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Abstract  

A new method of calculation of parameters of enthalpy relaxation models is proposed. Regression analysis treatment compares the experimental and calculated values of relaxation enthalpy. The experimental values of relaxation enthalpy are obtained by numerical integration of the difference between the two DSC curves. Contrary to the overall shape of the DSC curve the integral values are not affected by particular heat flow conditions during the DSC experiment. The Narayanaswamy's numerical model based on the Kohlrausch—William—Watts relaxation function was used to calculate the theoretical values of relaxation enthalpy. The application of the proposed method on the DSC experimental data of enthalpy relaxation of As2Se3 is shown.

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Abstract  

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments.

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Abstract  

The mathematical evaluation of the activation energy, E, of non-isothermal degradation reactions is usually made using the Ozawa/Flynn–Wall isoconversion principle and involves the numerical resolution of a set of integrals without closed form solution, which are solved by polynomial approximation or by numeric integration. In the present work, the isoconversion principle, originally described and maintained until now as an algebraic problem, was written as a set of ordinary differential equations (ODEs). The individual ODEs obtained are integrated by numeric methods and are used to estimate the activation energy of simulated examples. A least square error (LSE) objective function using the introduced ODEs was written to deal with multiple heating rate CaCO3 thermal decomposition TG experiments.

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Journal of Radioanalytical and Nuclear Chemistry
Authors: E. L. Dorval, M. A. Arribére, S. Ribeiro Guevara, I. M. Cohen, A. J. Kestelman, R. A. Ohaco, M. S. Segovia, A. N. Yunes, and M. Arrondo

Summary  

We have measured the cross sections, averaged over a 235U fission neutron spectrum, for the two high threshold reactions: 75As(n,p)75mGe and 75As(n,2n)74As. The measured averaged cross sections are 0.292±0.022 mb, referred to the 3.95±0.20 mb standard for the 27Al(n,p)27Mg averaged cross section, and 0.371±0.032 mb referred to the 111±3 mb standard for the 58Ni(n,p)58m+gCo averaged cross section, respectively. The measured averaged cross sections were also evaluated semi-empirically by numerically integrating experimental differential cross section data extracted for both reactions from the current literature. The calculations were performed for four different representations of the thermal-neutron-induced 235U fission neutron spectrum. The calculated cross sections, though depending on analytical representation of the flux, agree with the measured values within the estimated uncertainties.

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Journal of Radioanalytical and Nuclear Chemistry
Authors: Hai-Qing Zhang, Bang-Fa Ni, Wei-Zhi Tian, Gui-Ying Zhang, Dong-Hui Huang, Cun-Xiong Liu, Cai-Jin Xiao, Peng Nie, and Hong-Chao Sun

Abstract  

An expression of γ-ray efficiency for large samples is proposed based on numerical integration of efficiencies over compositional point sources. The widely used expression on radial variation of HPGe efficiency for point source originally proposed by Noguchi et al. (Int J Appl Radiat Isot 32:17–22, 1980 [<cite>1</cite>]) was amended and a new expression was proposed. A comparison between the two expressions indicates that the newly proposed expression brings about an obvious improvement, and Self-absorption correction for a voluminous source is also given out by using the EID principle. The functional relationship between HPGe efficiency for γ-rays from a point source and the spatial position of the source was established. The results of this study can be applied in order to determine γ attenuation effects of unknown bulky samples with various shapes and materials.

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Being interested in (rotation-)invariant pseudodifferential equations of satellite problems corresponding to spherical orbits, we are reasonably led to generating kernels that depend only on the spherical distance, i.\,e., in the language of modern constructive approximation form spherical radial basis functions. In this paper approximate identities generated by such (rotation-invariant) kernels which are additionally locally supported are investigated in detail from theoretical as well as numerical point of view. So-called spherical difference wavelets are introduced. The wavelet transforms are evaluated by the use of a numerical integration rule, that is based on Weyl's law of equidistribution. This approximate formula is constructed such that it can cope with millions of (satellite) data. The approximation error is estimated on the orbital sphere. Finally, we apply the developed theory to the problems of satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG).

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Modulated differential scanning calorimetry in the glass transition region

VI. Model calculations based on poly(ethylene terephthalate)

Journal of Thermal Analysis and Calorimetry
Authors: B. Wunderlich and I. Okazaki

Abstract  

Temperature-modulated calorimetry (TMC) allows the experimental evaluation of the kinetic parameters of the glass transition from quasi-isothermal experiments. In this paper, model calculations based on experimental data are presented for the total and reversing apparent heat capacities on heating and cooling through the glass transition region as a function of heating rate and modulation frequency for the modulated differential scanning calorimeter (MDSC). Amorphous poly(ethylene terephthalate) (PET) is used as the example polymer and a simple first-order kinetics is fitted to the data. The total heat flow carries the hysteresis information (enthalpy relaxation, thermal history) and indications of changes in modulation frequency due to the glass transition. The reversing heat flow permits the assessment of the first and higher harmonics of the apparent heat capacities. The computations are carried out by numerical integrations with up to 5000 steps. Comparisons of the calculations with experiments are possible. As one moves further from equilibrium, i.e. the liquid state, cooperative kinetics must be used to match model and experiment.

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The temperature-dependence of the electrical resistance of Al-Zn 78 wt.% was measured during linear cooling of the samples in the range of eutectoidal decomposition. The resulting resistancevs. temperature curves were analysed by:deriving the temperature-dependence of the volume fractionx(T) of theη precipitate;fitting the theoretical functionx(T)=x h(T)+x c(T) following from numerical integration of the reaction rate equations for the simultaneously occurring homogeneous (H) and cellular (C) precipitation processes.

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References [1] Bojanov , B. D. 1982 Oscillating polynomials of least L 1 -norm Hammerlin , G. (eds.) Numerical Integration

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] Dragomir , S. S. and Rassias , T. M. , Ostrowski Type Inequalities and Applications in Numerical Integration , Springer Netherlands, 2002 . [7

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