This paper develops a fuzzy multi-objective model for solving aggregate production planning problems that contain multiple products and multiple periods in uncertain environments. We seek to minimize total production cost and total labor cost. We adopted a new method that utilizes a Zimmermans approach to determine the tolerance and aspiration levels. The actual performance of an industrial company was used to prove the feasibility of the proposed model. The proposed model shows that the method is useful, generalizable, and can be applied to APP problems with other parameters.

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

  The experimentes were carried out by using a nutrient solution in the green house of Biology Dept , college of Education (Ibn Al- Haitham , University of Baghdad .) during 2001 -2002 growing season in order to determine the effect of sodium ion, by using four concentrations: (zero , 40,80,120. Mm), to study the appearance and physiological characteristics for two wheat varieties : IP A99 and Al-Kaid according to factorial experiment in completely randomized design for each concentration. The rcsults showed that the fourth concentration (120 Mm) for the Na ion is the most effective one on Leaf area, chlorophyll content, soluble carbohydrates, nitrogen content and protein percentage.        Moreove

In this research, hand lay- up technique is used to prepare samples from epoxy resin reinforced with multi- walled carbon nanotubes in different weight fractions (0, 2, 3, 4, 5) wt%. The immersion effect by sodium hydroxide solution (NaOH) at normality (0.3N) for a period of (15 days) on the thermal conductivity of nanocomposites was studied, and compared to natural condition (before immersion). The thermal conductivity of epoxy nanocomposites specimens were carried out using Lee’s disk method. The experimental results showed that thermal conductivity increased with increase weight fraction before and after immersion for all specimens, while the immersion effect leads to decrease thermal conductive values compared to thermal conductivi

Molecular interactions between 2-isopropenylnaphthalene-methacrylic acid (IPNMA) block copolymer( as a model for water- soluble polymer) and methanol at several temperatures were studied using fluorescence techniques , Fluorescence spectrum for (IPNMA) exhibits two emission bands at around 342 nm and 387 nm corresponding to the monomer and the excimer bands , respectively .The fluorescence spectra of dilute solution of (IPNMA) in methanol were recorded in temperature range of 8- 45?C . Plot of the excimer to monomer intensity ratio Ie/Im versus temperature was obtained, which shows double lines with positive slopes crossing at 25?C , the increasing of slope value above this temperature is s

This research presents a study for precipitating phosphorus (as phosphate ion) from simulated wastewater (5ppm initial concentration of phosphorus) using calcium hydroxide Ca(OH)₂ solution. The removal of phosphorus by Ca (OH)₂ solution is expected to be very effective since the chemical reaction is of acid-base type but Ca(OH)₂ forms complex compound with phosphate ions called. Hydroxyapatite Ca₅ (PO₄)₃OH. hydroxyapatite is slightly soluble in water. This research was directed towards sustainable elements as phosphorus. Kinetics of the dissolution reaction of hydroxyapatite was investigated to find the best factors to recover phosphorus. The effect of con

In the current study, haemoglobin analytes dissolved in a special buffer (KH₂PO₄(1M), K₂HPO₄(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10^-8 to 10^-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity  ≥99%  dielectric mirrors (dia

     In any natural area or water body, evapotranspiration is one of the important outcomes in the water balance equation. As a significant method and depending on monthly average temperature, estimating of potential Evapotranspiration depending on Thornthwaite method was adopted in this research review. Estimate and discuss evapotranspiration by using Thornthwaite method is the main objectives of this research review with considerable details as well as compute potential evapotranspiration based on climatologically data obtained in Iraq. Temperature - evapotranspiration relationship can be estimated between those two parameters to reduce cost and time and facilitate calculation of water balance in lakes, river, and h