Large component magnitude

Notice that the largest frequency component contained in the output is at the fundamental (1 kHz), but there is also a large component at the second harmonic (2 kHz). There are other frequencies contained in the output, but they are too small to be seen on the graph. Using the cursors we find that the magnitude of the component at 1 kHz is 7.4665 V, and the magnitude of the component at 2 kHz is 1.3958 V. 

This LLC acid resin displayed more than an order of magnitude higher selectivity for the desired ester product over dibenzyl ether side-product compared to amorphous Amberlyst-15, Nafion NR-50, and also an isotropic analog of the LLC acid resin. Control experiments revealed that a large component of the enhanced selectivity is due to the regular nanostructure present in the LLC acid resin, which is believed to afford a much more uniform local acid microenvironment for reactions to occur. This same LLC acid resin was subsequently found to catalyze the synthesis of dioctyl phtha-late (DOP) from phthalic anhydride and 2-ethyl-1-hexanol in toluene with a slightly higher overall yield of DOP than amorphous Amberlyst-15 [117]. Experiments revealed that the LLC acid resin is a much better catalyst for the... 

After the fpFW transformation the magnitude of the small component as compared to the large component has decreased in leading order in 1/c,... 

Here 50, denotes the observed deviation of the atmospheric O, concentration from a standard. The atmospheric tracer APO is dominated primarily by oceanic gas exchanges in addition to a relatively small contribution from fossil fuel not accounted for by the terrestrial stoichiometric factor (i.e., the fossil fuel component scaled by the factor Observations of the seasonal variation of APO in conjuction with surface-water oxy gen measurements have been used to constrain the large-scale magnitude of the air-sea gas exchange coefficient (Keeling et al, 1998) and of marine productivity (Six and Maier-Reimer, 1996 Balkan.ski et al, 1999). Mean annual gradients of APO have also been shown to provide powerful constraints on biogeochemical air-sea fluxes computed by ocean-circulation models with an embedded ocean carbon cycle (Stephens et al, 1998). 

We see that the magnetic dipole operator connects large and small components, but the prefactor c ensures that the results are of the same magnitude as expectation values between two large components. We can demonstrate this point by substituting for the small component using the approximate expression from the nonrelativistic limit... 

We reinstate the velocity of light c in this and in Section VI.F in order to appreciate the order of magnitude of the various terras. When contributions from C) are neglected, the expression in Eq, (162) equated to zero gives the following equations, in which the large (i = 1,2) and small (i = 3,4) components are separated. 

In Eq. (168), the first, magnetic-field term admixes different components of the spinors both in the continuity equation and in the Hamilton-Jacobi equation. However, with the z axis chosen as the direction of H, the magnetic-field temi does not contain phases and does not mix component amplitudes. Therefore, there is no contribution from this term in the continuity equations and no amplitude mixing in the Hamilton-Jacobi equations. The second, electric-field term is nondiagonal between the large and small spinor components, which fact reduces its magnitude by a further small factor of 0 particle velocityjc). This term is therefore of the same small order 0(l/c ), as those terms in the second line in Eqs. (164) and (166) that refer to the upper components. 

Many researchers have performed calculations that include the two large-magnitude components of the spinnors. This provides a balance between high accuracy and making the calculation tractable. Such calculations are often done on atoms in order to obtain the wave function description used to create relativistic core potentials. 

Coefficient of Linear Thermal Expansion. The coefficients of linear thermal expansion of polymers are higher than those for most rigid materials at ambient temperatures because of the supercooled-liquid nature of the polymeric state, and this applies to the cellular state as well. Variation of this property with density and temperature has been reported for polystyrene foams (202) and for foams in general (22). When cellular polymers are used as components of large stmctures, the coefficient of thermal expansion must be considered carefully because of its magnitude compared with those of most nonpolymeric stmctural materials (203). 

Previous studies of the interaction of energetic particles with suri ces have made it clear that under nearly all conditions the majority of atoms or molecules removed from a surface are neutral, rather than charged. This means that the chained component can have large relative fluctuations (orders of magnitude) depending on the local chemical matrix. Calibration with standards for surfaces is difficult and for interfaces is nearly impossible. Therefore, for quantification ease, the majority neutral component of the departing flux must be sampled, and this requires some type of ionization above the sample, often referred to as post-ionization. SALI uses effi-... 

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