System of linear equations

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…

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…

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…

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…

algebra somewhat originally was a generalization . The adjective " algebraic " usually denotes a relationship with algebra , such as in algebraic structure . For historical reasons, it may also indicate a relationship with the solutions of polynomial equations , algebraic numbers , algebraic extension or algebraic expression. It AGREES distinguishes between : Elementary algebra is the part of algebra that is usually taught in mathematics courses . Abstract algebra is the name given to…

to separate the proteins based on their molecular weight, the tertiary structure of the protein needs to be destroyed making the protein a linear molecule. Sodium dodecyl sulfate (SDS) plays an important role in this mechanism. Sodium dodecyl sulfate is an amphipathic detergent whose role is to break down the tertiary structure of a protein making it a linear molecule and also masking the native charge of the protein with a negative charge. By using SDS the protein involved in this experiment…

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…

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…

study was to estimate the age in a sample of Egyptian population based on the relationship between age and measurement of the tooth coronal index (TCI) in the mandibular permanent 1st molars in dental panoramic radiographs and to develop regression equations that can be used in…

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…