Line start definition

Fig. 17.4. Example of the library definition file for GLARE. Bold text indicates a dedicated keyword, text in Italic a user-defined alias, lines starting with a hash mark are comments, and normal text gives the keyword-associated parameters.

The labels used in the definition of the NMR-SIM spin system parameters depend to some extent upon personal preference. As with any programming language it is important to include comments comments not only makes the spin system file more readable, they also make it easier to keep track of any modifications to the file and help other users to understand the spin system definitions. Comment lines start with a semicolon ( ) and both the semicolon and the following text are ignored by the NMR-SIM processor. 

PASTA format contains a definition line and sequence characters and may be used as input to a variety of analysis programs (see Chapter 3). The definition line starts with a right angle bracket (>) and is usually followed by the sequence identifiers in a parsable form, as in this example ... 

Definition 6.2 (Input/output (I/O) power line) An input/output (I/O) power line starts from a modulated element and goes to a detector (De or Df element). 

If we set /c(x,y) = 0, we obtain a flank line starting in the valley-ridge-inflection point (VRI) at (0,0) where, per definition, the curvature of the contour line is zero. Its equation is... 

The first definitive studies of boron hydrides were carried out by Alfred Stock in Germany starting about 1912 (1). Through extensive and now classic synthetic studies, the field of boron hydride chemistry was founded with the isolation of a series of highly reactive, air-sensitive, and volatile compounds of general composition and This accomplishment required the development of basic vacuum line techniques for the... 

Even if this objective could not be attained completely, definition of the combustion mechanism would provide a basis for the development of specific propellants for novel uses, such as stop-start applications. The results of such basic research would also provide guide lines for eliminating those... 

FIGURE 13.6 The definition of the initial rate of reaction. The orange curves show how the concentration of N20, changes with time for five different initial concentrations. The initial rate of consumption of N20-, can be determined by drawing a tangent (black line) to each curve at the start of the reaction. 

Now that we have completed our expository interlude, we continue our derivation along the same lines we did previously. The next step, as it was for the constant-noise case, is to derive the absorbance noise for Poisson-distributed detector noise as we previously did for constant detector noise. As we did above in the derivation of transmittance noise, we start by repeating the definition and the previously derived expressions for absorbance [3],... 

Therefore, let us start by proposing a definition, one that can at least serve as a basis for our own discussions. Let us define linearity as The property of data comparing test results to actual concentrations, such that a straight line provides as good a fit (using the least-squares criterion) as any other mathematical function. ... 

Difficulty 3 can be ameliorated by using (properly) finite difference approximation as substitutes for derivatives. To overcome difficulty 4, two classes of methods exist to modify the pure Newton s method so that it is guaranteed to converge to a local minimum from an arbitrary starting point. The first of these, called trust region methods, minimize the quadratic approximation, Equation (6.10), within an elliptical region, whose size is adjusted so that the objective improves at each iteration see Section 6.3.2. The second class, line search methods, modifies the pure Newton s method in two ways (1) instead of taking a step size of one, a line search is used and (2) if the Hessian matrix H(x ) is not positive-definite, it is replaced by a positive-definite matrix that is close to H(x ). This is motivated by the easily verified fact that, if H(x ) is positive-definite, the Newton direction... 

Starting with the equalities given above and the definitions of Ky and Ny, we obtain a relation Ky = NyFiFj relating mutual helicity to the linking of ,- and B field lines and to their respective fluxes. 

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