A simplex algorithm for minimum fuel problems of linear discrete control systems

A simplex algorithm for solving the minimum fuel problem for linear discrete control systems is described. In this algorithm an initial basic feasible solution is available with no artificial variables needed. Also minimum computer storage is required. The algorithm is a simple and fast one. A numerical example is given     

Polygonal approximation of planar curves in the L 1 norm

An algorithm for obtaining a polygonal approximation in the L ₁, norm of a plane curve of arbitrary shape is presented. The L ₁ error norm in any segment is not to exceed a pre-assigned value. The given curve is first digitized and the algorithm is then applied to the discrete points. The algorithm uses linear programming techniques which makes it efficient and fast. Numerical results and comments are given.     

Thermodynamic and relative approach to compute glass-forming ability of oxides

This study deals with the evaluation of glass-forming ability (GFA) of oxides and is a critical reading of Sun and Rawson thermodynamic approach to quantify this aptitude. Both approaches are adequate but ambiguous regarding the behaviour of some oxides (tendency to amorphization or crystallization). Indeed, ZrO₂ and Al₂O₃ were inappropriately listed by Sun and Rawson to be glassformer oxides while being intermediate ones. We present a non-dimensional approach to value GFA of single oxide by affecting to each one of the coefficients (without measuring units). Obeying to the non-dimensional analysis rules, we introduce a neglected (in all prior thermodynamic models) characteristic: the isobaric heat capacity (C _p) of oxides, and execute a mathematical treatment of oxides thermodynamic data. We note this coefficient as thermodynamical relative glass-forming ability (ThRGFA) and formulate a model to compute it. Computed values of 2nd, 3rd, 4th and 5th period metal oxides reveal a clear differentiation between them. Indeed, all glass former oxides are characterized by ThRGFA values over 1·709. Moreover, the value intervals confirm the oxides classification into three groups (forming, intermediate and modifier) and sorting of the former ones in distinctive strong and fragile oxides.     

Solutions of minimum time problem and minimum fuel problem for discrete linear admissible control systems

In this paper the minimum time problem and the minimum fuel problem for discrete linear admissible control systems arc formulated (is one linear programming problem with two different objective functions. It is found that the obtained problem is very similar to the dual form of the linear programming problem for the discrete linear L₁ approximation problem. An efficient dual simplex algorithm for the latter problem is used with the necessary modification* to obtain the solution of either of the former problems. Numerical results show that the present, method compares favourably with other known methods.     

The effect of concentration of chymosin on the yield and sensory properties of camel cheese and on its microbiological quality

The transformation of camel milk into soft cheese by using chymosin and yoghurt starter culture (Streptococcus thermophilus and Lactobacillus bulgaricus) was investigated. The cheese yield and sensory properties were related to the concentration of chymosin. A yield of 16.74 g/100 mL of milk was obtained with a chymosin concentration of 1.7 mL/L of milk. The cheeses obtained with concentrations ranging between 1.0 mL and 2.9 mL of chymosin/L of milk scored highly regarding their sensory properties and had an acceptable microbiological quality. This study demonstrated that cheesemaking from camel milk can be made successfully providing that the appropriate chymosin concentration is used; and that 1.7 mL of chymosin/L of milk was optimal.     

Competitive Contribution of Catalyst and Adsorption Roles of TiO2 on the Degradation of AO7 Dye During Plasma Treatment

In order to investigate the role of TiO2 during plasma treatment,the degradation of the dye AO7 has been studied by gliding arc discharge in the presence of a TiO2 catalyst(CGAD).The results revealed that the adsorption of the dye on TiO2 is a physical adsorption in accordance with Langmuir isotherm,with a constant of adsorption KL=0.52 mg/L and a maximum adsorption capacity b=18.1 mg/g.The temperature variation of the reaction medium made it possible to consider thermodynamic parameters.Indeed,the adsorption is exothermic(enthalpy:△H 0),and spontaneous(free enthalpy:△G 0).The negative entropy(△S0) confirms the afnity of the dye molecules for TiO2.20 min of CGAD treatment in the presence of an optimal quantity of TiO2(2 g/L enabled us to bleach the solution of AO7(100 μM) completely.The discoloration rate with and without the addition of TiO2 was 100% and 28%,respectively.40 additional minutes of treatment allowed a total abatement of the chemical oxygen demand.The elimination of AO7 molecules during the plasma-catalytic treatment follows Langmuir-Hinshelwood(L-H) model kinetics.According to this model,the speed constant is kr=14.97 mg · L 1· min 1and the adsorption coefcient is KL-H = 0.010 L/mg.The latter being negligible compared to kr,adsorption is therefore weakly performed during the plasma treatment.     

Piece wise linear least–squares approximation of planar curves

Two algorithms for solving the piecewise linear least–squares approximation problem of plane curves are presented. The first is for the case when the L ₂ residual (error) norm in any segment is not to exceed a pre–assigned value. The second algorithm is for the case when the number of segments is given and a (balanced) L ₂ residual norm solution is required. The given curve is first digitized and either algorithm is then applied to the discrete points. For each segment, we obtain the upper triangular matrix R in the QR factorization of the (augmented) coefficient matrix of the resulting system of linear equations. The least–squares solutions are calculated in terms of the R (and Q) matrices. The algorithms then work in an iterative manner by updating the least–squares solutions for the segments via up dating the R matrices. The calculation requires as little computational effort as possible. Numerical results and comments are given. This, in a way, is a tutorial paper.