(ii) By virtue of the symmetry of equation (23) we can suppose that (Vert xVert ge Vert yVert ).
Moreover, by virtue of its symmetry under rotations, the EPR-Bohm wave function has the property that any component of spin, i.e., any direction, can be used in this decomposition.
Wang modified the weighting vector and simplified the diagonal matrix of eigenvalues by virtue of the symmetry properties, then they gave the solution in constraints of both sensitivity function (SF) and side-lobe level by the SOCP [12].
By virtue of the symmetry, the theorem can be proved by the same method as employed in the proof of Case III.1 and hence we know that (2.2) satisfies B_{N}cap{ mathrm{III}_{(M,M }}to B_{N}cap{ mathrm{VI}}_{(M tilde{varepsilon},Mtilde{varepsilon} )} and B_{N}cap{mathrm{VI}_{(M,M }}to B_{N} cap{ mathrm{III}_{(M tilde{varepsilon},Mtilde{varepsilon} )}} with (tilde{varepsilon}>1).
Our main concern now is to control the third derivatives of u in the last line of (2.7) and for this we adapt the key identities in the proof of Lemma 2.1 in [10], which follow by differentiating (F(P_alpha r P^t_alpha )), for (rin Gamma ), with respect to (alpha ) and setting (alpha = 0), where (P_alpha = mathrm{exp} alpha Dtau )) is orthogonal by virtue of the skew symmetry of (Dtau ).
By virtue of their molecular symmetry, mtCKs are also able to cross-link two membranes.
This led to the opening of a high-frequency PnBG, by virtue of this discrete symmetry breaking associated with the displacement fields.
This assumption is reasonable by virtue of the approximate rotational symmetry of the eigenvector distribution under our choice of random graph model, which we expect to be close (heuristically) to the eigenvector distribution of the symmetric Gaussian ensemble [19, 20].
This contrasts with our original tetraintercalator 1, in which there is overall C2 symmetry by virtue of a symmetric middle linker and two external linkers with N to C directionality pointing away from the center.
