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We introduce different bases for the vector space of Sp(2) Sp(1)-invariant, translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas.BernigAndreasSolanesGil.Proceedings of the London Mathematical Society...
Coulomb-stress theory has been used for years in seismology to understand how earthquakes trigger each other. Whenever an earthquake occurs, the stress field changes, and places with positive increases are brought closer to failure. Earthquake models tha
The kinematic restrictions which reject virtual and infrared corrections arise in our approach from a double-counting-exclusion (DCE) condition, which separates the LO and NLO contributions (see below). For the sake of definiteness and clarity, we hereafter will refer to this scheme as to NLO....
The quantities used in these formulas (Eqs.9,10,11and12) are shown in Fig.6. Figure 6 (A) Geometry for the determination of the angular distance along the great circle between point P and the pole of rotation PoR (NNorth Pole,Ocenter of the Earth,rEarth’s radius, modified after Ref...
The Pτ(q2) including NP contribution due to VR is enhanced but FLD∗0(q2) is decreased in the reasonable kinematic region. After considering the presence of additional SR coefficient, one can see that dΓ/dq2 depends on SR and SR2. So there is no cancellation in the numerator and ...
A product formula for valuations on manifolds with applications to the integral geometry of the quaternionic line - Bernig () Citation Context ...the kinematic formulas requires a lot more work and has been completed only very recently [19], [14]. Alesker [5] showed that dimVal SU(2) ...
Therein, k is the permeability; g is the acceleration due to gravity; 𝜈ν is the kinematic viscosity, which can be obtained from the dynamic viscosity (𝜇μ) and fluid (water) density (𝜌ρ): 𝜈=𝜇𝜌ν=μρ (2) The porosity n can be derived from the empirical relationship...
If we define ζ=p1+/p+ as one of the pion pair's momentum fraction, other kinematic variables of the two pions can be chosen as(4)p1−=(1−ζ)ηmB2,p2+=(1−ζ)(1−r2)mB2,p2−=ζηmB2. We assume that the B→ηc(ρ,ρ′,ρ″→)ππ decays can proceed mainly ...
It was verified that \(P_{1}\) did not have inverse kinematic solutions while \(P_{2}\) had inverse kinematic solutions through the Robotics Toolbox for MATLAB. Due to the IK problem of the 7-DOF manipulator has not been studied using the multi-objective method in the previous ...