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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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TL;DR: In this paper, the authors considered non-autonomous (1.2) third-order differential equations, where a(t, b(t)y c(t), g, h, p are continuous real-valued functions depending only on the arguments shown.
Abstract: (1.2) x+a(t)f(x, Λ, x)x+b(t)g(x9 x)+c(t)h(x) = p(t, x, i, x) where a(t), b(t)y c(t) are positive continuously differentiate and /, g, h, p are continuous real-valued functions depending only on the arguments shown, and the dots indicate the differentiation with respect to t. The asymptotic property of solutions of third order differential equations has received a considerable amount of attention during the past two decades, particularly when (1.2) is autonomous. Many of these results are summarized in [11]. A few authors have studied non-autonomous third order differential equations. K. E. Swick [13] considered the following equations

13 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the asymptotic approximation of some functions defined by the q-Jackson integrals, for a fix q ∈]0, 1[.
Abstract: This paper aims to study the asymptotic approximation of some functions defined by the q-Jackson integrals, for a fix q ∈]0, 1[. For this purpose, we shall attempt to extend the classical methods b...

13 citations

Journal ArticleDOI
TL;DR: In this paper, the authors deal with the asymptotic stability analysis of a discrete dynamical inclusion whose right-hand side is a convex process and provide necessary and sufficient conditions for weak stability.

13 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the asymptotic evolution of trace-nonincreasing homogeneous quantum Markov processes (both types, discrete and continuous Markov dynamical semigroups) equipped with a subinvariant faithful state in the Schrodinger and the Heisenberg picture.
Abstract: Markov processes play an important role in physics and in particular in the theory of open systems. In this paper we study the asymptotic evolution of trace-nonincreasing homogeneous quantum Markov processes (both types, discrete quantum Markov chains and continuous quantum Markov dynamical semigroups) equipped with a subinvariant faithful state in the Schrodinger and the Heisenberg picture. We derive a fundamental theorem specifying the structure of the asymptotics and uncover a rich set of transformations between attractors of quantum Markov processes in both pictures. Moreover, we generalize the structure theorem derived earlier for quantum Markov chains to quantum Markov dynamical semigroups showing how the internal structure of generators of quantum Markov processes determines attractors in both pictures. Based on these results we provide two characterizations of all asymptotic and stationary states, both strongly reminding in form the well-known Gibbs states of statistical mechanics. We prove that the dynamics within the asymptotic space is of unitary type, i.e. quantum Markov processes preserve a certain scalar product of operators from the asymptotic space, but there is no corresponding unitary evolution on the original Hilbert space of pure states. Finally simple examples illustrating the derived theory are given.

13 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526