Harmonization product defined

To the pharmaceutical world, the meaning of analytical methods validation is the process to confirm that a method does what it purports to do, that is, to document through laboratory studies that the measurement procedure can reliably assess the identity, strength, and/or quality of a bulk drug substance, excipient, or finished pharmaceutical product. To provide consistent, worldwide regulatory expectations, previously unavailable, the International Conference on Harmonization has defined the methods validation... 

Perhaps surprisingly, there has been a variation in the definition of the terms infant , child and adolescent between texts or stndies. To overcome this, the International Commission on Harmonization has defined these terms for regulatory purposes (European Agency for the Evaluation of Medicinal Products, 2000). These definitions and age bands (Table 1.1) broadly represent the ages at which the major changes... 

The center of the wavepacket thus evolves along the trajectory defined by classical mechanics. This is in fact a general result for wavepackets in a harmonic potential, and follows from the Ehrenfest theorem [147] [see Eqs. (154,155) in Appendix C], The equations of motion are straightforward to integrate, with the exception of the width matrix, Eq. (44). This equation is numerically unstable, and has been found to cause problems in practical applications using Morse potentials [148], As a result, Heller introduced the P-Z method as an alternative propagation method [24], In this, the matrix A, is rewritten as a product of matrices... 

In Section 4.8, Equations 4.78,4.79 and Table 4.1 develop the connections between the harmonic oscillator rigid rotor partition function and isotope chemistry as expressed by the reduced partition function ratio, RPFR = (s/s ) f. RPFR is defined in Equation 4.79 as the product over oscillators of ratios of the function [u exp(—u/2)/ (1 - exp(u))]... 

TABLE E.3 Products of Two Real Spherical Harmonic Functions ylmp, with Normalization Defined in Appendix D ... 

Three consensus guidelines define the core of the ICH s involvement in harmonization of pharmaceutical quality systems—Q8 Pharmaceutical Development, Q9 Quality Risk Management, and Q10 Pharmaceutical Quality Systems (in addition, each of the guidance documents cites critical areas of overlap with Q6A Specifications Test Procedures and Acceptance Criteria for New Drug Substances and New Drug Products Chemical Substances). 

The U.S. Food and Drug Administration (FDA) defines novel (new) pharmaceutical excipients as those substances used in the United States for the first time in a human drug product or by a new route of administration (1). The International Conference on Harmonization of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) includes sections in its Common Technical Document (CTD) that details the information required for the approval of novel (new) excipients. Information on the control of excipients is included in Section P.4 of the CTD, and any additional information that may be required should be included in Appendix A.3 of the CTD. 

In the Born-Oppenheimer approximation, the molecular wave function is the product of electronic and nuclear wave functions see (4.90). We now examine the behavior of if with respect to inversion. We must, however, exercise some care. In finding the nuclear wave functions fa we have used a set of axes fixed in space (except for translation with the molecule). However, in dealing with if el (Sections 1.19 and 1.20) we defined the electronic coordinates with respect to a set of axes fixed in the molecule, with the z axis being the internuclear axis. To find the effect on if of inversion of all nuclear and electronic coordinates, we must use the set of space-fixed axes for both fa and if el. We shall call the space-fixed axes X, Y, and Z, and the molecule-fixed axes x, y, and z. The nuclear wave function of a diatomic molecule has the (approximate) form (4.28) for 2 electronic states, where q=R-Re, and where the angles are defined with respect to space-fixed axes. When we replace each nuclear coordinate in fa by its negative, the internuclear distance R is unaffected, so that the vibrational wave function has even parity. The parity of the spherical harmonic Yj1 is even or odd according to whether J is even or odd (Section 1.17). Thus the parity eigenvalue of fa is (- Yf. 

The vibrational overlap integrals play a key role in electron transfer. A region of vibrational overlap defines values of the normal coordinate where a finite probability exists for finding coordinates appropriate for both reactants and products. The greater the overlap, the greater the transition rate. The vibrational overlap integrals can be evaluated explicitly for harmonic oscillator wavefunctions. An example is shown in equation (26) for the overlap between an initial level with vibrational quantum number v = 0 to a level v = v where the frequency (and force constant) are taken to be the same before and after electron transfer. 

Equations (4.329) for a solid assembly and (4.332) for a magnetic suspension are solved by expanding W with respect to the appropriate sets of functions. Convenient as such are the spherical harmonics defined by Eq. (4.318). In this context, the internal spherical harmonics used for solving Eq. (4.329) are written Xf (e, n). In the case of a magnetic fluid on this basis, a set of external harmonics is added, which are built on the angles of e with h as the polar axis. Application of a field couples [see the kinetic equation (4.332)] the internal and external degrees of freedom of the particle so that the dynamic variables become inseparable. With regard to this fact, the solution of equation (4.332) is constructed in the functional space that is a direct product of the internal and external harmonics ... 

The generation of attosecond laser pulses in high-harmonic generation is a natural consequence of the physics discussed in Sects. 3.2 and 3.3. As discussed in Sect. 3.3, the ionization that launches the electron into the continuum is a highly non-linear phenomenon that will favor field maxima in the femtosecond driver laser. Following this ionization step, and in the spirit of the results presented in Sect. 3.2, the electrons will be accelerated by the oscillatory field of the laser and move along relatively well-defined trajectories that carry the electron back to the parent ion at well-defined times. Consequently, we expect the electron-parent ion recombination and the XUV production to occur only during a small portion of the optical cycle. 

The absorption spectrum consists of sequences of transitions from v" = 0, 1, 2 to various v levels in the upper state, and the relative intensities of the vibration-rotation bands are given primarily by the product of the FCF value and a Boltzmann term, which can be taken to be exp — hcv v /kT). Common choices for the i/r s are harmonic oscillator and Morse wavefunctions, whose mathematical form can be found in Refs. 7 and 9 and in other books on quantum mechanics. The harmonic oscillator wavefunctions are defined in terms of the Hermite functions, while the Morse counterparts are usually written in terms of hypergeometric or Laguerre functions. All three types of functions are polynomial series defined with a single statement in Mathematica, and they can be easily manipulated even though they become quite complicated for higher v values. 

The set of quantum numbers of a level also serves to define the corresponding wave-function, which in the usual approximation is written as a product of one-dimensional harmonic oscillator functions,... 

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