Internal variation

Heat and mass transfer limitations are rarely important in the laboratory but may emerge upon scaleup. Batch reactors with internal variations in temperature or composition are difficult to analyze and remain a challenge to the chemical reaction engineer. Tests for such problems are considered in Section 1.5. For now, assume an ideal batch reactor with the following characteristics ... 

The studies show that the observed crystal volume is in fact composed of the fractional contributions from the unit cell volumes of the HS and LS isomers of the compound and a linear volume change with temperature as expressed in Eq. (128). Similarly, the observed lattice constants are formed from a deformation contribution proportional to the HS fraction and a contribution from thermal expansion following Eq. (131). This is a convincing demonstration that it is the internal variation of the molecular units occurring in the course of the spin-state transition which determines, at least in principle, the observed crystal properties. 

The fit of the data to a single isochron indicates that individual anorthites from both B1 and B2 inclusions are internally isotopically homogeneous despite large internal variations in Mg and Na content and extensive mineralogical alteration. The slope of the single-crystal isochron is the same as that of the B1 isochron. 

Kanis JA, Johnell O, De Laet C et al. (2002) International variations in hip fracture probabilities implications for risk assessment. J Bone Miner Res 17(7) 1237-1244 Kemppainen H, Raiha I, Sourander L (1997) Clinical presentation of peptic ulcer in the elderly. Gerontology 43(5) 283-288... 

The similarity of samples can be evaluated by using geometrical constructs based on the standard deviation of the objects modeled by SIMCA. By enclosing classes in volume elements in descriptor space, the SIMCA method provides information about the existence of similarities among the members of the defined classes. Relations among samples, when visualized in this way, increase one s ability to formulate questions or hypotheses about the data being examined. The selection of variables on the basis of MPOW also provides clues as to how samples within a class are similar, and the derived class model describes how the objects are similar, with regard to the internal variation of these variables. 

T(r). The coefficient a is a measure for the internal variation of the scattering length density discussed in Sect. 3.2, problem 2 [36]. The coefficient /3 differs from zero only in case of dendritic structures which are not centrosymmetric [37]. A comprehensive discussion of Eq. (7) and the three different terms including their derivation may be found in [5]. Here it suffices to note that as deter-... 

If in addition to a thermodynamic driving force, a system has kinetic mechanisms available to produce a phase transformation (e.g., diffusion or atomic structural relaxation), the rate and characteristics of phase transformations can be modeled through combinations of their cause (thermodynamic driving forces) and their kinetic mechanisms. Analysis begins with identification of parameters (i.e., order parameters) that characterize the internal variations in state that accompany the transformation. For example, site fraction and magnetization can serve as order parameters for a ferromagnetic crystalline phase. 

In most obsidian provenance studies, the ability to employ compositional differences to discriminate between sources depends, to a certain extent, on the number of elements measured. Because instrumental neutron activation analysis (INAA) is capable of measuring 25-30 elements in obsidian with excellent precision, numerous combinations of trace and major elements are available for comparing differences between sources. The main requirements for success are that all sources have been located and analyzed, and that the internal variation measured within the sources be smaller than the compositional differences measured between the sources (23). 

Lauffer RB, Iron stores and the international variation in mortality from coronary artery disease, Med Hypoth 1991 35 96-102. 

Wynder and Shigematsu (15) were the first to suggest that nutritional factors in general and specifically differences in fat intake may be responsible for the international variation in colon cancer incidence. Subsequent descriptive epidemiologic studies have found a strong positive association between colon cancer mortality or incidence in different countries and per capita availability in national diets of total fat (4,16) and of animal fat, estimated from food balance sheets. Such international correlations may be supportive of a hypothesis, but they should be interpreted with caution because the dietary data were based not on actual intake information but on food disappearance data. 

The evidence that lamellae 15 nm thick can enter the hexagonal phase came from electron diffraction of specimens annealed as low as 236 °C at 0.54 GPa, 3 K lower than the maximum of the corresponding differential thermal analysis peak recorded for bulk polymer under the same conditions. At this annealing temperature lamellae were still entire, i.e. essentially of unaltered thickness although with some internal variation. No attempt was then made to anneal at lower temperatures and determine the orthorhombic/hexagonal transition temperature for this thickness. Such experiments offer, nevertheless, a direct approach by which the quantities of Eq. 9 may be determined. 

B.P. The results of the analyses for strontium and barium are shown in Figures 3 and 4. These two populations represent the same types of organisms in similar environments, the main difference between the two sites being age. The Wawawii results show a variation in both strontium and barium concentrations that is consistent with data from several archaeological sites (13 16,17). The Lind Coulee results, on the other hand, show extreme internal variations in both strontium and barium concentrations. At present neither elk nor bison occur in the immediate vicinity of these sites. The Wawawii elk are consistent with modem elk from nearby Northern Idaho (13,16). However, only the lower end of the Lind Coulee distribution is similarly consistent. 

Figure 10 The tungsten isotopic composition of Apollo 15 basalt 15555 shows no internal variation as a function of TaAV, consistent with its low exposure age (source Lee et al, 2002).

The methods for compensation that may be available in the case of injury (these often have marked international variations). 

Rosery H, Bergemann R, Maxion-Bergemann S (2005) International variation in resource utilisation and treatment costs for rheumatoid arthritis a systematic literature review. Pharmacoeconomics, 23 243-257. 

In few Hungarian laboratories the subjective judgement of chromosome aberration identification did not exceed the 5% intersc(xer variability in contrast to the international variations [12,17,18]. In order to equalize methods, use was made of the same chemicals. Selected metaphase scoring and comparison of slides are always undertaken. Therefore, common histoical control data in cases are used, if no matched controls are possible. This makes our cytogenetic monitoring easier than the procedures in bigger countries. 

No error can be calculated in which a single sample alone is measured. One element during the development of an assay is that the random error can be measured for many samples. This generally tends to be a compound of the internal variations of all aspects of sample analysis, and thus an overall generalized error can be calculated and "imposed" on all samples. 

The long-term fluctuations in temperature, precipitation, wind, and all other aspects of the Earth s climate. External processes, such as solar-irradiance variations, variations of the Earth s orbital parameters (eccentricity, precession, and inclination), lithosphere motions, and volcanic activity, are factors in climatic variation. Internal variations of the climate system also produce fluctuations of sufficient magnitude and variability to explain observed climate change through the feedbaek proeesses interrelating the components of the elimate system, climate sensitivity... 

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