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Bai, Z. and Wang, H. , On positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl. , 270 (2) (2002), 357–368. H W. On positive solutions of some

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KUSANO, T. and NAITO, M., Nonlinear oscillation of fourth order differential equations, Canad. J. Math. 28 (1976), 840-852. MR 55 #3420 Nonlinear oscillation of fourth order differential equations

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References [1] Kamo , K. , Usami , H. 2002 Oscillation theorems for fourth-order quasilinear ordinary differential equations Studia Sci. Math. Hungar. 39 385 – 406

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, X. H. , Existence of infinitely many homoclinic orbits for fourth-order difference systems containing both advance and retardation , Appl. Math. Comput. , 217 ( 9 ) ( 2011 ), 4408 – 4415 . [12

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] Afrouzi , G. A. , Heidarkhani , S. and O’Regan , D. , Existence of three solutions for a doubly eigenvalue fourth-order boundary value problem , Taiwanese J. Math. , 15 ( 2011 ), 201 – 210 . [4

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Abstract  

This paper is concerned with nonoscillatory solutions of the fourth order quasilinear differential equation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(p(t)\left| {u''} \right|^{\alpha - 1} u'')'' + q(t)\left| u \right|^{\beta - 1} u = 0,$$ \end{document}
where α > 0, β > 0 and p(t) and q(t) are continuous functions on an infinite interval [a,∞) satisfying p(t) > 0 and q(t) > 0 (ta). The growth bounds near t = ∞ of nonoscillatory solutions are obtained, and necessary and sufficient integral conditions are established for the existence of nonoscillatory solutions having specific asymptotic growths as t→∞.

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oscillation of a beam tapering in accordance with a fourth-order parabola, Strength of Materials , Vol. 12, No. 9, 1980, pp. 98–103. Trapezon A. G. Bending oscillation of a beam tapering in

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Periodica Mathematica Hungarica
Authors: István Berkes, Lajos Horváth, Piotr Kokoszka and Qi-man Shao

Summary  

We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary weekly dependent process. We also study the a.\ s.\ behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that, after appropriate normalization, the estimator converges a.s. in the long-range dependent case as well. In both cases, our conditions involve fourth order cumulants and assumptions on the rate of growth of the truncation parameter appearing in the definition of the Bartlett estimator.

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Abstract  

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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