Arguments definition

The bilinear form in the argument of the exponential must be definite positive to have a well defined physics. This leads to constraints on the elements of the matrix A, as we shall see below. 

No definite experiments have been carried out with regard to the relative stability of the tautomers of 2-substituted indazolones 111. On the basis of basicity arguments, (he hydroxy tautomer 111a was considered to be preferred [96JCS(P2)2263],... 

For each data set examined, the onset of the gel effect (which is the initial value for the integration of the differential equations) was taken at the point where there is a departure from linearity in the conversion-time plot. While a good argument can be made ( ) for using another definition of the onset of the gel effect, the data available did not allow for a more detailed approach. 

It follows that for a special value of one parameter, the observed value of y is independent of the second parameter. This happens at Ii= a2/ai2 or I2 = -ai/ai2 any of these values determines y= a -aia2/ai2, the so called isoparametrical point. The argument can evidently be extended to more than two independently variable parameters. Experimental evidence is scarce. In the field of extrathermodynamic relationships, i.e., when j and 2 are kinds of a constants, eq. (84) was derived by Miller (237) and the isoparametrical point was called the isokinetic point (170). Most of the available examples originate from this area (9), but it is difficult to attribute to the isoparametrical point a definite value and even to obtain a significant proof that a is different from zero (9, 170). It can happen—probably still more frequently than with the isokinetic temperature—that it is merely a product of extrapolation without any immediate physical meaning. 

Retracing the argument used to justify point (2), it is clear that, in a multiply connected space, a given path is only coupled to those paths into which it can be continuously deformed. By definition, these are all the paths that belong to the same homotopy class. Paths belonging to different homotopy classes are thus decoupled from one another [41 5]. For a reactive system with a Cl that has the space of Fig. 1, this means that a path with a given winding number n is coupled to all paths with the same n, but is decoupled from paths with different n. As a result, the Kernel separates into [41-45]... 

By definition, the Laplacian of U represents the divergence of the attraction field, and, correspondingly, its value characterizes the density of masses at same point. Now the following question arises. What does the Laplacian tells us about the behavior of the potential To answer this question we first consider the simplest case, when U depends on one argument, x, Fig. 1.7a. Then, we can represent the derivatives as ... 

A dummy argument or a function name appears twice in a subprogram definition statement. 

Despite his laboratory s outward calm, Carothers was poised on the brink of an almost superhuman outpouring of scientific achievement. Over the next three years, between 1929 and 1931, he would transform the chaos of organic polymer chemistry with a clarity of focus and definition. He would settle the argument between Staudinger and the rest of Europe s chemists. As a leading polymer scientist later commented, Carothers work was a volcanic eruption, the reverberations of which are still being felt. ... 

We can extend this result a little. If we examine Example III-4, we see that we have altered P(A,B) to form P(A,B) by changing subschema (n+1). Since f and g are assumed to be distinct from the function letters a and b and from each other, if we enter (n+1) with different values for u and v the subscheme will not violate the definition of freeness. But if ws enter (n+1) with val(u) = val(v), then the subscheme behaves like the scheme in Example III-2, which we have seen is not strongly equivalent to any free scheme. Hence, similar arguments will show that now P(A,B) is strongly equivalent to some free scheme if and only if the Correspondence Problem for (A,B) has no solution. 

If we try to define a "free" recursion scheme in the same way we defined a free program scheme - every path is an execution sequence - we find that although the intuitive meaning is clear, it is very hard to formalize this concept. Exactly how should one define a "path" in a recursion scheme Or an "execution sequence" It is possible to do so by a moderately complex tree recursion. argument. Instead we will give a "syntactic" definition akin to the one we established as a theorem for program schemes. 

A definition of Chemometrics is a little trickier of come by. The term was originally coined by Kowalski, but nowadays many Chemometricians use the definition by Massart [4], On the other hand, one compilation presents nine different definitions for Chemometrics [5, 6] (including What Chemometricians do , a definition that apparently was suggested only HALF humorously ). But our goal here is not to get into the argument over the definition of the term, so for our current purposes, it is convenient to consider a perhaps somewhat simplified definition of Chemometrics as meaning multivariate methods of data analysis applied to data of chemical interest . 

Alternatively, the definition of the mean transition time (5.4) may be obtained on the basis of consideration of optimal estimates [54]. Let us define the transition time i) as the interval between moments of initial state of the system and abrupt change of the function, approximating the evolution of its probability Q(t.X(t) with minimal error. As an approximation consider the following function v /(f,xo, ) = flo(xo) + a (xo)[l(f) — l(f — i (xo))]. In the following we will drop an argument of ao, a, and the relaxation time d, assuming their dependence on coordinates of the considered interval c and d and on initial coordinate x0. Optimal values of parameters of such approximating function satisfy the condition of minimum of functional ... 

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