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Complex zeros

The resonances are then obtained by searching for the complex zeros of the zeta functions (4.12) in the complex surface of the energy. Assuming that the action is approximately linear, S(E,J) = T(E - Ei), while the stability eigenvalues are approximately constant near the saddle energy E, the quantization condition (4.12) gives the resonances [10]... [Pg.556]

The obtained from the slope of vs. [cf. Eq. (2.95)] is near zero and it is inferred that this value indicates a value of zero for the translational entropy of the ion. A similar result was obtained for the solvated complex. Zero translational entropy for a solvated ion is a reasonable conclusion. Thus, for most of its time, the ion is still in a cell in the solution and only occasionally does it jump into a vacancy, or if it shuffles about, its movement is so constrained compared with that of a gas that it may approach zero. [Pg.130]

The stability of the compounds varies according to the complexed zero-valent metal and data are summarised in Scheme 16. [Pg.292]

Now that we ve factored it, we can compare the sections to our standard BiQuad forms given in Equation 3.11 and see that this filter gives us two resonances one at r = 0.99,/= 3/8 SRATE and one at r=0.99,/ = 7/8 SRATE. It also gives us one complex zero pair at r = 1.0,/= 5/7 SRATE. Finally, it implements a single zero at/= 0. Since the transfer function is just a product of these, we can rewrite it as a chain of simple filter segments ... [Pg.35]

Figure 4.27 The progression from (a) discrete molecular complexes ( zero-dimensional ) through (b) two-dimensional polymers using an axially blocked octahedral metal to (c) infinite three-dimensional structures containing guests. Figure 4.27 The progression from (a) discrete molecular complexes ( zero-dimensional ) through (b) two-dimensional polymers using an axially blocked octahedral metal to (c) infinite three-dimensional structures containing guests.
The zeros of an FIR hlter may Ue anywhere in the z plane because they do not impact on the stability of the hlter however, if the weighting coefficients are real and symmetric, or anti-symmetric, about their center value M/2, any complex zeros of the hlter are constrained to Ue as conjugate pairs coincident with the unit circle or as quartets of roots off the unit circle with the form (l/p)e , (l/p)e ) where p and 9 are, respectively, the radius and angle of the hrst zero. Zeros that Ue within the unit circle are termed minimum phase, whereas those which Ue outside the unit circle are called maximum phase. This distinction describes the contribution made by a particular zero... [Pg.811]

RhJiR) in terms of the complex zeros of l-p Cj(fe) = 0 (i.e., the poles kj. In general, an infinite number of poles contribute to this expansion, and some convergence problans related to the theoretical long tail of the direct correlation functions are encountered [185, 188, 200], However, the asymptotic behavior can be extracted by keeping only the pole =iy and the pair of lowest y -lying poles that are denoted conventionally by = x, +iy. Pure monotonic exponential decay or exponentially damped oscillatory decay can be identified from these poles. [Pg.116]


See other pages where Complex zeros is mentioned: [Pg.175]    [Pg.120]    [Pg.65]    [Pg.224]    [Pg.105]    [Pg.308]    [Pg.177]    [Pg.735]    [Pg.113]    [Pg.45]    [Pg.224]    [Pg.31]    [Pg.65]    [Pg.65]    [Pg.57]    [Pg.393]    [Pg.149]    [Pg.134]    [Pg.402]    [Pg.57]    [Pg.166]    [Pg.354]    [Pg.119]    [Pg.447]    [Pg.536]   
See also in sourсe #XX -- [ Pg.138 ]




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Intramolecular oxidation of zero-valent complexes

Molybdenum zero-valent complexes

Nickel zero-valent complexes

Palladium zero-valent complexes, addition

Platinum zero-valent complexes, addition

Zero-Valent Binuclear Nickel Complexes

Zero-valent transition metal complexes

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