Similarity theorem

To derive the decomposition formula we require two theorems, the shift theorem and the similarity theorem. The shift theorem states that if/(r) has DHT H(v) then/(r+ a) has DHT... 

A similar theorem is called the quasi-ergodic theorem by Brennan. See footnote 5. 

Except for alternating signs, the antisymmetrical case yields similar theorems. 

This is sometimes called the similarity theorem. The horizontal stretching of a function in one domain results in horizontal contraction and amplitude growth in the other. In fact, these changes occur in such a way that the area under the curve in the other domain remains constant. 

A similar theorem can be derived for the condition of volume moderation, by using equations (2.7), (17.6) and (4.41). An adiabatic isothermal system only exhibits volume moderation if... 

Remark 10.11 (Security for the signer forwards). Currently, security for the signer backwards has been assumed in the one-time scheme and proved in the new scheme. If one wanted to obtain a similar theorem for security forwards, one would have to increase the parameter a in Construction 10.9 by adding log2(iV). because the attacker has more chances to come into a situation where he can make an improvable successful forgery. The same holds for the following constructions. ... 

The following theorem provides a formula for the capacity of an information hiding system with a maximum distortion constraint. It s similarity to Theorem (2.1) is apparent and its proof is omitted since it is identical in essence to the proof given in [GP80]. A similar theorem for the more general case of IHS, with mean distortion constraint is proved in [BCWOO]. 

Take care on the correct units. Try to explain the findings. There are further tests of interest Work out similarity theorems for other shapes of the molecules than spheres. Estimate whether the molecule radii obtained from the relation are in the correct range. Take notice that Lord Kelvin established such considerations [17,18]. 

The similarity theorem is a specific statement of a more general law of signal processing, the uncertainty principle ... 

The second important relationship is the Greetf-Ostrogradsky theorem, or the divergence theorem (also called the Gauss theorem, but this leads to confusion with a similar theorem bearing the same name in electrostatics seen in case study B5) ... 

If the factors W are equal to the weighting factors the ensemble differential virial theorem for spherically symmetric systems is obtained. A similar theorem is valid for the ground state (Nagy and March 1989). 

A quite similar theorem is valid in the cases where a finite number of terms that belong to some quantum numbers (like n and 1) of the unperturbed system are obtained by perturbation theory. It is the theorem used to transform the ordering for weak magnetic or electric fields into the ordering for strong fields. Its reads terms with equal m do not cross. Its validity rests on the fact that the values W of the terms with equal m are obtained as the roots of an algebraic equation... 

A similar theorem can be established for mhC logics, uniformly replacing the propositional variable pi with the formula opj. In this case, the output polynomial is equal to the polynomial for p replacing the input variable x with the hidden variable Xp.. This result could be used to compute satisfiability of CPL formulas in a non-deterministic way, taking the translation of a CPL formula to a mbC logic (with a conservative translation), by uniformly replacing all propositional variables pi with opi and setting 1 to all input variables. 

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