SIMPLS algorithm

A simple algorithm can be developed (see App. E) to target the minimum total number of shells (as a real, i.e., noninteger number) for a stream set based on the temperature distribution of the composite curves. The algorithm starts by dividing the composite... 

This actually translates into a fairly simple algorithm, based closely on the standard velocity Verlet method. Written in a Fortran-like pseudo-code, it is as follows. At tire start of the run we calculate both rapidly-varying (1) and slowly-varying (F) forces, then, in the main loop ... 

With the availability of computerized data acquisition and storage it is possible to build database libraries of standard reference spectra. When a spectrum of an unknown compound is obtained, its identity can often be determined by searching through a library of reference spectra. This process is known as spectral searching. Comparisons are made by an algorithm that calculates the cumulative difference between the absorbances of the sample and reference spectra. For example, one simple algorithm uses the following equation... 

The standard k- model simulates the turbulenee in the reaetor. For flow within the porous eatalyst bed, however, we suppress the turbulenee. We enter the appropriate physieal properties of the system, and employ standard boundary eonditions at the impermeable walls and the reaetor outlet. To represent the turbulenee of the feed stream at the inlet, we treat it as pipe-flow turbulenee. These model equations ean then be solved for instanee, via the well-known Simple algorithm [3]. To faeilitate fast eonvergenee, it is useful to make a reasonable initial guess of the pressure drop aeross the eatalyst bed. 

If the timestep is short relative to the velocity relaxation time, the solvent does not play much part in the motion. Indeed, if y = 0, there are no solvent effects at all. A simple algorithm for advancing the position vector r and velocity v has been given by van Gunsteren (van Gunsteren, Berendsen and Rullmaim, 1981) ... 

In general, the molecular parameters involved in the potentials f/ (r) and U r) are different, and the dependence of E on AF has no such simple form. However, simple algorithms exist which allow numerical calculations of this dependence for... 

Below, a simple algorithm for determining the slacks between every pair of batches for product i and product k with cleaning times is presented. 

A simple algorithm [17] makes it possible to find the probability of any fragment of macromolecules of Gordonian polymers. Comparison of these probabilities with the data obtained by NMR spectroscopy provides the possibility to evaluate the adequacy of a chosen kinetic model of a synthesis process of a particular polymer specimen. The above-mentioned probabilities are also involved in the expressions for the glass transition temperature and some structure-additive properties of branched polymers [18,19]. 

The macromolecular density matrix built from such displaced local fragment density matrices does not necessarily fulfill the idempotency condition that is one condition involved in charge conservation. It is possible, however, to ensure idempotency for a macromolecular density matrix subject to small deformations of the nuclear arrangements by a relatively simple algorithm, based on the Lowdin transform-inverse Lowdin transform technique. 

D. D. Clayton, in W. D. Arnett and J. W. Truran (eds.), Nucleosynthesis Challenges and New Developments, University of Chicago Press 1985, p. 65, gives a description and simple algorithms for GCE and nucleo-cosmochronological calculations on the basis of his standard inflow models. Our simple inflow model shares some... 

However, the above mentioned problem can be solved with the use of a rather simple algorithm (291, 445) (Scheme 3.184). 

As there is no simple algorithm which can generate a solution just in one step several algorithms have to be combined [7-10]. Those algorithms which may improve the solution are called operators. The overall combinatorial solution algorithm consists of many operators. Any operator may work in any combination on the solution. Some examples are ... 

A simple algorithm based on an arbitrary adjustment of /3 (a modified Mar-quardt s method) is listed in Table 6.1. 

There are several different PLS algorithms, the most common of which are the NIPALS algorithm [1,64], the SIMPLS algorithm [65], and the Bidiagonalization algorithm [66]. These algorithms are somewhat more... 

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