Reductio

At this stage, we are ready to prove that Kramers theorem holds also for the total angular momentum F. We will do it by reductio ad absurdum. Then, let Itte) be the eigenvector of H with eigenvalue E,... 

Joseph, Robert Joseph. "Ben Jonson a study of language and the reductio ad absurdum in three of his major comedies." M.A. thesis, Pennsylvania State University, 1971. 

Finally, we can demonstrate that the degeneracy is even when the total angular momentum quantum number F is half-integer, again via a reductio ad absurdum method. Suppose that the degeneracy of the eigenstates is k, then we... 

A kinetic argument shows that ay - oy always. Any imbalance between these two would lead to an angular acceleration of a volume element. If this volume element were shrunk, then the torque would reduce in proportion to the linear dimension cubed, but the moment of inertia would reduce in proportion to the fifth power of the linear dimension, so that the angular acceleration would increase as the reciprocal of the square of the size of the volume element, becoming infinite in the limit. Thus reductio ad absur-dum, ay = cry. Hence there are only six independent components of the stress tensor. 

If there were consensus on all of these matters—and there is—you would have, at least, to concede that half of the objectivity battle—that of reliability and with if face validity—was won. Otherwise you would be forced to hypothesize that the consensus about formal properties was illusory and that the subjects (including me ) were just making up stories to satisfy expectations. This argument invites a reductio ad absurdum rejection. What motive could possibly be satisfied in this way And how could all of the subjects know what was expected of them, as the very notion of formal properties is recent and the specification of them an ongoing project Many people don t even understand what the term means when it is explained to them. 

This equation leads to a reductio ad absurdum that may provide a significant refinement of the helical conductor model. It will be noted that as the step helices (ya = 180°) approach the absolutely planar zigzag chain structure (ya = /b = 180°) they acquire very large cross sections. The index of helieity approaches a constant value of about 0.385 but the expected residue rotations approach infinity. (See Table 12). This result is, at least intuitively, absurd. 

We now prove statement (ii) of the lemma by reductio ad absurdum Assume that Cn,o 7 0- Then the asymptotic form of S iw a r) is given by (62) and we conclude that... 

In order to prove that the densities n(r, t) and n (r, t) will become different infinitesimally later than to, we have to demonstrate that the right-hand side of Eq. (25) cannot vanish identically. This is done by reductio ad absurdum Assume... 

Equipment Size of Feed (mm) Size of Product (mm) Reductio Ratio Capacity (tons/hr) Power Consumption (kW... 

Reductive cycUzatiom are susceptible to reductio interfere with the cyclt 1,7-enynes is obsersed ii 1,10-phenanthroline-Pd( 11... 

We can now show that and t)2 yield dilferent densities reductio ad absurdum. We have... 

This equation, together with the variational principle, allowed Hohenberg and Kohn [1] to show by a trivial reductio ad absurdum that there is a one-to-one relationship between the density p and the external potential Oext- This implies that the energy E is a functional of the electronic density of the ground state i.e., for a given external potential u,... 

The form (128) suffers from the nonlinearity of H in the external vector potential The standard reductio ad absurdum of the HK-argument only works if H is linear in the external potentials. Thus no existence theorem can be proven with (128). On the other hand, such a proof is possible for the form (129), using the density n and the gauge dependent current jp - c/e)V x m as basic DFT... 

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