Authors:Rolando Cavazos-Cadena and Daniel Hernández-Hernández
This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically
distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central
Based on the transfer function model of the observed citation distribution and the expression of the cumulative citation probability
distribution, parameters of 12 citation distributions are identified from statistical data of age distributions of references
of 10 journals in JCR using the parameter optimization fitting method. At same time, based on the steady state solution of
differential equations of the publication delay process and data of publication delays of 10 journals, the publication delay
parameters of every journal are identified using the fitting method. Identified parameters of every journal citation distribution
are compared with the journal’s publication delay parameters and some valuable conclusions are deduced.
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.
In this paper, the internal law of delay in the secondary literature publishing process is presented. The process is demonstrated
to abide by the partial differential equation of periodical literature publishing process. A definite solution of the publishing
delay process is derived. Accordingly, the expression of average publication delay indicator based on the particular solution
is deduced. Then the problem is studied that some information of primary literatures is missed in information retrieval, and
the relationship is established between the average delay indicator and the miss ratio of primary literatures in the index
periodicals or databases. Also it is proposed that the primary literature should be used as a supplemental tool in information
retrieval to guarantee the recall ratio.