Q-modulation

Lemme II 1.1. Soient f X — S up morphisme de schemas, quasi—compact et quasi-separe, P un Q -Module quasi-coherent. Alors, les conditions suivantes sont dquivalentes ... 

The purification process was scaled up 10-fold from 100 to 1000 cm2 of stacked 142 mm disks. The scale-up exhibited a good separation with a 7 log reduction in endotoxin levels. The yield was 98% with a final purity of 98.2%. This process was again scaled up with the modular configuration described previously (Fig. 3). Two 30-layer 4 m2 Q modules were used in conjunction with a 1 m2 C module. The chromatograms appeared very similar to the 1000 cm2 purification. The product purity was found to be 99.7% with < 0.002 endotoxin units per microgram of product and 0.003 pg DNA per microgram of product. The final product exceeded the clinical pharmaceutical specifications for this product. 

FIGURE 13 Small-scale separation of antisense oligonucleotides on Q modules. MA Q15 (Sarto-bind 15 cm2) flow rate 5 mL/min buffer A 20 m/Vt NaOH buffer B 20 mM NaOH plus 2.5 M NaCI sample 20 mer phosphorothioate crude, ISIS 2302 gradient 0- 100% B in 10 min. 

We denote by Lie (U) the sheaf of Q -modules whose sections over... 

In eq 29, 1/k is the characteristic decay length for the pure water. As reference 22 pointed out, Sii(R) displays periodic oscillations with some wavenumber q, modulated by a decaying envelope of some characteristic width . Then Sti(()) has a maximum centered at Q = q% with a width -1. In this situation when 2 >> / (k2 + ql)1 2 (22), the main contribution to the integral is given by Q — q, so that we obtain... 

HAR 97] Harada a., Tran-Cong Q., Modulated Phases Observed in Reacting Polymer Mixtures with Competing Interactions , Macromolecules, vol. 30, pp. 1643-1650, 1997. 

Raman intensity reflects the degree to which the phonon mode s atomic displacement Q modulates the dielectric response s at the laser frequency co. Consequently, studies of the resonant Raman intensity of various excitations can be particularly useful for exploring the coupling between these excitations and the electronic bands in complex oxides [47-49]. 

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

The transition is fully classical and it proceeds over the barrier which is lower than the static one, Vo = ntoColQl- Below but above the second cross-over temperature T 2 = hcoi/2k, the tunneling transition along Q is modulated by the classical low-frequency q vibration. The apparent activation energy is smaller than V. The rate constant levels off to its low-temperature limit k only at 7 < Tc2, when tunneling starts out from the ground state of the initial parabolic term. The effective barrier in this case is neither V nor Vo,... 

Borgis et al. 1989 Suarez and Silbey 1991a], where q is a particular coupling coordinate from the set qj which modulates the barrier (we assume for simplicity that there is only one such coordinate), and the exponential form of A is accounted for by the Gamov-factor nature of this term. 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

Different values of will result if the integral limits (i.e., band width) or modulation transfer function in the integral change. All surface characterization instruments have a band width and modulation transfer function. If rms roughness values for the same surface obtained using different instruments are to be compared, optimally the band widths and modulation transfer functions would be the same they should at least be known. In the case of isotropic surface structure, the spatial frequencies p and q are identical, and a single spatial frequency (/>) or spatial wavelength d= /p) is used to describe the lateral dimension of structure of the sample. 

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