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Sine, defined

We now define the effect of a translational synnnetry operation on a fiinction. Figure Al.4.3 shows how a PHg molecule is displaced a distance A X along the X axis by the translational symmetry operation that changes Xq to X = Xq -1- A X. Together with the molecule, we have drawn a sine wave symbolizing the... [Pg.162]

There is a maximum number of modes possible, defined by tlie range of accessible angles. For sine 0 < 1, tlie maximum allowed value of modes is tlie greatest integer smaller tlian lQJ2d) or... [Pg.2865]

We use the sine series since the end points are set to satisfy exactly the three-point expansion [7]. The Fourier series with the pre-specified boundary conditions is complete. Therefore, the above expansion provides a trajectory that can be made exact. In addition to the parameters a, b and c (which are determined by Xq, Xi and X2) we also need to calculate an infinite number of Fourier coefficients - d, . In principle, the way to proceed is to plug the expression for X t) (equation (17)) into the expression for the action S as defined in equation (13), to compute the integral, and optimize the Onsager-Machlup action with respect to all of the path parameters. [Pg.271]

The two terms correspond to different polarization of phonons. The cosine term corresponds to displacements along the rotation axis or the direction tp = 0. The sine contribution arises from the phonons polarized along the line tp = The interaction (6.29) does not change the symmetry of the (p potential, and, in this respect, it is symmetric coupling, as defined in sections 2.3 and 2.5. Nonetheless, the role of the cosine and sine couplings is different. The former ( breathing modes ) just modulate the barrier (6.22), while the latter ( shaking modes ) displace the potential. [Pg.121]

Turboexpander thermal effieieney (TTE isentropie) is defined as the ratio of aetual work produeed by the fluid, divided by the work produeed from the isentropie expansion proeess. Depending on gas eomposition, expansion ratio, and liquid formation, TTE varies between 80%-90%. These high effieieneies are the result of improvements to the thermodynamie and meehanieal design of turboexpanders sinee the early 1960s and their use in gas proeessing plant applieations. [Pg.429]

A positive vane angle produees prewhirl in the direetion of the impeller rotation, and a negative vane angle produees prewhirl in the opposite direetion. The disadvantage of positive prewhirl is that a positive inlet whirl veloeity reduees the energy transfer. Sinee Vg is positive aeeording to the Euler equation defined by... [Pg.229]

The saturated volume at 100 F is then 14.09+0.97 = 15.06. A eurve of sueh values is shown in Figure 28. Sinee humid volume is defined as the volume of any mixture, expressed as eubic feet of mixture per pound of dry air, and since both the specific and saturated values are on the basis of 1 lb of dry air, the humid volume for any humidity may be obtained directly by interpolation between the curves for specific and saturated volumes. [Pg.129]

The rate is defined as an intensive variable, and the definition is independent of any partieular reaetant or produet speeies. Beeause the reaetion rate ehanges with time, we ean use the time derivative to express the instantaneous rate of reaetion sinee it is influeneed by the eomposition and temperature (i.e., the energy of the material). Thus,... [Pg.110]

Here the induetion period is determined by the time needed for a eritieal nueleus to grow to a deteetable size. An expression for the induetion period may be found by integrating the respeetive kinetie expressions for erystal growth between the eharaeteristie dimensions of a eritieal nueleus, and a deteetable erystal, fy. And sinee fy 3> r, the following equations may be defined. [Pg.133]

Note that Tsai and Pagano s angle of rotation is oppositely defined to that in Figure 2-10, so the sine terms in Equation (2.98) are also of opposite sign. [Pg.86]

Sinee our system in the slit is anisotropie and inhomogeneous, it makes sense to eonsider the loeal pressure tensor, Eq. (42), whieh depends on the distanee z from the adsorbing wall. If one defines Px = Pxx Py = Pyy ... [Pg.597]

Sinee there are six unknowns and three equations, there are three independent variables. We ean associate these with any three elementary independent modes of point defect formation which conserve the numbers of atoms. These are like basis vectors for representing arbitrary point defect concentrations. Let us define them as follows ... [Pg.341]

The functions versed sine, coversed sine, and exterior secant are defined as vers 0=1- cos 0 covers 0=1- sin 0 exsec 0 = sec 0 - 1... [Pg.29]

The system transmits 5 bits/s with a phase-shift-keying system. Four sine waves are necessary to define the phase with a negligible chance of error. Assume a perfect pipe, drill collar ID same as the drill pipe and no wave reflections at the drill pipe ends. [Pg.953]

Brennan M-L and et al. (2002) A tale of two controversies. Defining both the role of peroxidases in nitrotyro-sine formation in vivo using eosinophil peroxidase and myeloperoxidase-deficient mice, and the natnre of the peroxidase-generated reactive nitrogen species. J Biol Chem 277 17415-17427. [Pg.517]

The phase spectrum 0(n) is defined as 0(n) = arctan(A(n)/B(n)). One can prove that for a symmetrical peak the ratio of the real and imaginary coefficients is constant, which means that all cosine and sine functions are in phase. It is important to note that the Fourier coefficients A(n) and B(n) can be regenerated from the power spectrum P(n) using the phase information. Phase information can be applied to distinguish frequencies corresponding to the signal and noise, because the phases of the noise frequencies randomly oscillate. [Pg.529]

Fig. 1.10 Soft rf pulses (left) in the shape of a sine (sin x/x) function, and their Fourier transforms (right), being equivalent to the excited slice in the presence of a constant magnetic field gradient. The well defined sine function (top) produces an excitation that is a slice... Fig. 1.10 Soft rf pulses (left) in the shape of a sine (sin x/x) function, and their Fourier transforms (right), being equivalent to the excited slice in the presence of a constant magnetic field gradient. The well defined sine function (top) produces an excitation that is a slice...
The angle between the most divergent rays that can pass through an objective is termed the angular aperture (AA) of the objective. It is customary to express the aperture of an objective in terms of the sine of this angle, and to define the numerical aperture (NA) ... [Pg.132]

This means that R is proportional to the sine of the dihedral angle between the two double bonds, with the positive sense defined in Scheme 2. Such a dependence confirms the diene rule because positive angles define positive helicity and imply positive R. [Pg.120]

Other integrals of importance arc the sine and cosine integrals Ci(a ), Si (a ), which are defined by the equations... [Pg.12]


See other pages where Sine, defined is mentioned: [Pg.213]    [Pg.59]    [Pg.1292]    [Pg.1550]    [Pg.540]    [Pg.314]    [Pg.292]    [Pg.400]    [Pg.510]    [Pg.301]    [Pg.328]    [Pg.653]    [Pg.5]    [Pg.664]    [Pg.219]    [Pg.513]    [Pg.521]    [Pg.524]    [Pg.529]    [Pg.562]    [Pg.326]    [Pg.107]    [Pg.17]    [Pg.32]    [Pg.24]    [Pg.164]    [Pg.410]    [Pg.412]    [Pg.277]    [Pg.465]   
See also in sourсe #XX -- [ Pg.1870 ]




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