K space

The magnetization profile in the y-direction is recovered by Fourier transfonnation with respect to G. B1.14.2.4 2D SPIN-ECHO FT IMAGING AND K-SPACE... 

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

Isc = r.m.s. value of fault current in Amperes = 45 000 A K = space factor for rectangular conductors, determined from the curves of Figure 28.7, corresponding to... 

These reciprocal lattice vectors, which have units of and are also parallel to the surface, define the LEED pattern in k-space. Each diffraction spot corresponds to the sum of integer multiples of at and at-... 

We calculate the quantity V(k) by inverse Fourier transform, by summing V up to the six shell of neighbors. This method favorably contrasts with the evaluation of V(k) directly in k-space and is justified by the fast convergence of V with the shell number... 

Aluminum fluoride (AIF3), calcium fluoride (CaF2) and their physical mixture (denoted as Mixed hereafter for abbreviation) were prepared. The amount of copper was adjusted to be 10 wt.%. The reaction was carried out in the fixed-bed reaction system under the reaction temperature of 923 K, space velocity of 15,000 h, 10% R22 in N2-balacne and atmospheric... 

The rate of convergence of the Steepest Descent method is first order. The basic difficulty with steepest descent is that the method is too sensitive to the scaling of S(k), so that convergence is very slow and oscillations in the k-space can easily occur. In general a well scaled problem is one in which similar changes in the variables lead to similar changes in the objective function (Kowalik and Osborne, 1968). For these reasons, steepest descent/ascent is not a viable method for the general purpose minimization of nonlinear functions, ft is of interest only for historical and theoretical reasons. 

However, in order to be able to apply the inverse Fourier transformation, we need to know the dependence of the signal not only for a particular value of k (one gradient pulse), but as a continuous function. In practice, it is the Fast Fourier Transform (FFT) that is performed rather than the full, analytical Fourier Transform, so that the sampling of k-space at discrete, equidistant steps (typically 32, 64, 128) is being performed. 

Fig. 3.4.3 (a) Two-dimensional k-space acquisition using SPI or SPRITE. The k-space data acquisition is indicated numerically. High magnetic field gradient amplitudes are applied at the extremities of k-space. (b) A generic two-dimensional centric scan SPRITE method. The... 

X02 = 0.1. They examined the effect of temperature (673 to 798 K), space-time (0.01 ts 4 s), and cycling strategy on rate enhancement. Resonance was observed for rs = 0.1 s with P > 1 for temperatures up to 770 K at a cycle period of about 1000 s. Above 770 K, rqss > r so that resonance disappeared. The quasi-steady-state rate, rqss, decreased rapidly with de-... 

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