Symmetry properties and cocycle properties of the Maslov index are then easily obtained.
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Unfortunately, several desirable properties are not available with compactly supported orthogonal wavelets, e.g., symmetry and piecewise polynomial structure.
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New symmetry and operational properties of the Fourier transform are derived.
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For a differential equation, a theoretical proof of the relationship between the symmetry and the one-parameter invariant group is given: the relationship between symmetry and the group-invariant solution is presented.
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The computation of symmetry-breaking bifurcation points inZ2×Z2-symmetric nonlinear problems
This paper deals with the aberrations of optical systems consisting of cylindrical components with their axes, parallal and having a common axis of symmetry. By symmetry and by a proper choice of the parameters for describing an optical ray, it is found that for primary aberrations the independent aberration terms amount to eight. For a. telescopic system the number of terms reduces to six. By method of vector analysis, it is further proved that the skew rays passing through such a systems is eq...
Dispersion relations for pion production in pion-nucleon colHssions are discussed. The scattering amplitude is written in a form, in which the operators of nucleon field are extracted from the state vectors of initial and final state. The kinematies and symmetry, properties are worked out in detail and the contribution of bound state is evaluated.
The crystal structure of ethylenediaminetetraacetic acid has been determined by the method of symmetry elements. The crystal is monoclinic, space group C_(2h)~6, with parameters Each unit cell has four molecules. The interatomic distances are calculated and discussed.