generalization of this rate equation which projected by F. Kargi , that is assumed to be useful both in the case that the total enzyme or substrate is in excess and the quasi-steady-state is produced. We conclude that this generalization is not enough dramatically and put another generalization based on application of the quasi-steady-state conservation equations and condition for both substrate and enzyme. The standard HMM equation is obtain via (a) applying the conservation equation only for…
The Leontief model is an attempt in this direction. Based on the assumption that each industry in the economy has two types of demands: external demand (from outside the system) and internal demand (demand placed on one industry by another in the same system), the Leontief model represents the economy as a system of linear equations. The Leontief model was invented in the 30’s by Professor Wassily Leontief (picture above) who developed an economic model of the United States economy by dividing…
and catastrophic. As the energy associated with crack at a=ac is maximum, we can compute the value of critical crack length by equating the first derivative of total energy (S+U) to zero. (∂ (S+U))/∂a=2 γ - 〖σ_(f^.)〗^2/E πa=0 From the above equation, the stress can be written as: σf = √((2Eγ )/πa) It is important to note that Griffith’s original work was true for brittle materials, specifically glass rods. When a ductile material is considered, an accurate fracture model cannot be provided…
established on the following hypotheses: (1) uniformly energetic adsorption sites, (2) monolayer coverage, and (3) no lateral interaction between adsorbed molecules [26]. A mathematical expression of the Langmuir isotherm is given by the following equation: Where qe (mg/g) is the amount of dye adsorbed on the solid adsorbent at equilibrium, qm (mg/g) is the maximum adsorption capacity, KL (L/mg) is the Langmuir equilibrium constant, and Ce (mg/L) is the EBT dye…
variable bounds, and other problem constants. While shadow values directly quantify the total objective incentive to constraint changes; this invention also analyzes incremental improvements in each objective term and other process variables. In both linear and nonlinear optimization analyses, skilled users may perform sensitivity analysis for individual parameters (see Fiacco 1976; Ganesh and Biegler 1987). This invention improves this by expanding the practice to the systematic…
Linear programming which is also known as “Linear Optimization” is a way to achieve best outcomes in a Mathematical Model using different linear solutions .Linear Programming is a special case of Mathematical Optimization .Linear programming can be applied to a wide variety of fields of study, and has proved useful in planning, routing, scheduling, assignment, and design, such as in transportation or manufacturing industries. The method of Linear Programming was originally developed by American…
the document. In particular, the probability $P(d/q)$ of a document $d$ conditioning on query $q$ as likelihood relevant represent the QLM models citep{ponte1998sigir}. Applying Baye 's rule on $P(d/q)$ to get: egin{equation} label{BayesQLM} P(d/q) = frac{P(q/d)P(d)}{P(q)} end{equation} where $P(q)$ could be ignored as it is equivalent across all documents. Also, the document prior $P(d)$ could be ignored as it is uniformly the same across all documents. The document prior $P(d)$ could be the…
on the spectral action balance equation rather than the spectral energy balance equation. The evolution of the action density N is governed by Komen et al. [13]: ∂N/∂t+∇_x ⃗ ∙[((c_g ) ⃗+U ⃗ )N]+(∂c_θ N)/∂θ+(∂c_σ N)/∂σ=S_tot/σ where, N(σ.θ) is the action density spectrum, x is space, t is time,θ is wave direction, σ is relative frequency, S_tot is the source term total, and c_g represents the propagation velocity. The first term in the left hand side of the equation represents the local rate of…
model as the R² value is 0.9697. The hypothesis that the reaction would be first order was also supported, which can be seen in graph 2 of the results, where the natural log of the molarity was plotted against time and the trendline was linear, with the equation of ln(M) = 0.0016t + 0.1434. This is because…
Have in mind that the points (80, 0.9) and (70, 0.7) are on the supply curve, we solve the system with 2 equation and unknown variables. So, 80 = a + b *0.9 and 70= a + b* 0.7, concluding to a= 35 and b=50. Thus, supply curve for chicken meat in 2014 (and 2013) is Qs=35+50*P. The price elasticity of supply is: εs = (ΔQ/ΔΡ)*(Ρ/Q) = (80-70)/ (0.9-0.7)*(0…