Reciprocal functions

Detectivity. Detector sensitivity (1,2) is expressed in terms of the minimum detectable signal power or noise equivalent power (NEP) given in units of watts or W. The reciprocal function when normalized for detector area, M, and noise bandwidth, is defined as detectivity, D, in units of /W. Thus,... 

The activities are expressed as reciprocal functions and are referred to No. 7 as unity, so that the smaller the number the greater the activity. The results with Nos. 3 to 7 indicate that the esterifying acid has considerable influence both on the nature of the action and its intensity. None of the amino-alcohols used matches tropine as a source of spasmolytic action of the neurotropic type. 

The removal of heat within an enclosed space must be considered as a multi-step heat transfer process. Heat passes from the occupants or equipment to the air within the space, and from there to the refrigerant or chilled water. It follows that the temperature differences at each step are a reciprocal function of the air mass flow. Where there is a high latent heat load within the space, the relative humidity will also vary with the air flow - the variation being higher with low air flow. 

Thus, a plot ofl/tA], versus time will be linear with a slope k. The graph, by virtue of the reciprocal function, tends to spread out and emphasize the least accurate points near the end. An alternative procedure is to use a rearranged form,... 

The evaluation function Q = / 1 (z) that transfers measured z-values into information on Q may be the reciprocal function of one of the following calibration functions (Danzer [1995a]) ... 

Most conventional scavenging is based on the concept of complementary reactivity. In the simplest cases, electrophilic and nucleophilic species are sequestered via a reciprocally functionalized support (Scheme 2.11 see also Tab. 2.1) likewise, acids and bases can be removed via salt formation with a solid-supported base or acid. 

Pi is the steady state or final value of the coefficient of friction, and N is the corresponding maximum number of cycles after which there is no further degradation in p. n is a power law exponent and is positive. Other functions such as an exponential function or a reciprocal function can be used in place of the power law as far as they eliminate the boundary condition of p(A ) = Pi for the number of cycles greater than A i. However, any realistic friction degradation function should always be consistent with independent experimental measurements. 

From a hyperbolic modification of any spectral parameter as a function of the added ligand concentration, the reciprocal function of the hyperbolic can be plotted. In fact, a reciprocal function of a hyperbolic is linear, while a reciprocal function of a linear plot is not linear. Therefore, in order to determine the value of A Fmax from the experiments of Figure 13.6b, it is important to plot the reciprocal function using all the data, mainly those in the curvature, since these data are part of the curvature and are the closest to the value of AFmax we are looking after. 

There are two types of electron correlation static and dynamic. The static correlation is related to the behavior of HF method at the dissociation limit of the molecule and deals with the long range behavior of this approach. On the other hand dynamic electron correlation is related to the electron repulsion term and is the reciprocal function of a distance between two electrons and thus represents short range phenomena. However, it should be noted that the electron correlation in the HF method is included in the indirect manner by the consideration of an electronic motion in an effective potential field due to the nuclei and the rest of the electrons and due to the inclusion of electron spin. Therefore, despite the known shortcomings, HF method has been extensively used in chemical calculations and has been quite successful for systems which are not extensive for electron correlation. 

For a benchmark production speed of 100,000 tablets per hour (Fig. 19), dwell time distribution follows an inverse power relationship, which is expected because dwell time is a reciprocal function of the press speed. In general, all production presses should be qualified with respect to dwell and contact times per benchmark output. Ideally, product development must be done on a laboratory press that can match (in terms of the dwell time) the target production output. 

Figure 3 The vapour pressure as a reciprocal function of temperature for water. The slopes of the tangents to the curve are the enthalpies of vaporisation.

The methodology has evolved along two routes, distinguishable in terms of the relationship between the template molecule and the polymerisable sub-units. In essence, the bonds between reciprocal functionalities on the template and the polymerisable units can be either covalent or non-covalent. The latter has become the method of choice in the majority of recently reported work and this review will therefore largely focus on the main concepts and mechanisms of this approach. 

An alternative approach to covalent imprinting was used by Shea and coworkers [27, 28]. Their tactic was similar, in that a template molecule was used to pre-position reciprocal functional groups within a polymeric cavity, but these studies used the reversibility of the reaction of ketones with 2-(p-vi-nylphenyl)-1,3-propanediol (VPD) to give ketals as a means of positioning and removing the template (Figure 6.6). 

This effect has particular relevance for the specificity of the polymer. Figure 6.25 illustrates that, for a non-template ligand, provided one or more reciprocal functional groups are present and steric restraints are minimal, cross-reactive binding can occur. 

Electronic energy transfer can take place by two mechanisms exchange interaction and dipole-dipole interaction. Exchange interaction requires a collision between a donor (D) and acceptor (A) and diminishes as an exponential function of the distance between D and A. Dipole-dipole interaction can operate over a greater distance and decreases as a reciprocal function of the distance. Because of the different functions of the distance between D and A, electronic energy transfer can be expected to be conducted mainly via dipole-dipole interaction in a diffusion restricted medium, solid phase. A qualitative expression for the rate constant (k) of dipole-dipole interaction is shown in Equation 1 ... 

In recent years, the extrapolation procedure developed separately by Yasuda and Shedlovsky has been reported [20,21,99] to provide pXa values from partially aqueous solutions that can sometimes closely approximate the values found in purely aqueous solutions. The Yasuda-Shedlovsky equation [Eq. (12)] can be used to correlate apparent pKg values in different solvent polarities (psl a) to approximate the aqueous pK value by extrapolation as a reciprocal function of the dielectric constant (e) of each of the cosolvent mixtures ... 

Separated metallic or semiconducting islands on top of insulator layers have been widely studied since 1960 s, and the subject received attention even nowadays [9]. The authors agree with the model where the lateral conductivity is determined by a tunneling mechanism between islands (or nanocrystals), while the concentration of carriers taking part in the conduction is thermally activated. The activation energy is reciprocal function of the NC diameter. So, the conductivity (and correspondingly, resistivity) is the exponential function of the NC size. However, in our case, a power function was obtained for the sheet resistance and NC size. The origin of this relation is not clear yet. 

At difference with p-MCPT, energy terms obtained by averaging or by projection with (0 are different, since the reciprocal function to 0) varies with the Fermi-vacuum choice. In this work we investigate the averaging procedure defined by... 

The reciprocal functions are cotangent of angle A, written cotA = 1 / tanA = bla... 

Here n and a are both positive constants. Doi and Edwards also derived a complicated damping function from the mbe model, which is close to the empirical reciprocal function with a = 0.2 (Larson 1988). 

Note that this restriction is less stringent than the classical assumption in Equation 9.68 requiring that both constitutive properties should be individually scalars. Notably, it allows nonlinear reciprocal functions that combine in a commutative way to produce a scalar. This is the hypothesis that makes the system a harmonic oscillator because its state variables behave in just proportions (which is the Greek etymology of harmony). The above definition of the natural pulsation (Oq corresponds exactly to the classical definition of the pulsation (o, made for modeling an oscillator, without distinguishing the two pulsations. 

Dispersion is the variation of the index of refraction with the wavelength of the incident light. Its variation as a function of wavelength is a reciprocal function also called Abbe s equation ... 

Note that although photon energy is directly proportional to frequency, it is a reciprocal function of wavelength. 

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