RETRACTED: Asymptotic constancy for a differential equation with multiple state-dependent delays

This article has been retracted: please see Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy).This article has been retracted at the request of the Journal Editor.The article is very similar to the following papers: (1)'Asymptotic behavior of solutions to a system of differential equations with state-dependent delays', by Lijuan Wang, published in J. Comput. Appl. Math., 228 (2009) 226–230. (2) 'Asymptotic behavior of solutions to a differential equation with state-dependent delay' by Lequn Peng, published in Comput. Math. Appl., 57 (2009) 1511–1514.All these articles were written using the same Latex file, treating very similar problems in exactly the same way. The authors of the papers knew about the similarity between the papers, but did not make any reference to each other, and therefore violated the Ethical Rules of Publishing, at the time the papers were submitted for publication. The scientific community takes a very strong view on this matter and apologies are offered to readers of the journal that this was not detected during the submission process

Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

Boolean Delay Equations: A simple way of looking at complex systems

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time. They represent therewith metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil's staircases and ``fractal sunbursts``. All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades in earthquake modeling and prediction, as well as in genetics. In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid earth problems. The former have used small systems of BDEs, while the latter have used large networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space (``partial BDEs``) and discuss connections with other types of dynamical systems, including cellular automata and Boolean networks. This research-and-review paper concludes with a set of open questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular the discussion on partial BDEs is updated and enlarge

Thermal Transients in District Heating Systems

Heat fluxes in a district heating pipeline systems need to be controlled on the scale from minutes to an hour to adjust to evolving demand. There are two principal ways to control the heat flux - keep temperature fixed but adjust velocity of the carrier (typically water) or keep the velocity flow steady but then adjust temperature at the heat producing source (heat plant). We study the latter scenario, commonly used for operations in Russia and Nordic countries, and analyze dynamics of the heat front as it propagates through the system. Steady velocity flows in the district heating pipelines are typically turbulent and incompressible. Changes in the heat, on either consumption or production sides, lead to slow transients which last from tens of minutes to hours. We classify relevant physical phenomena in a single pipe, e.g. turbulent spread of the turbulent front. We then explain how to describe dynamics of temperature and heat flux evolution over a network efficiently and illustrate the network solution on a simple example involving one producer and one consumer of heat connected by "hot" and "cold" pipes. We conclude the manuscript motivating future research directions.Comment: 31 pages, 7 figure

Micro-Arcsecond Radio Astrometry

Astrometry provides the foundation for astrophysics. Accurate positions are required for the association of sources detected at different times or wavelengths, and distances are essential to estimate the size, luminosity, mass, and ages of most objects. Very Long Baseline Interferometry at radio wavelengths, with diffraction-limited imaging at sub-milliarcsec resolution, has long held the promise of micro-arcsecond astrometry. However, only in the past decade has this been routinely achieved. Currently, parallaxes for sources across the Milky Way are being measured with ~10 uas accuracy and proper motions of galaxies are being determined with accuracies of ~1 uas/y. The astrophysical applications of these measurements cover many fields, including star formation, evolved stars, stellar and super-massive black holes, Galactic structure, the history and fate of the Local Group, the Hubble constant, and tests of general relativity. This review summarizes the methods used and the astrophysical applications of micro-arcsecond radio astrometry.Comment: To appear in Annual Reviews of Astronomy and Astrophysics (2014

On the dynamics of linear functional differential equations with asymptotically constant solutions

We discuss the dynamics of general linear functional differential equations with solutions that exhibit asymptotic constancy. We apply fixed point theory methods to study the stability of these solutions and we provide sufficient conditions of asymptotic stability with emphasis on the rate of convergence. Several examples are provided to illustrate the claim that the derived results generalize, unify and in some cases improve the existing ones