Results 11 to 20 of about 857,676 (288)
A generalization of slowly varying functions [PDF]
Proceedings of the American Mathematical Society, 1986 This note establishes that if the main part of the definition of a slowly varying function is relaxed to the requirement that lim sup x → ∞ ψ ( λ x ) / ψ ( x ...
Drasin, D., Seneta, E.
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Very slowly varying functions. II [PDF]
Colloquium Mathematicum, 2009 This paper is a sequel to both Ash, Erdos and Rubel AER, on very slowly varying functions, and BOst1, on foundations of regular variation. We show that generalizations of the Ash-Erdos-Rubel approach -- imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property -- lead naturally to the ...
N. H. Bingham, A. J. Ostaszewski
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Axioms, 2021 In this paper, we consider systems of singularly perturbed integro-differential equations with a rapidly oscillating right-hand side, including an integral operator with a slowly varying kernel.
Abdukhafiz Bobodzhanov +2 more
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A Seneta's Conjecture and the Williamson Transform [PDF]
Sahand Communications in Mathematical Analysis, 2023 Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$
Edward Omey, Meitner Cadena
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On the lateral vibrations of an elastic rod with varying compressive force [PDF]
Theoretical and Applied Mechanics, 2004 We study lateral vibration of a simply supported axially compressed elastic rod with rotary inertia. The axial force is assumed to be a function of time. Stability of the solution is examined.
Stanković Bogoljub +1 more
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On the stability of a class of slowly varying systems
Journal of Inequalities and Applications, 2018 Slowly varying systems are common in physics and control engineering and thus stability analysis for those systems has drawn considerable attention in the literature. This paper uses the “frozen time approach” to derive Lyapunov inequality conditions for
M. F. M. Naser +3 more
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Differences of Slowly Varying Functions
Journal of Mathematical Analysis and Applications, 2000 A positive non-decreasing function \(F\) belongs to the class \(\text{O}\Pi^+\) if \(\limsup(t\to\infty)(F(st)- F(t))= M(s)\) is finite for every \(s> 1\). Given a non-decreasing slowly varying function \(L\), if, whenever it is written as a sum \(L= F+G\) of two non-decreasing functions, both \(F\) and \(G\) are slowly varying, \(L\) is said to have ...
Janković, Slobodanka +1 more
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Mathematics, 2023 In this paper we study the Marcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences under sublinear expectation. Specifically, we establish complete convergence in the Marcinkiewicz–Zygmund-type strong law of large ...
Shuxia Guo, Zhe Meng
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Aequationes Mathematicae, 1972 Let \(\varphi\) be a positive non-decreasing real valued function defined on \([0, \infty)\), and let \(f\) be any real valued function defined on \([0, \infty)\). We say that \(f\) is \(\varphi\)-slowly varying if \(\varphi (x)[f(x+ \alpha)-f(x)] \to 0\) as \(x \to \infty\) for each \(\alpha\). We say that \(f\) is uniformly \(\varphi\)-slowly varying
Erdös, P. +2 more
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A Characterization of B-Slowly Varying Functions [PDF]
Proceedings of the American Mathematical Society, 1976 A measurable function φ > 0 \varphi > 0 that satisfies the limit condition lim x → ∞ ( φ ( x + t φ ( x ) ) /
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