N operator

This process is continued until there is only one component. For this reason, the number N is taken as a power of 2. The vector [yj] is filled with zeroes, if need be, to make N = 2 for some p. For the computer program, see Ref. 26. The standard Fourier transform takes N operations to calculation, whereas the fast Fourier transform takes only N log2 N. For large N, the difference is significant at N = 100 it is a factor of 15, but for N = 1000 it is a factor of 100. 

N = operation under rated conditions / = at rest and de-energized and 6, = temperature rise reached during one duty cycle ( -= 0)... 

N = operation under rated conditions V = operation on no-load and 0, = temperature rise attained during one duty cycle = corresponding to the no-load heating... 

D = period of starling N = operation under rated conditions F = electric braking and... 

Ly = Vibration Limit mils (thousandth of an ineh), or mm (mils x 25.4) N = Operating speed (RPM)... 

N = operating speed, alternatively maximum continuous speed, rpm... 

This problem can be solved by the standard elimination method rec uiring 0 /h) = 0 N) operations, the amount of which is proportional to the total number N of nodal points of the grid = k,- = ih, 0 [Pg.548]

As can readily be observed, 0 N) operations are needed in giving F and their amount is proportional to the total number of the grid nodes. This is certainly so with any difference scheme, whose pattern is independent of the grid. From equation (2) it is easily seen that the stable scheme (2) will be economical once the users perform 0 N) operations while solving equation (2). 

Let economical operators Ba, a = 1,2,..., p, be. such that 0(N) operations are necessary in connection with solving the equation... 

In equation (8.32) the operator P is any one of the N operators, including the identity operator, that permute a given order of particles to another order. The summation is taken over all N permutation operators. The quantity dp is always - -1 for the symmetric wave function Ps, but for the antisymmetric wave function Wa, dpis-l-l(—l)if the permutation operator P involves the... 

One sees immediately that the singlet functions have space parts that are symmetrical and spin parts that are antisymmetrical with respect to interchange of the electron coordinates, while the converse is true for the triplet functions. Since the Hamilton operator H[. .. n) operates only on space parts which for and are identical, it is apparent that these three functions... 

It is simple to contract an RDM by applying the expression of the N operator. Thus... 

Scott and Kucera (49) have prepared a 500,000 plate colun n operated in GPC. High-efficiency GPC columns are easier to operate since all compounds are, in principle, eluted before the inert p>eak, i.e., by the definition used in this work, k is negative. 

In the usual case in which and G are sparse matrices produced by constraints involving only a few nearby beads, the projection may be completed in N) operations by first solving the system of equations... 

In models of beads with full hydrodynamic interactions, for which the mobility tensor is represented by a dense matrix, the Cholesky decomposition of H requires 3N) /6 operations. Eor large N, this appears to be the most expensive operation in the entire algorithm. The only other unavoidable 0 N ) operation is the LU decomposition of the K x K matrix W that is required to solve for the K constraint forces, which requires /3 operations, or roughly... 

Therefore the weight that remains unextracted at the end of n operations will be... 

In discussing planes of symmetry and inversion centers, attention was directed to the fact that only one operation, reflection, is generated by a symmetry plane, and only one operation, inversion, by an inversion center. A proper axis of order / , however, generates n operations, namely Cn, C , Cl.C +I, C2( = ). 

We have already seen that, if a molecule possesses a proper axis, C , and also a twofold axis perpendicular to it, there must then necessarily be n such twofold axes. The n operations, E, C , CJ,. . . , . C" l, plus the n twofold rotations constitute a complete set of symmetry operations, as may be verified... 

Kunii, D. and Levenspiel, 0. (1990). Entrainment of Solids from Fluidized Beds. I. Holdup of Solids in the Freeboard, n. Operation of Fast Fluidized Beds. Powder Tech., 61,... 

Now, return to the time-evolution operator with the aid of the N operator ... 

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