Two steps

Having found the best nonintegrated sequence, most designers would then heat integrate. In other words, the total problem is not solved simultaneously but in two steps. Moving outward from the center of the onion (see Fig. 1.6), the separation layer is addressed first, followed by the heat exchanger network layer. 

Unless there are constraints severely restricting heat integration, sequencing of simple distillation columns can be carried out in two steps (1) identify the best few nonintegrated sequences and (2) study... 

In this figure the next definitions are used A - projection operator, B - pseudo-inverse operator for the image parameters a,( ), C - empirical posterior restoration of the FDD function w(a, ), E - optimal estimator. The projection operator A is non-observable due to the Kalman criteria [10] which is the main singularity for this problem. This leads to use the two step estimation procedure. First, the pseudo-inverse operator B has to be found among the regularization techniques in the class of linear filters. In the second step the optimal estimation d (n) for the pseudo-inverse image parameters d,(n) has to be done in the presence of transformed noise j(n). 

V.A. Mikhnev and P. Vainikainen, Profile inversion of stratified dielectric media using the two-step reconstruction, Proc. of the 27 European Microwave Conf, Jerusalem, 8-12 September 1997, pp. 584-588. 

There is a two-step process to predict the detectable detail - object diameter diagram. The optimal data collection parameter settings to maximise SNRAproj for the defect to the surrounding material - Optimal... 

This definition implies that the direction of the vector d was taken into account and that the coefficient c(i,j,fd)sndc(j,i,f,-d) may be different. So, the symmetrical matrix consists of a two step operation ... 

The linkage of the properties of the imaging system and of the properties of the entire radioscopic system, including the geometrical imaging constellations, with the user-demanded detail detectability is brought about in two steps. 

To describe the X-ray imaging system the projection of 3D object points onto the 2D image plane, and nonlinear distortions inherent in the image detector system have to, be modelled. A parametric camera model based on a simple pinhole model to describe the projection in combination with a polynomal model of the nonlinear distortions is used to describe the X-ray imaging system. The parameters of the model are estimated using a two step approach. First the distortion parameters for fixed source and detector positions are calculated without any knowledge of the projection parameters. In a second step, the projection parameters are calculated for each image taken with the same source and detector positions but with different sample positions. 

The figures 9 and 10 show the A-Scans of these two steps. Figure 9 presents the velocity measurement of the longitudinal wave parallel to the surface in the first step and figure 10 presents the A-Scan of the thickness measurement in the second step. 

Liouville s theorem is a restatement of mechanics. The proof of the theorem consists of two steps. 

For a bimolecular reaction, this situation is easily illustrated by simply writing the reaction as a sequence of two steps... 

Energy redistribution is the key primary process in chemical reaction systems, as well as in reaction systems quite generally (for instance, nuclear reactions). This is because many reactions can be separated into two steps ... 

Here each < ) (0 is a vibrational wavefiinction, a fiinction of the nuclear coordinates Q, in first approximation usually a product of hamionic oscillator wavefimctions for the various nomial coordinates. Each j (x,Q) is the electronic wavefimctioii describing how the electrons are distributed in the molecule. However, it has the nuclear coordinates within it as parameters because the electrons are always distributed around the nuclei and follow those nuclei whatever their position during a vibration. The integration of equation (Bl.1.1) can be carried out in two steps—first an integration over the electronic coordinates v, and then integration over the nuclear coordinates 0. We define an electronic transition moment integral which is a fimctioii of nuclear position ... 

Infrared pulses of 200 fs duration with 150 of bandwidth centred at 2000 were used in this study. They were generated in a two-step procedure [46]. First, a p-BaB204 (BBO) OPO was used to convert the 800 mn photons from the Ti sapphire amplifier system into signal and idler beams at 1379 and 1905 mn, respectively. These two pulses were sent tlirough a difference frequency crystal (AgGaS2) to yield pulses... 

Conventional associative ionization (AI) occurring at ambient temperature proceeds in two steps excitation of isolated atoms followed by molecular autoionization as the two atoms approach on excited molecular potentials. In sodium for example [44]... 

We prove our statement in two steps First, we consider the special case of a Hilbert space of three states, the two lowest of which are coupled strongly to each other but the third state is only weakly coupled to them. Then, we extend it to the case of a Hilbert space of N states where M states are strongly coupled to each other, and L = N — M) states, are only loosely coupled to these M original states (but can be stiongly coupled among themselves). 

Another way to overcome the step-size restriction fc < is to use multiple-time-stepping methods [4] or implicit methods [17, 18, 12, 3). In this paper, we examine the latter possibility. But for large molecular systems, fully implieit methods are very expensive. For that reason, we foeus on the general class of scmi-implicit methods depicted in Fig. 1 [12]. In this scheme. Step 3 of the nth time step ean be combined with Step 1 of the (n - - l)st time step. This then is a staggered two-step splitting method. We refer to [12] for further justification. 

The semiclassical approach to QCMD, as introduced in [10], derives the QCMD equations within two steps. First, a separation step makes a tensor ansatz for the full wavefunction separating the coordinates x and q ... 

The retrosynthetic analysis is performed in two steps in a first step, SYNGEN dissects the skeleton to find all fully convergent bondsets which utili2e starting material skeletons found in two successive levels of cuts. A bondset is a set of skeletal bonds that is cut during the retrosynthetic analysis or formed in any given synthesis. 

The technique for this calcu latioii in volves two steps. Th e first step computes the Hamiltonian or energy matrix. The elem en ts of this matrix are integrals involving the atomic orbitals and terms obtained from the Schrddiiiger equation. The m ost importan t con -... 

Since the first formulation of the MO-LCAO finite basis approach to molecular Ilartree-Pock calculations, computer applications of the method have conventionally been implemented as a two-step process. In the first of these steps a (large) number of integrals — mostly two-electron integrals — arc calculated and stored on external storage. Th e second step then con sists of the iterative solution of the Roothaan equations, where the integrals from the first step arc read once for every iteration. 

---