Reciprocal relations origins

Equation (2.9) is known as the reciprocity relation or cross-differentiation identity. It follows from the fact that the order of differentiation of our original function 2 == z x, y) with respect to x and y is immaterial. Mathematically this is written... 

Origin of Reciprocal Relations 1. A General Wavepacket Other Phase-Modulus Relations... 

Note that the contribution to the stress from the nematic potential is independent of the deformation rate and is therefore elastic. The coefficients i are known as the Leslie viscosities. (The factors of V2 in the equations do not appear in the original literature because of different definitions of D and 52.) The Onsager reciprocal relations from irreversible thermodynamics require that 2 + 3 = 6 - 5. Conservation of angular momentum must also be satisfied by the director, which takes the form... 

The deviation vector q, with origin at the end of the reciprocal lattice vector h, has two components, q y horizontal, positive rightwards going, and q vertical, positive upwards going. For the symmetric reflection, these components are related to the deviations of specimen ( ) and analyser ( ) from their zero... 

The second step consists of calculating a convolution of interatomic vectors between s)unmetry-related molecules of the correctly oriented model placed at different origins, with the experimental Patterson fimction. The reciprocal version of the... 

Beliefs about other people can also be difficult to validate. An element of self-fulfilling prophecy can be at work. If you perceive someone else as, for example untrustworthy, that perception is likely to be reciprocated in the way he or she relates back to you. You are thus confirmed in your original beliefs, or at least you get no evidence to disconfirm them. 

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