Approximate Analysis

Rice J.R. (1968) A path-independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35, 379-386. 

Attenuation occurs because the tensile release, which is traveling at an elastic longitudinal wave speed, Q, overtakes the tensile front traveling at a plastic wave speed Cp < Q. Assuming a pulse as shown in Fig. 8.10 with a stress rate in the tensile front and tensile release of a and b, respectively, an approximate analysis shows that the peak will decay by an amount... 

The rea.son for this choice of low pressure ratio is illustrated by an approximate analysis [12], which extends the graphical method of calculating gas turbine pierformance described in Chapter 3. If the gas turbine higher plant is assumed to ojjerate on an air standard cycle (i.e. the working fluid is a perfect gas with a constant ratio of specific heats, y), then the compressor work, the turbine work, the net work output and the heat supplied may be written as... 

An extension of the approximate analysis of Section 7.6 suggests that the pressure ratio for both the combined and higher level plants, for the example given there, should be about 48 which is higher than that used in the ABB plant (about 30). 

Other questions which will have to be studied in more detail refer to the role of micelle interactions. Note that they are not included in the approximate analysis sketched above. Von Gottberg et al. [142] have argued that excluded volume interactions between micelles are responsible for the shght... 

Richt-aualyse /. guide analysis, approximate analysis, -blei, n. plumb line, plummet, richten. irt. direct, turn arrange, adjust, align, set, straighten orient dress raise, erect judge. — v.r. turn, rise, conform. 

Roh-alkohol, m. crude (or raw) alcohoL -analyse, /. rough or approximate analysis, -antimon, n. crude antimony, -arbeit, /, (Metal.) ore smelting, -asbest, m. crude asbestos. -aufbereitung, /. preliminary preparation, -benzol, n. crude benzene, benzol (or benzole), -blei, n. crude lead, -blende, /. (Mining) crude blende, -block,... 

Determine structural response based on approximate analysis... 

MIMOS II has three temperature sensors one on the electronics board and two on the SH. One temperature sensor in the SH is mounted near the internal reference absorber, and the measured temperature is associated with the reference absorber and the internal volume of the SH. The other sensor is mounted outside the SH at the contact ring assembly. It gives the approximate analysis temperature for the sample on the Martian surface. This temperature is used to route the Mossbauer data to the different temperature intervals (maximum of 13, with the temperature width software selectable) assigned in memory areas. Shown in Fig. 3.21 are the data of the three temperature sensors taken on Mars (rover Opportunity at Meridiani Planum) in January 2004 between 12 10 PM on Sol 10 (10 Martian days after landing) and 11 30 AM on Sol 11. The temperature of the electronics board inside the rover is much higher than the temperatures inside the SH and the contact plate sensor, which are nearly identical and at ambient Martian temperature. 

An approximate analysis of polymer adsorption as a set of sequential reactions leads to a simple equation for the adsorption isotherm expressed in terms of three parameters. Comparison of the model with recently published statistical theories reveals remarkable agreement in both the general shape of the isotherms and the predicted effects of molecular weight. The problems of applying such models to experimental data are discussed. 

J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, J. Appl. Mech., 1968, 35,379 386. 

The ability to predict Su is limited by the same factors used to predict the autoignition or flammability limits. However, an approximate analysis first considered by Mallard and Le Chatelier in 1883 [7] can be useful for quantitative estimates. 

The constant 3 is an order of magnitude estimate which depends on the approximate analysis for the model of Figure (4.10). In addition, the burning rate m " and the properties a and cp should be evaluated at some appropriate mean temperature. For example, in Equation (4.34), the more correct expression for is... 

Steward (1964) [4] and (1970) [5] presented a rigorous but implicit approximate analysis for both axisymmetric and two-dimensional strip fire plumes respectively, including combustion and variable density effects. 

Of all the approximate analysis methods, there is one that deserves special attention, because it is the only one that operates quite well at high coverages, where... 

J. E. Bailey and V. Hatzimanikatis, Effects of spatiotemporal variations on metabolic control Approximate analysis using (log)linear kinetic models. Biotechnol. Bioeng. (1997). 

The discovery of Sc occurred separately from the above work. In 1840, C. J. A. Scheerer reported a new mineral euxenite which had been found near Jolster in Norway. An approximate analysis was made and many elements were detected including lanthanoids. Lars Fredrik Nilson in 1879 reported the isolation of2g of SC2O3 if om working up 10 kg of euxenite plus someresidues from several other minerals. 

Very much more is known about the theory of concentration gradients at electrodes than has been mentioned in this brief account. Experimental methods for observing them have also been devised, based on the dependence of refractive index on concentration (the Schlieren method) by means of interferometry (O Brien, 1986). Nevertheless, the basic concept of an effective diffusion-layer thickness, treated here as varying in thickness with fi until the onset of natural convection and as constant with time after convection sets in (though decreasing in value with the degree of disturbance, Table 7.10), is a useful aid to the simple and approximate analysis of many transport-controlled electrodic situations. A few of the uses of the concept of 8 will now be outlined. 

Mancke.R.G., Dickie,R.A., Ferry,J.D. Dynamic mechanical properties of cross-linked rubbers. V. An approximate analysis of the modulus contributions of trapped and untrapped entanglements. J. Polymer Sci., Part A-2 6,1783-1789 (1968). 

APPROXIMATE ANALYSIS — We call an analysis as approximate if only the minimum information is employed which is needed to derive the stellar parameters. The minimal information consists on the equivalent widths of one He I and one He II line... 

An approximate analysis using equation (13) for description of the accumulation curve for defects in Cu (Fig. 7 in [45]) yields the value Uq = uqvq m 1.2, which clearly indicates an aggregation effect [35], This result was obtained on the basis of estimates of values of p and vp obtained in the same paper with the assumption of the absence of the correlation in genetic pairs. (Evidently taking account of correlation would have led to an even larger value of the Uq parameter.)... 

FERROZIRCONIUM. Alloys used in ihe manufacuire of steel, il) 12-15%. silicon 39-43%. iron 40-45% application steel of high silicon content. (2) 35-40%- zirconium alloy. Approximate analysis zirconium 35-50%. silicon 47-52%. iron 8-12% application steel of low silicon coniem. 

The periodic response of a linear viscoelastic cooling tower to a prescribed recurring sequence of pressure fluctuations and earth accelerations are analyzed. An approximate analysis, based on the bending theory of shells, is presented. The problem is reduced to a double sequence of boundary-value problems of linear ordinary differential equations. 19 refs, cited. 

D.M. Binding, An Approximate Analysis for Contraction and Converging Flows, J. Non-Newt. Fluid Mech., 27 173-189 (1988). 

Attempts were made to measure the kinetics of adsorption on the other oxides. In the case of MgO, the uptake was very small and very approximate kinetic measurements at pressures of 10-2 mm. and below gave activation energies of the order of 10-15 kcal./mole, whereas with ZnO the uptake was complicated by oxidation of Zn atoms exposed during the outgassing process an approximate analysis gave an activation energy of 15 6 kcal./mole for what appeared to be true chemisorption at low pressures ( 5 mm.) near saturation. 

Ficocelli Varracchio, E. (1990). Positron excitation of He a random phase approximation analysis of experimental results. J. Phys. B At. Mol. Opt. Phys. 23 L779-L785. 

Base hydrolysis of glycine ethyl ester - mechanistic analysis and use of experimental data to confirm the mechanism, an approximate analysis, 321-328 a full analysis, 336-339... 

Proximate (approximate) analysis is a scheme developed originally in 1865 by Henneberg and Stohmann of the Weende Experiment Station in Germany to analyse the main components. It is often referred to as the Weende System and has been refined over time. The system consists of determinations of water (moisture), ash, crude fat (ether extract), CP and crude fibre (CF). It attempts to separate carbohydrates into two broad classifications CF (indigestible carbohydrate) and N-free extract (NFE, or digestible carbohydrate). NFE is measured by difference rather than by direct analysis. 

In general it is desirable to solve the non-linear models by an approximate analysis to give analytical solutions that can be used for checking the numerical procedures and for evaluating the numerical results. A role of ADM is to take a place just in between the roles of analytical and numerical methods. 

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