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Lakshmikantham, V., Wen, L. and Zhang, B., Theory of Differential Equations with Unbounded Delay , Kluwer Acad. Publ. (Dordrecht, Boston, London, 1994). MR 95m :34112

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. Egghe , L. Rousseau , R. 2000 The influence of publication delays on the observed ageing distribution of scientific literature Journal of the American Society for Information

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Hale, J. K. AND Kato, J., Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11-41. MR 58 #11793 Phase space for retarded equations with infinite

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Abstract  

In this paper we analyse the growth in scientific results of natural sciences in terms of infinite dynamical system theory. We use functional differential equations to model the evolution of science in its sociological aspect. Our model includes the time-to-build of fundamental notions in science (time required to understand them). We show that the delay parameter describing time required to learn and to apply past scientific results to new discoveries plays a crucial role in generating cyclic behaviour via the Hopf bifurcation scenario. Our model extends the de Solla Price model by including death of results as well as by incorporating the time-to-build notion. We also discuss the concepts of knowledge and its accumulation used in economic growth theory.

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Abstract  

In this survey paper the delay 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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\dot x(t) = - \mu x(t) + g(x(t - 1))$$ \end{document}
(t) = −µx(t) + g(x(t − 1)) is considered with µ ≥ 0 and a smooth real function g satisfying g(0) = 0. It is shown that the dynamics generated by this simple-looking equation can be very rich. The dynamics is completely understood only for a small class of nonlinearities. Open problems are formulated.

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Scientometrics
Authors: Ed Rinia, Thed. Van Leeuwen, Eppo Bruins, Hendrik Van Vuren, and Anthony Van Raan

Abstract  

As part of a larger project to investigate knowledge flows between fields of science, westudied the differences in speed of knowledge transfer within and across disciplines. The agedistribution of references in three selections of articles was analysed, including almost 800.000references in journal publications of the United Kingdom in 1992, 700.000 references inpublications of Germany in 1992, and more than 11 million references in the world total ofpublications in 1998.The rate of citing documented knowledge from other disciplines appears to differ sharplyamong disciplines. For most of the disciplines the same ratio's are found in the three data sets.Exceptions show interesting differences in the interdisciplinary nature of a field in a country. Wefind a general tendency of a citation delay in case of knowledge transfer between different fieldsof science: citations to work of the own discipline show less of a time lag than citations to work ina foreign discipline. Between disciplines typical differences in the speed of incorporatingknowledge from other disciplines are observed, which appear to be relatively independent of timeand place: for each discipline the same pattern is found in the three data sets. The disciplinespecific characteristics found in the speed of interdisciplinary knowledge transfer may be point ofdeparture for further investigations. Results may contribute to explanations of differences incitation rates of interdisciplinary research.

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Abstract  

Based on the simulation study of the publication delay control process [Yu & al., 2005], transfer function models of delay control processes by adjusting the accepted contribution flux and the published contribution flux are identified using system identification. According to Cybernetics, the feedback control system of the publication delay is designed and control processes are simulated and analyzed when the average publication delay are regarded as the controlled object. On the basis of the relation between the average publication delay and the deposited contribution quantity, another control method is proposed that the deposited contribution quantity is regarded as the controlled object and the simulation result proves that the method is an excellent means and can help editors expediently manage their journals and control publication delays.

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Summary  

Based on the transform function model of the observed citing process, the analytical expression of the age distribution of citations is deduced, and it is theoretically proved that the peak value of the citation distribution curve would fall and shift backward along with increasing the average publication delay and the peak age has a direct proportion relation with the pure delay and would be prolonged along with increasing the delay or decreasing the aging rate. The influence of the average publication delay on three ISI indicators impact factor, immediacy index and cited half-life are studied; in one subject discipline, the bigger the delay, the lower the three indicators of journals. Using the sensitivity theory, sensitivity formulae of the three indicators to publication delay parameters are deduced and it is found that responses of these indicators to changes of publication delays are different according to different time constant of the aging process; The faster the aging rate of a discipline literature is, the worse the influence of publication delays on the indicators of journals in the discipline.

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Abstract  

Some new linear and nonlinear delay integral inequalities of G-B-B type are obtained which generalize some results of O. Akinyele [1], P. Ch. Tsamatos and S. K. Ntouyas [16]. Application examples are also given.

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Summary  

Based on the convolution formula of the disturbed aging distribution (Egghe&Rousseau, 2000) and the transfer function model of the publishing delay process, we establish the transfer function model ofthe disturbed citing process. Using the model, we make simulative investigations of disturbed citation distributions and impact factors according to different average publication delays. These simulative results show that the bigger increment the average publication delays in a scientific field, the larger shift backwards of the citation distribution curves and the more fall the impact factors of journals in the field. Based on sometheoretical hypotheses, it is shown that there exists theoretically an approximate inverse linear relation between the field (or discipline) average publication delay and the journal impact factor.

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