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Garrione, Resonance and rotation numbers for planar Hamiltonian systems: multiplicity results via the Poincare- Birkhoff theorem, Nonlinear Anal. 74 (2011), 4166-4185.A. Boscaggin and M. Garrione, Resonance and rotation numbers for planar Hamil- tonian systems: multiplicity results via the ...
The eigenvalues (7.3.47) are complex (λz and λt are purely imaginary, while λx±iy are arbitrary complex numbers) and bounded (owing to s being a unit vector): (7.3.52)|λz|≤1,|λx±iy|≤1,|λt|≤1. 7.3.2.2 Continuous spectra of translation operators The translation operator...
Theorem 2.4 (Theorem 2.2 of [11]). Let z denote the canonical generator of the algebra C(T) of continuous functions on the unit circle, and let ψ ǫ : B ǫ →C(T) be the unique homomorphism such that ψ ǫ (x n ) = z for all n. If ǫ < 2, then ψ ǫ ...
(Schou et al.1998), which can also be considered as equatorial superrotation. The angular velocity decreases monotonically from the equator to the pole by about 30% throughout the convective envelope. A deviation from a cylindrical profile expected from the Taylor-Proudman theorem is observed. ...
The set of three-dimensional complex numbers is not closed under multiplication. Pro of (freely adopted from Kenneth O. May 1966): 2 2 Assume that the usual rules of arithmetic for complex numb ers hold, and that i = j = 1. The pro of is by contradiction, so we assume that a ...
By applying linear stability theory and normal mode analysis method, a semi-circle theorem is derived. The mathematical analysis on the onset of thermal convection in a couple-stress fluid under rotation in a porous medium for the case of rigid boundaries shows that the complex growth rate σ ...
(Apply Euler's theorem.) Considering rotation around the bond highlighted in red in the given compound, draw Newman projections for the most stable and least stable conformations. Determine the symmetries of the stretching modes for CH_3Cl . Determine the reducible representation for the...
, n- 1, anm and bnm are defined by expressions (2.2.8) and (2.2.10), and Wαβare components of complex rotation matrix (3.3.60). PROOF Taking the scalar product of both sides of Eq. (3.3.55) with ix, iiy, and iz, we obtain the statement of the theorem. COROLLARY 7 Summing...
, n- 1, anm and bnm are defined by expressions (2.2.8) and (2.2.10), and Wαβare components of complex rotation matrix (3.3.60). PROOF Taking the scalar product of both sides of Eq. (3.3.55) with ix, iiy, and iz, we obtain the statement of the theorem. COROLLARY 7 Summing...