This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples

A new Turbidimetric method characterized by simplicity, accuracy and speed for determination of iron(III) in drug samples by continuous flow injection analysis. The method was based on the formation of complex for iron(III) with 8-hydroxyquinoline in presence of ammonium acetate as a medium for the formation of deep green precipitate and this precipitate was determined using homemade Linear Array Ayah-5SX1-T-1D continuous flow injection analyser. The optimum parameters were 2.6 mL.min-1 flow rate using H2O as a carrier, 1.9 mL.min-1 (14 mmol.L-1) ammonium acetate, 2.4 mL.min-1 (14 mmol.L-1) 8-hydroxyquinoline, 60 L sample volume and open valve for the purge of the sample segment. Data treatment shows that linear range 0.1-8.0 mmol.L-1

This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

  Necessary and sufficient conditions for the operator equation I AXAX n  * , to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

Chemical pollution is a very important issue that people suffer from and it often affects the nature of health of society and the future of the health of future generations. Consequently, it must be considered in order to discover suitable models and find descriptions to predict the performance of it in the forthcoming years. Chemical pollution data in Iraq take a great scope and manifold sources and kinds, which brands it as Big Data that need to be studied using novel statistical methods. The research object on using Proposed Nonparametric Procedure NP Method to develop an (OCMT) test procedure to estimate parameters of linear regression model with large size of data (Big Data) which comprises many indicators associated with chemi