Harmonics, general

The harmonized general chapters on CE in the European, Japanese, and United States Pharmacopoeias are discussed. In addition, specific pharmacopoeial monographs prescribing CE methods in the current pharmacopoeias are described and the analytical instructions evaluated. 

The allowed wavefunctions for the particle on a sphere are called spherical harmonics, generally written... 

Pharmacopeial Forum, Harmonization, General Chapter <905> Uniformity of Dosage Units. Pharm Forum 2001, May-June, 27 3) 2615—2619. 

International Harmonization—General Monographs on Dosage Forms and Pharmacotechnological Test Methods Seville, Spain October 1998... 

Neglecting all of the higher-order (cubic and quartic) cross terms in eq. (32) yields the harmonic-general-plus-anharmonic valence force... 

Then the anharmonic terms can be modelled or calculated directly in internal coordinates. If the internal coordinates are independent there is a unique transformation from the normal-coordinate force field to the internal-coordinate one, and in particular a harmonic general force field may be calculated from the normal-coordinate one alternatively the harmonic general force field may be calculated uniquely from any global PES by the chain rule. If there are redundancies, then these procedures do not yield unique force constants. In such cases one should model the force field directly in internal coordinates or introduce subsidiary conditions on the force constants. 

A valence force field includes only valence coordinates and principal force constants a general force field also includes interactions. Thus the harmonic valence terms are the principal ones in the first sum in eq. (35), the harmonic general field consists of the whole first sum, and the anharmonic valence terms comorise the second sum. 

CE is now recognized as a mature technique alongside HPLC and other modern analytical techniques. A harmonized general monograph that presents both theoretical and practical considerations of the technique has been recently adopted by the Pharmacopoeial Discussion Group (PDG) for implementation into the USP, the... 

Main J, Mandelshtam V A, Wunner G and Taylor H S 1998 Harmonic inversion as a general method for periodic orbit quantization Nonlinearity1015... 

Now, consider the general case of a V2 multiply excited degenerate vibrational level where V2 > 2, which is dealt with by solving the Schrddinger equation for the isotropic 2D harmonic oscillator with the Hamiltonian assuming the fonn [95]... 

Is the temperature 1/0 related to the variance of the momentum distribution as in the classical equipartition theorem It happens that there is no simple generalization of the equipartition theorem of classical statistical mechanics. For the 2N dimensional phase space F = (xi. .. XN,pi,.. -Pn) the ensemble average for a harmonic system is... 

A molecule may show both electrical and mechanical anharmonicity, but the latter is generally much more important and it is usual to define a harmonic oscillator as one which is harmonic in the mechanical sense. It is possible, therefore, that a harmonic oscillator may show electrical anharmonicity. 

A normal mode of vibration is one in which all the nuclei undergo harmonic motion, have the same frequency of oscillation and move in phase but generally with different amplitudes. Examples of such normal modes are Vj to V3 of H2O, shown in Figure 4.15, and Vj to V41, of NH3 shown in Figure 4.17. The arrows attached to the nuclei are vectors representing the relative amplitudes and directions of motion. 

As for a diatomic molecule, the general harmonic oscillator selection mle for infrared and Raman vibrational transitions is... 

The reciprocals of the terms of the arithmetic-progression series are called harmonic progression. No general summation formulas are available for this series. 

This can be defined by the most severe external fault at which the schetne will remain inoperative. It should also remain inoperative in healthy conditions. That is it should be immune to the momentary voltage or current transients and normal harmonic contents in the circulating current. Series LC-filter circuits are generally provided with the relay coil to suppress the harmonics and to detect the fault current more precisely. 

Generally, a few harmonic quantities are always present in an a.c. system, as normally some non-linear loads always constitute a power system. These harmonics may not affect the operation of the inductive loads connected on the system as much as a capacitive load or a communication network that may be running in parallel or in the vicinity of such a power system. 

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