Results 1 to 10 of about 1,023,532 (301)

A Hierarchy of Time-Scales and the Brain

PLoS Computational Biology, 2008
In this paper, we suggest that cortical anatomy recapitulates the temporal hierarchy that is inherent in the dynamics of environmental states. Many aspects of brain function can be understood in terms of a hierarchy of temporal scales at which representations of the environment evolve. The lowest level of this hierarchy corresponds to fast fluctuations
Stefan J. Kiebel, Jean Daunizeau, Karl J. Friston   +2 more
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Mathematica Applications on Time Scales [PDF]

, 2005
Stefan Hilger introduced the calculus on time scales in order to unify continuous and discrete analysis in 1988. The study of dynamic equations is an active area of research since time scales unifies both discrete and continuous processes, besides many others.
Ahmet Yantir, Ünal Ufuktepe
openaire   +2 more sources

The time scale logarithm

Applied Mathematics Letters, 2008
The author defines the time scale logarithm and considers some of its properties. \(C_n^1(\mathbb{T},\mathbb{R})\) is a set of nonvanishing continuously delta differentiable functions, \(M_m(C_n^1(\mathbb{T},\mathbb{R}))\) is the set of \(m\times m\) differentiable and invertible matrices with the entries in \(C_n^1(\mathbb{T},\mathbb{R})\).
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Hermite’s equations on time scales

Applied Mathematics Letters, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorota Mozyrska, Ewa Pawluszewicz
openaire   +1 more source

The Lie Brackets on Time Scales

Abstract and Applied Analysis, 2012
The Lie derivative, which has a wide range of application in physics and geometry, is trying to be examined on time scales. Firstly, nabla Lie bracket is defined on two-dimensional time scales.
H. Kusak, A. Caliskan
doaj   +1 more source

Random integral equations on time scales [PDF]

Opuscula Mathematica, 2013
In this paper, we present the existence and uniqueness of random solution of a random integral equation of Volterra type on time scales. We also study the asymptotic properties of the unique random solution.
Vasile Lupulescu, Cristina Lungan
doaj   +1 more source

Logistic equation on time scales

Examples and Counterexamples
We propose a new dynamic logistic equation that, in contrast with the one available in the literature, preserves the non-negativity of its solutions, which is an essential property for biological meaning.
Márcia Lemos-Silva, Delfim F.M. Torres
doaj   +1 more source

Some Opial-Type Inequalities on Time Scales

Abstract and Applied Analysis, 2011
We will prove some dynamic inequalities of Opial type on time scales which not only extend some results in the literature but also improve some of them. Some discrete inequalities are derived from the main results as special cases.
S. H. Saker
doaj   +1 more source

Lacunary statistical boundedness on time scales

Advances in Difference Equations, 2021
In this paper, we introduce the concept of lacunary statistical boundedness of Δ-measurable real-valued functions on an arbitrary time scale. We also give the relations between statistical boundedness and lacunary statistical boundedness on time scales.
Bayram Sözbir, Selma Altundağ
doaj   +1 more source

Steffensen's Integral Inequality on Time Scales

Journal of Inequalities and Applications, 2007
We establish generalizations of Steffensen's integral inequality on time scales via the diamond- dynamic integral, which is defined as a linear combination of the delta and nabla integrals.
Ozkan Umut Mutlu, Yildirim Hüseyin
doaj   +2 more sources