Remission fraction

Use of the mathematics for plane parallel described in the last section requires that each layer in a sample has a single set of spectroscopic properties an absorption fraction, a remission fraction, and a transmission fraction. This mathematics may be straightforwardly applied to homogeneous layers such as plastic sheets. In order to apply the mathematics to samples of particulate solids meaningfully, we need to establish a method for determining the properties of a layer of the sample from the properties of the individual particles. 

The absorption is a property of a molecule and can be well represented as a continuum, but remission is a property of an interface and may not be well represented as a continuum. In the absence of absorption, the remission is independent of the thickness of a layer. The remission fraction from a single representative layer is dependent only on the fraction of the cross-sectional surface area occupied by each type of particle and the remission power of the material of which the particle is composed. In the presence of absorption, the remission fraction diminishes (causing a reduction in the remission coefficient). 

For cases where we know the thickness of the representative layer, it is possible to calculate the absorption and remission fractions for the representative layer from the remission and transmission fractions of any sample of known finite thickness, d. The absorption fraction, Ai, of a layer is given by [1 - exp(—ATd)]. (This is the value given by the plane parallel mathematics for a layer that has no remission. In the symbolism being used, the subscript refers to the number of layers. Thus A2 would refer to the properties of two layers, not to second layer.) By implication, the absorption of a single particle, a, is given by [1 - exp(-Ard)]. 

A remission coefficient may be defined as the remission fraction of the representative layer divided by the thickness of the representative layer. For cases where the thickness of the representative layer is not known, the plane parallel mathematics can be used to obtain absorption and remission coefficients as described above. This requires an assumption that a sample can be well represented as a continuum. In this linear region, for a given linear absorption coefficient the absorption fraction of a particle is proportional to its thickness, and the following conditions will be observed (and will be seen in the... 

For the case where the remission fraction is the same for all particle types, A R,T) is equal to li(Vjaj/Sjrj) which is the basis for statement 3 above. 

We will begin our series of examples by assuming that we are mixing particles that have a drastically different absorption fraction but the same remission fraction. The plot in Figure 3.6a shows how f(Roo) (denoted there as K-M) and a/r vary as a function of the particle fraction of graphite in a mixture of graphite (infinite absorption) and NaCl (zero absorption), with each assumed to have a remission fraction of 0.04. The value of 0.04 was chosen because it is the specular reflectance at normal incidence from the surface of a planar sample with a refractive index of 1.5. The value of f(Roo) was calculated from the Dahm Equation (3.84). Because the function A(/ , T) is constant for... 

Just above, we considered particles with vastly different absorptivities, and the same remission fraction. If we have two particles with the same refractive index but different absorptivity, the remission fraction will not be the same. The remission fraction from a highly absorbing particle (from which all the remission comes from the front surface) will be roughly half that of a lightly absorbing particle (where the remission comes from both the front and rear surfaces). It is the remission from the front surface that sets the upper limit on the K-M function. 

In this model, the relationship between the fraction R of incident light that exits the coating (the remission) and the constants K and S characterizing absorption and scattering, respectively, is given by the formula... 

The symptoms of OCD generally arise in an insidious manner, though acute onset of OCD has been reported. Considerable evidence indicates that OCD, once it arises, is a chronic lifetime disorder. Even with treatment, only a small fraction of OCD sufferers experience complete remission of their symptoms. Although patients with OCD are seldom, if ever, completely symptom free, the severity of the illness fluctuates over time. During periods of heightened stress, patients with OCD are especially prone to symptomatic exacerbation. Eor example, the postpartum period,... 

The absorption fraction of a particle is related to the volume of the particle. Thus, the larger the volume of a particle, the more of the incident light is absorbed. In contrast, reflectance is related to the particles surface area, being in turn dependent on material porosity. The absorption/remission function relates to the fraction of absorbed light, the fraction of remitted (or back scattered) light, and the fraction of light transmitted by a representative layer... 

Efficacy Only drugs known to be somewhat effective against the same tumor when used alone should be selected for use in combination. If available, drugs that produce complete remission in some fraction of patients are preferred to those that produce only partial responses. 

Until recently, lithium carbonate was the universally preferred treatment for bipolar disorder, especially in the manic phase. With the approval of valproate and olanzapine for this indication, a smaller fraction of bipolar patients now receive lithium. This trend is reinforced by the slow onset of action of lithium, which has often been supplemented with concurrent use of antipsychotic drugs or potent benzodiazepines in severely manic patients. The overall success rate for achieving remission from the manic phase of bipolar disorder has been reported to be 60-80%. However, among patients who require hospitalization, success rates are considerably lower. A similar situation applies to maintenance treatment, which is about 60% effective overall but less in severely ill patients. These considerations have led to increased use of combined treatment in severe cases. After mania is controlled, the antipsychotic drug may be stopped, then the benzodiazepine and lithium continued as maintenance therapy. 

In the majority of cases of idiopathic hypercalcemia of infancy the course is a self-limiting one. The disease on the one hand may clear up fully after a few weeks on the other hand it may drag on for months with intermittent remissions and exacerbations. In some cases the infant suffers from a comparatively trivial transient illness. In others, and fortunately a minority, he may be critically ill and suffer permanent sequelae. In a group of 45 cases reported in the literature (B5, C3, D3, F7, L6, Ml, M3, S2) there were six deaths, but of course the real death rate will be only a fraction of this because many milder cases will not have been reported or will not have been recognized. 

Electrophoretic analysis of these fractions revealed that radioactivity corresponded to the area of the electropherogram in which the primary and secondary intrinsic factor-related B12 binders were localized (see Section 1.9.3). Administration of material containing bound radioactive vitamin B12 to patients with pernicious anemia in remission demonstrated its high intrinsic factor activity on urinary excretion test (Table 4). This indicates that intrinsic factor in gastric juice and intrinsic factor-related vitamin Bi2 binders either have a molecular weight above 200,000 or,... 

Non-specular reflection is another term for diffuse reflection. Also the German term Remission may be used to denote the English term diffuse reflection. This is the fraction on the total incident light that is reflected and varies with the wavelength distribution of the incident light. 

Samples used to demonstrate this method were soil fulvic acid (SFA) and water fulvic acid (WFA), both well-characterized materials obtained from Dr. James H. Weber at the University of New Hampshire (19). Figure 1 shows that the chromatographic method resulted in four fractions separated for the SFA. The use of IP-RP-HPLC with the biological buffer MES resulted in sufficient separation to eliminate the need for gradients as have been used in previous studies (13-17). Simultaneous collection of UV (254 nm) and fluorescence (A citation = 332 nm and Remission = 42 nm) data showed similar chromatograms with peaks at the same retention times except in the case of the more non-polar (later-eluting) fractions which did not exhibit measurable fluorescence. This result is similar to that reported by Lombardi et al. (75) for marine DOM. Figure 2 shows a very similar separation for WFA. 

If light falls on to a white powder, a fraction of it is returned by regular reflection from the crystal surfaces, governed by the grain size distribution. The smaller the crystals are, the smaller is this regular reflection. The bulk of the incident radiation, however, penetrates into the layer of powder to a depth which depends on its wave length, returns to the surface after repeated scattering and is then emitted as a diffuse reflection (remission) in hemispherical form. 

Remission and transmission of each sublayer is determined by the equation proposed by Bodo. Bodo assumes that the fraction a of the incident radiation is reflected from the individual layer and is attenuated by absorption to the fraction (1 - a) In our calculation K represents the sum of the absorption of a sample K and the absorption of a layer/, and d is the particle size (layer thickness). On the bottom of the layer, the fraction (1 - a) of the radiation, still present, is again reflected, so that the fraction (1 - a)2 passes through, etc. We thus obtained a geometrical series both for the reflected and the transmitted radiation flux. Fig 2. 

There are situations where the assumptions of proportionality of the absorption coefficients and constancy of remission coefficient are reasonable. If the fraction of light absorbed by a single particle is small, the assumptions are good. In order to describe other situations, it is desirable to use an approach that does not suffer from the complexities of coefficients referred to above. In the following examples, we will illustrate the use of the approach of discontinuum theory as embodied in the representative layer theory. 

Here the upper case letters A, R, and T are used to denote the fractions of incident light absorbed, remitted, and transmitted by a sample of any thickness. The lower case letters are used to denote the corresponding fractions for a single layer or particle. For samples of infinite thickness, the K-M function,/(7 oo), and the Absorption-Remission function, A(R, T), are related by a simple factor of two. The K-M equation, as originally derived, contains a quantity related to scatter in its denominator, which with the assumption of isotropic scatter, is twice the magnitude of r. 

In order to be able to characterize the surfaces of the mixtures by image analysis with visible radiation, mixtures were made from raw materials of contrasting colors. A white product and a black product were chosen wheat and rape seed meal. Four series totaling forty samples were built from mixtures from 0 to 100% of wheat by steps of 10% fine wheat with fine rape seed meal, fine wheat with coarse rape seed meal, coarse wheat with fine rape seed meal, and coarse wheat with coarse rape seed meal. Figure 3.11 shows experimental data (as diamonds) for the mixtures of fine wheat with fine rape seed meal (i.e., passed through the same size sieve). The remission of visible radiation from the mixtures increased with the concentration of white wheat. The reflectance values were not placed on a straight line between the raw fractions. ... 

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