(2.1) reduces to an ideal gas EOS. Eq. (2.1) is usually written as: (2.2)P=RTV−b−aV2 To find the molar volume from pressure and temperature, this equation may be rearranged in the following form: (2.3)V3−(b+RTP)V2+(aP)V−abP=0...
equations in this chemical equation balance calculator so that you can practice and balance equations. Also there is a chemistry periodic table under the chemical equation balancer calculator so that you can add values from there. You can also learn all about periodic table equations to understand ...
Show that the solutions of the indicial equation of this equation are ℓ and − (ℓ + 1) 5. Find a series solution to the equation of the form u(r)=∑n=0∞anrn+ℓ 6. Find a series solution of the radial equation for the hydrogen atom. Show moreView chapter Book 2014, Int...
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Moran’s index is an important spatial statistical measure used to determine the presence or absence of spatial autocorrelation, thereby determining the selection orientation of spatial statistical methods. However, Moran’s index is chiefly a statistica
Find a minimum of the peaks function, which is included in MATLAB®, in the region x2+y2≤4. To do so, create optimization variables x and y. Get x = optimvar('x'); y = optimvar('y'); Create an optimization problem having peaks as the objective function. Get prob = optimpro...
The subscript \({\textbf{x}}_i\) on the expectation value indicates that the expectation is taken over all stochastic trajectories that start at \({\textbf{x}}_i\). The task of optimal control theory, as described by Bellman26, is to find the control \({\textbf{u}}(s)\) for ...
hybridizes the Subset Selection of Maximum Dissimilarity Method (SSMD) with Multi-gene Genetic Programming (MGP) and Pareto-optimality (PO) to find an accurate equation forϕrwith wide range applicability. The final predictive equation resulted from POMGGP modeling was assessed in comparison with ...
To find the secondary field, we have to use the solution of Laplace’s equation that decreases as the distance from the ellipsoid increases. Let us assume that the second type of solution has the form (3.124)Us(ξ,η,ς)=BG1(ξ)F2(η)F3(ς). This presentation is very natural ...
Macroscopic quantities are defined on the scale of an REV that has a volume δVi=biδAi. The phase distribution function γα may be used to obtain the part of the REV volume occupied by the α -phase, denoted δVα: (A.1)δVα=∫δViγα(X+x,t)dv. When modeling a multiphase...