The Abel’s and Dirichlet’s criterions for convergence of series in analysis are very basic classical results and both require
the monotonicity condition. In this note we show that the monotonicity condition in these criterions can be generalized to
RBV condition, while cannot be generalized to quasimonotonicity.
To verify the universal validity of the ``two-sided'' monotonicity condition introduced in , we will apply it to include
more classical examples. The present paper selects the Lp convergence case for this purpose. Furthermore, Theorem 3 shows that our improvements are not trivial.
Authors:P. Dimotakis, B. Symeopoulos, and M. Demetriou
The monotonic kinetics of isothermal yield of51Cr(VI) in51Cr(III)-doped potassium chromate reveals a common mechanistic scheme with that of neutron irradiated K2CrO4, including two first order processes during the examined first hour. One of them is fast and the other very slow, but both seem to be controlled by two thermal coefficients.
The paper aims to develop a model of nonlinear economic growth — with simple assumptions — which explains both Japan’s
-shape convergence path and the UK’s declining path toward the US between 1870–2000, and the development of other countries, as well as post-war reconstruction. According to the model, progress in stock of knowledge is formed by a quadratic formula of the relative development of follower countries.The model draws on four recent theories. Firstly, Romer’s theory, which approaches a country’s level of development by using the number of its products (Romer 1990), secondly, Jones’ idea theory with a slight modification (Jones 2004), third, the theory of quality of institutions, which determines economic performance (North 1993), and finally, the theory of physical and human capital. The first part of the paper sets up the production function, the second determines the growth rate and analyses the reconstruction path, while the third draws up model forecasts.
Chaundry and Jolliffe  proved that if ak is a nonnegative sequence tending monotonically to zero, then a necessary and sufficient condition for the uniform convergence
of the series Σk=1∞ak sin kx is limk→∞kak = 0. Lately, S. P. Zhou, P. Zhou and D. S. Yu  generalized this classical result. In this paper we propose new classes
of sequences for which we get the extended version of their results. Moreover, we generalize the results of S. Tikhonov 
on the L1-convergence of Fourier series.