Numerical search

The huge number of websites on the Internet (about 2,5 billion web pages December, 2002) containing chemical information is a great challenge when one is attempting to find specific information on a topic. Therefore numerous search engines have been developed and offered that provide fast access to the data. 

Autothermal reactor for methanol synthesis using a numerical search technique... 

When f7 is differentiated, a fourth-order polynomial in D results no simple analytical solution is possible to obtain the optimum value of D. A numerical search is therefore better for obtaining Dopt and should be based on/7 (rather than examining dfJdD = 0). However, such a search will need to be performed for different values of V and the design pressure, parameters which are embedded in Equation (/). Recall that Equations (0 and (m) are based on a design pressure of 250 psi. Happel and Jordan (1975) presented the following solution for (L/D)opt ... 

Carry out the initial and one additional stage of the numerical search for the minimum of... 

We can reach the minimum of fix) in two stages using first s° and then s1. Can we use the search directions in reverse order From x° = [1 l]T we can carry out a numerical search in the direction s° = [—4 —2]T to reach the point x1. Quadratic interpolation can obtain the exact optimal step length because /is quadratic, yielding a = 0.27778. Then... 

The Ferry trapping factor is therefore (1 — 2v0/vc)2. Unfortunately, the simple extrapolation procedure of Kraus (286) can no longer be applied, but numerical search techniques should still suffice to determine Me. 

We randomly perturb the ground state and evolve the perturbation with a given wave vector k in time numerically, searching for any exponential increase of its amplitude which would be a signature of the instability. An example of such a perturbation is presented in Fig. 21. For all velocity field models, the parameter space... 

The emperical parameters S Q, S2Q, K-Q, K, A E-, and AE were determined by a numerical search routine. Figure 3 compares the theoretical curves with the experimental data and represents a satisfactory curve fit. 

A numerical search routine was applied to determine the value of K and A E. Figure 4 compares the theoretical curve with the experimental data and represents a satisfactory curve fit. The total sulfur content and SRC sulfur content for hydrotreated product were plotted (Figure 5), and a linear relationship was shown to exist between them. 

Motivated by the observed decay rate discrepancy between QED theory and experiment for At, numerous searches have been performed for forbidden, small or exotic decay modes. An exotic decay branch, besides o-Ps —> 37, with roughly 10-3 branching ratio could be causing the higher decay rate and is given by A 0bs = + A exotic- Many candidate decay branches have been proposed in... 

This statistical method is used for the estimation of parameters of -> electrode reaction by fitting a theoretical relationship to experimentally obtained data. This is achieved by minimizing the sum of squared deviations of the observed values for the dependent variable from those predicted by the model. Nonlinear least-square estimations can not be performed algebraically and numerical search procedures are used [i]. The Mar-quardt algorithm is commonly applied in the calculations performed by commercially available computer programs [ii]. 

Numerical search of minimum < ) in space of parameters gives the following results b/a =... 

The use of ORACLE to store the atomic data comprising a molecule does not necessarily mean that ORACLE has to be used to search it. In some cases, such as 3D searching the ORACLE standard text and numeric search engines offer nothing of use and proprietary applications have to be used. It is important to realise that the term database refers to a convenient subset of values or ORACLE tables not to specific files. 

Under any conditions Eq. (6) can be solved by simultaneously integrating the four equations (8) and (10) and choosing w at each step to be the value that maximizes the right-hand side of (6). If little is known about the structure of the policy a direct numerical search for this value of w is always safe, and is no great problem for the digital computer. 

The Fink method of numerical searching of the data file relies more on d spacings than on intensities. It was originally designed for use with electron diffraction patterns, where observed line intensities are not always directly related to structure and therefore not always a reliable guide to identification. 

Locate the proper f/, group in the numerical search manual. 

Extracted from the numerical search manual (Inorganic Compounds, Hanawalt Method). The three strongest lines appear in bold-face type. Intensities (rounded off) are shown by the... 

The addition of lithium diallylcuprate to a, E-unsaturated carbonyl compounds is highly substrate dependent. Good yields can only be obtained with doubly activated esters as shown in (14) and (15). The importance of the conjugate addition has prompted numerous searches for procedures and methods to effect asymmetric induction. One recent example is the use of (S)-2-(methoxymethyl)pyrrol-idine as a chiral copper ligand (Scheme 48). ... 

There are 38 possible individual numerical search fields, e.g. J -factor, chemical class, journal code number, space-group number, etc. Numerical tests are specified using the general construet ... 

Analytical studies for choosing the parameters of due date rules include [88] and [108]. Seidmann and Smith [88] consider the CON due date policy in a multi-machine environment under the objective of minimizing the weighted sum of earliness, tardiness and lead time penalty (the same objective function is also considered in [87]). They assume that the shop is using a priority discipline for sequencing, such as FCFS or EDD, and the probability distribution of the flow time is known and is common to all jobs. They show that the optimal lead time is a unique minimum point of strictly convex functions can be found by simple numerical search. 

These risk measures can be used for both VaR type and MtT type risks. Values of R(a), PLe(r), and PLa r) can be read from the risk table for VaR type risks or calculated using the risk fimction for MtT type risks. When the risk table does not have the desired value, an interpolation method can be used to estimate the real value. Numerical search methods can be used to find out the corresponding a value for a certain risk value from the MtT type risk functions. In order to get ER, extra calculations need to be done based on the VaR type risk table or the MtT type risk function. 

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