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. 1962 Fourier Analysis on Groups Interscience Publishers . [8] Ruzsa , I. Z. 1993 Solving a linear equation in a

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Abstract  

A small scale (100 mL) calorimeter is developed. It includes a glass vessel submerged in a thermostatic bath, a compensation electrical heater, and a control system. The typical operation mode consists on introducing the solvents and part of the reactants into the vessel, to stabilise a temperature of the bath (T j) some degrees below the desired process temperature (T p) and to adjust the reaction mass temperature (T r) to T p using the electrical heater. An oscillating set point is established for Tr, which produces an oscillating response of the applied compensation power (Q c). Finally, the rest of reactants are dosed to the vessel. A small deviation of T r and T p is observed. Even though it can be avoided improving the tuning of the controller, it can be useful for enhancing the calculation of the heat capacity of the reaction mixture (C P). The signals of T r, Q c and T j are processed on-line using the FFT (Fast Fourier Transform) method as the mathematical tool used to analyse the data obtained, producing accurate values of the heat evolved (Q c) by the process, the heat transfer coefficient (UA), and the heat capacity of the reaction mixture (C P).

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. Optimum methods in statistics 1997 Vass P 2010: Fourier Analysis (in Hungarian). Graduate Studies in Mathematics, Miskolc

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Abstract  

In dealing with phenomena which show a linear response such as viscoelastic or dielectric properties, measurements are carried out by observing the relationship between the stimulus applied to the sample and the response from the sample. Since the Fourier analysis technique is effective in obtaining this relationship, two types of circuitries based on Fourier analysis have been created. Both DMA and dielectric measurement were used to evaluate these circuitries. Results were satisfactory, especially with respect to tanδ precision.

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Резюме  

С. А. Теляковский [12] распостронил теорему Боянича [2], которая является количестбенным вариантом широко известной в классическом анализе фурье турье теореяы Дирихле-Жордана. Наша цель — расширять теорему Теляковского с одномерных на двумерные ряды фурье функций ограниченной вариации в смысле Харди и Краузе. Указанные теоремы Харди [5] и Морица [7] для таких же функций являются последствиями нашей теоремы, доказанной в ∂той стаье.

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Bosanquet, L. S. , Review on G. Sunouchi’s paper “Notes on Fourier analysis, XVIII, Absolute summability of series with constant terms”, Mathematical Reviews , 11 (1950), 654. Bosanquet L. S

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Abstract  

The measured signal of the temperature-modulated differential scanning calorimetry (TMDSC) is discussed in the case of polymer melting. The common data evaluation procedure of TMDSC-signals is the Fourier analysis. The resulting information is the amplitude and the phase shift of the first harmonic of the periodic heat flow component. It is shown that this procedure is not sufficient for quantitative discussions if deviations from the symmetric curve shape occur in the measured heat flow curves. For polymer melting it is demonstrated that asymmetric curves will be measured if the experimental temperature amplitude is too large. In this paper a data evaluation method is presented, which is based on the Fourier transform of the measured curves. The peaks of the first and second harmonics in the resulting spectra are used for the analysis of the asymmetry of the measured curves. In the case of polymer melting this analysis yields the maximum temperature amplitude which follows a correct linear data evaluation. This maximum temperature amplitude depends on the material.

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Abstract

Grapevine berry shape has important marketing value in the table grape commerce, hence variability evaluation of this characteristic is highly important. In this study berry shape of 5 table grape genotypes: “Fanny”, “Lidi”, “Hamburgi muskotály”, “Moldova”, and “Orsi” were compared. To evaluate the shape variability graphic reconstruction and elliptic Fourier analysis have been carried out. Shape outlines have been investigated and Principal Component Analysis (PCA) has been performed with the SHAPE software package. PCA of the contours showed that 6 out of the 77 principal components were effective to describe shape attributes. The first 6 PCs explained 94.51% of the total variance. PC1 associated with the width and length of the berry. PC2 related to the shape of the top and bottom of the berries, while PC3 linked to the ratio of the top and the bottom width. ANOVA of the principal component scores revealed significant difference among the genotypes. Results suggest that morphology of the berry is a variable not only among but within the accessions. Our findings confirmed that elliptic Fourier descriptors (EFDs) would be a powerful tool for quantifying grapevine berry morphological diversity.

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