Weak solutions to the master equation of a potential mean field game 57:26 Controlling Human Microbiota 48:56 Describing interacting particle systems via partial differential equations and g 30:38 Differential Equations and Algebraic Geometry - 1 56:20 Epidemic Model-Based Benchmark for Optimal...
If F(x) = x + 1 what is the equation of F(x^2)(linear transformation from f(x) to f(x^2)). When is a transformation a projection? Use the geometric definition of cross product to find 3 \overrightarrow j \times ( \overrightarrow j + \overrightarrow i). \\\overrightarrow ...
The cross product in the envelope equation represents a line normal to the surface, while ∂ρ/∂τ is the relative velocity of the two surfaces at the common point, τ is the tool rotation angle and τ is the rotor lead defined per unit of the rotor rotation angle:r(t,ϑ)=[xh...
By combining the dot and cross products, Maxwell's four equations collapse into one (of course, this can also be achieved in tensor notation). The improvement is even more startling for the Dirac equation, which actually takes the form of a simple generalization of Maxwell's equations in ...
Note that Kirchhoff Current Law (KCL) has been used in the second equation of (11). Note also that the magnetic and electric field is null outside the channels \(\alpha _k\). The PV can be computed for every channel using equation (10), i.e., \({\varvec{s}}_{\alpha _k}={...
The Y-axis geometric error motion pose can be described by the following equation: $${\varvec{g}}^{e}_{FY} ({{\varvec{\uptheta}}}) = e^{{\hat{\xi }_{y} \theta_{y} }} e^{{\hat{\xi }_{{E_{{\text{Y}Y}} }} \theta_{{E_{{\text{YY}}} }} }} e^{{\hat{\...
The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the ...
Since [Math Processing Error]π1(S) is a one-relator group, the images of the elements [Math Processing Error]αi are solutions of a single algebraic equation which defines a subvariety of [Math Processing Error]G2g, the so-called representation variety. The Lie group G acts continuously ...
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Two great circles on a sphere of radius R. ε=φRsinsR where φ is the opening angle between the two great circles at the North Pole and the arc length s parameterizes the curves. Note that ε satisfies the “equation of motion,” (12.3)d2εds2=−Kε where K is the Gaussian ...