Random phase

Keller G 1986 Random-phase-approximation study of the response function describing optical second-harmonic generation from a metal selvedge Rhys. Rev. B 33 990-1009... 

Closs G L and Miller R J 1979 Laser flash photolysis with NMR detection. Microsecond time-resolved CIDNP separation of geminate and random-phase polarization J. Am. Chem. Soc. 101 1639—41... 

A second method is to use a perturbation theory expansion. This is formulated as a sum-over-states algorithm (SOS). This can be done for correlated wave functions and has only a modest CPU time requirement. The random-phase approximation is a time-dependent extension of this method. 

RPA, and CPHF. Time-dependent Hartree-Fock (TDFIF) is the Flartree-Fock approximation for the time-dependent Schrodinger equation. CPFIF stands for coupled perturbed Flartree-Fock. The random-phase approximation (RPA) is also an equivalent formulation. There have also been time-dependent MCSCF formulations using the time-dependent gauge invariant approach (TDGI) that is equivalent to multiconfiguration RPA. All of the time-dependent methods go to the static calculation results in the v = 0 limit. 

RPA (random-phase approximation) ah initio method used for computing nonlinear optical properties... 

Motivated by a puzzling shape of the coexistence line, Kierlik et al. [27] have investigated the model with Lennard-Jones attractive forces between fluid particles as well as matrix particles and have shown that the mean spherical approximation (MSA) for the ROZ equations provides a qualitatively similar behavior to the MFA for adsorption isotherms. It has been shown, however, that the optimized random phase (ORPA) approximation (the MSA represents a particular case of this theory), if supplemented by the contribution of the second and third virial coefficients, yields a peculiar coexistence curve. It exhibits much more similarity to trends observed in... 

The simplest polarization propagator corresponds to choosing an HF reference and including only the h2 operator, known as the Random Phase Approximation (RPA). For the static case oj = 0) the resulting equations are identical to those obtained from a Time-Dependent Hartree-Fock (TDHF) analysis or Coupled Hartree-Fock approach, discussed in Section 10.5. 

Figure l.The CPA-LSDA-ASA results for the energy of bcc (fat lines) and fee (thin lines) random and ordered alloys. The fee random phase is the referenee energy and defines zero in the graph. The random phases are given in full drawn lines and the ordered phases are given in dashed lines. 

Dieie is a relationship between these different behaviours of the above alloys in the random phase and the peculiarities of their phase diagrams mentioned in the Introduction. In order to show this, we need a little digression on the ETT theory. At T, neglecting the finiteness of quasi-... 

O Brien S, Moore JO, Boyd TE et al (2007) Randomized phase III trial of fludarabine plus cyclophosphamide with or without oblimersen sodium (Bcl-2 antisense) in patients with relapsed or refractory chronic lymphocytic leukemia. J Clin Oncol 25(9) 1114-1120... 

In astronomy, we are interested in the optical effects of the turbulence. A wave with complex amplitude U(x) = exp[ irefractive index, resulting in a random phase structure by the time it reaches the telescope pupil. If the turbulence is weak enough, the effect of the aberrations can be approximated by summing their phase along a path (the weak phase screen approximation), then the covariance of the complex amplitude at the telescope can be shown to be... 

The random phase error of a wavefront which has passed through turbulence may be expressed as a weighted sum of orthogonal polynomials. The usual set of polynomials for this expansion is the Zernike polynomials, which... 

Coupled Hartree-Fock values within the Random Phase approximation... 

Figure 4 Conduction band levels and excitation levels of infinite periodic hydrogen chains by using different approximations of the polarization propagator. The left part refers to the crystalline orbital energy differences, namely, the Hartree-Fock excitation energies the right part refers to the random phase approximation results obtained by using 41 k-points in half the first Brillouin zone.

In the random phase approximation, the transition amplitude from state 0) to l) for any one electron operator O may be written as... 

In this contribution, we have shown that the Bethe sum rule, like the Thomas-Reiche-Kuhn sum rule, is satisfied exactly in the random phase approximation for a complete basis. Thus, in calculations that are related to the generalized oscillator strengths of a system, the Bethe sum rule may be used as an indicator of completeness of the basis set, much as the Thomas-Reiche-Kuhn... 

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... 

Thiboutot D, Thieroff-Ekerdt R, Graupe K (2003) Efficacy and safety of azelaic acid (15%) gel as a new treatment for papulopustular rosacea results from 2 vehicle-controlled, randomized, phase III studies. J Am Acad Dermatol 48 836-845... 

Abciximab Emergent Stroke Treatment Trial Investigators. Emergency administration of abciximab for treatment of patients with acute ischemic stroke results of a randomized phase 2 trial. Stroke 2005 36 880-890. 

Saue and Jensen used linear response theory within the random phase approximation (RPA) at the Dirac level to obtain static and dynamic dipole polarizabilities for Cu2, Ag2 and Au2 [167]. The isotropic static dipole polarizability shows a similar anomaly compared with atomic gold, that is, Saue and Jensen obtained (nonrelativ-istic values in parentheses) 14.2 for Cu2 (15.1 A ), 17.3 A for Ag2 (20.5 A ), and 12.1 A for Au2 (20.2 A ). They also pointed out that relativistic and nonrelativistic dispersion curves do not resemble one another for Auz [167]. We briefly mention that Au2 is metastable at 5 eV with respect to 2 Au with a barrier to dissociation of 0.3 eV [168, 169]. 

Phase II investigates the compound s efficacy and safety in controlled clinical trials for a specific therapeutic indication. To eliminate as many competing factors as possible, Phase II trials are narrowly controlled. They are characterized as small—several hundred subjects with the indicated disease or symptoms—and are closely monitored. The control may be either a placebo study arm or an active control arm. The endpoint measured may be the clinical outcome of interest or a surrogate. Phase II trials may last for several months or even several years. Early pilot trials to evaluate safety and efficacy are called Phase Ila. Later trials, called Phase lib, are important tests of the compound s efficacy. These trials may constitute the pivotal trials used to establish the drug s safety and efficacy. At least one pivotal trial (most frequently a large, randomized Phase III study) is done. Only about one third of compounds entered into Phase II will begin Phase III studies [61],... 

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