Eucalyptus oil from Iraqi Eucalyptus Camadulensis leaves was studded using water distillation methods. The amount of Eucalyptus oil has been determined in a variety of extraction temperature and agitation speed. The effect of water to Eucalyptus leaves (solvent to solid) ratio and particle size of Eucalyptus leaves has been studied in order to evaluate the amount of Eucalyptus oil. The optimum experimental condition for the Eucalyptus oil extraction was established as follows: 100 C extraction temperature, 200 rpm agitation speed; 0.5 cm leave particle size and 6: 1 ml: g amount of water to eucalyptus leaves Ratio.

Leaching process applied for the extraction of bio active compounds from dried roots of (Elecampane) Inula helenium. Ethanol, hexane and distillated water were used as solvents. Roots were soaked with ethanol (5% w/v) with various concentration of ethanol (30 to 98%) at one day to know effect concentration of the solvent with concentration of bio active compound in Inula helenium. The same procedure was done using hexane as solvent. Also distilled water was used as solvent for extraction 5%(w/v) where plant material was soaked in water at different temperatures (25, 40, 65, 80, and 90) C. In all solvents undertaken, the effect of time duration on active ingredient (Thymol, Isoalatolactone, Alatolactone, 10-isobutyryl-oxy 8-9-epoxy thymol is

This research presents the possibility of using banana peel (arising from agricultural production waste) as biosorbent for removal of copper from simulated aqueous solution. Batch sorption experiments were performed as a function of pH, sorbent dose, and contact time. The optimal pH value of Copper (II) removal by banana peel was 6. The amount of sorbed metal ions was calculated as 52.632 mg/g. Sorption kinetic data were tested using pseudo-first order, and pseudo-second order models. Kinetic studies showed that the sorption followed a pseudo second order reaction due to the high correlation coefficient and the agreement between the experimental and calculated values of q_e. Thermodynamic parameters such as enthalpy change (ΔH

A liquid membrane process of Alkaloids extraction from Datura Innoxia solution was studied applying pertraction process in rotating discs contactor (RDC). Decane as a liquid membrane and dilute sulphuric acid as stripping solution were used. The effect of the fundamental parameters influencing the transport process, eg type of solvent used, effect of disks speed, amount of liquid membrane and effect of pH for feed and strip solution. The transport of alkaloids was analysed on the basis of kinetic laws of two consecutive irreversible first order reactions. Thus, the kinetic parameters (k1, k1,, tmax, and) for the transport of alkaloids were determined. The effect of organic membrane type on percentage of Alkaloids transport was found to be i

Biosorption is an effective method to remove toxic metals from wastewaters. In this study biosorption of lead and chromium ions from solution was studied using Citrobacter freundii and Citrobacter kosari isolated from industrial wastewater. The experimental results showed that optimum grwoth temperature for both bacteria is 30oC and the optimum pH is 7 &6 for C. freundii and C. kosari respectively. While the optimum incubation period to remove Pb and Cr for C. freundii and C. kosari is 4 days and 3days respectively. Also the biosorption of Pb and Cr in mixed culture of bacteria and mixed culture of Pb and Cr was investigated. Result indicate that uptake of Cr and Pb for C.freundii, C. kosari and in mixes culture of both bacteria is 58%, 53%

This studies deals with investigated the potential of a Iraqi bentonite clay for the adsorption of bromo phenol red dye from contaminated water. Impulse adsorption experiments were performed. The contact time influence of initial dye concentration, temperature, pH, ionic strength, partical size adsorbent and adsorbent dosage on bromo phenol red adsorption are investigated in a series of batch adsorption experiments. Adsorption equilibrium data were analyzed and described by the Freundlich, Langmuir and temkin isotherms equations. Thermodynamic parameters inclusive the Gibbs free energy (∆G• ), enthalpy (∆H• ), and entropy (∆S• ), were also calculated. These parameters specified that adsorption of bromo phenol red onto bentonite

The development of economic and environmentally friendly extractants to recover cobalt metal is required due to the increasing demand for this metal. In this study, solvent extraction of Co(II) from aqueous solution using a mixture of N,N0-carbonyl difatty amides (CDFAs) synthesised from palm oil as the extractant was carried out. The effects of various parameters such as acid, contact time, extractant concentration, metal ion concentration and stripping agent and the separation of Co(II) from other metal ions such as Fe(II), Ni(II), Zn(III) and Cd(II) were investigated. It was found that the extraction of Co(II) into the organic phase involved the formation of 1:1 complexes. Co(II) was successfully separated from commonly associated metal