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In the present paper, by means of the successive approximations method, the local or global existence and uniqueness theorems for a stochastic functional differential equation of the Ito type are proved.

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Abstract  

We discuss two techniques useful in the investigation of periodic solutions of broad classes of non-linear non-autonomous ordinary differential equations, namely the trigonometric collocation and the method based upon periodic successive approximations.

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We study the existence, uniqueness and continuous dependence of solutions for systems of ordinary differential equations including also delay problems with initial and periodic conditions. Results are obtained by using the comparison method and the theory of differential inequalities.

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The existence and uniqueness of solutions of more general Volterra-Fredholm integral equations are investigated. The successive approximations method based on the general idea of T. Wazewski is the main tool.

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General theorems on the existence, uniqueness and convergence of successive approximations for classical solutions of the Cauchy problem are given. Results are based on a comparison method and on the axiomatic approach to equations with unbounded delay. The nonlinear comparison operator is investigated. Examples of nonlinear comparison problems and phase spaces are given.

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A method has been developed for the correction of counting losses in NAA for the case of a mixture of short-lived radionuclides. It is applicable to systems with Ge detectors and Wilkinson or successive approximation ADC's and will correct losses from pulse pileup and ADC dead time up to 90%. The losses are modeled as a constant plus time-dependent terms expressed as a fourth order polynomial function of the count rates of the short-lived radionuclides. The correction factors are calculated iteratively using the peak areas of the short-lived radionuclides in the spectrum and the average losses as given by the difference between the live time and true time clocks of the MCA. To calibrate the system a measurement is performed for each short-lived nuclide. In a test where the dead time varied from 70% at the start of the measurement to 13% at the end, the measured activities were corrected with an accuracy of 1%.

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. Poore, M.E.D. 1962. The method of successive approximation in descriptive ecology. In: Advances in Ecological Research. Vol. 1, Academic Press, New York. pp. 35-68. The method of successive approximation in

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): Successive approximations to a model for short term memory . Acta Psychologica , 27 , 285 – 292 . 75. Tales , A. , Newton , P. , Troscianko , T. , Butler , S. ( 1999 ): Mismatch

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