Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

Where Are the Goalposts? Generational Change in the Use of Grammatical Gender in Irish

The Irish language is an indigenous minority language undergoing accelerated convergence with English against a backdrop of declining intergenerational transmission, universal bilingualism, and exposure to large numbers of L2 speakers. Recent studies indicate that the interaction of complex morphosyntax and variable levels of consistent input result in some aspects of Irish grammar having a long trajectory of acquisition or not being fully acquired. Indeed, for the small group of children who are L1 speakers of Irish, identifying which “end point” of this trajectory is appropriate against which to assess these children’s acquisition of Irish is difficult. In this study, data were collected from 135 proficient adult speakers and 306 children (aged 6–13 years) living in Irish-speaking (Gaeltacht) communities, using specially designed measures of grammatical gender. The results show that both quality and quantity of input appear to impact on acquisition of this aspect of Irish morphosyntax: even the children acquiring Irish in homes where Irish is the dominant language showed poor performance on tests of grammatical gender marking, and the adult performance on these tests indicate that children in Irish-speaking communities are likely to be exposed to input showing significant grammatical variability in Irish gender marking. The implications of these results will be discussed in terms of language convergence, and the need for intensive support for mother-tongue speakers of Irish.

ON THE EXISTENCE OF A CONDITIONALLY PERIODIC SOLUTION OF A QUASILINEAR SYSTEM DIFFERENTIAL EQUATION IN THE CRITICAL CASE

In the theory of nonlinear oscillations one often encounters conditionally periodic oscillations resulting from the superposition of several oscillations with frequencies incommensurable with each other. When finding a solution to a resonant quasilinear differential system in the form of a conditionally periodic function, the problem of a small denominator arises. Consequently, the proof of the existence and even more the construction of such a solution is not an easy task. In this article, drawing on the work of V.I. Arnold, I. Moser, and other researchers proved the existence and constructed a conditionally periodic solution of a second-order quasilinear differential system in the critical case. Accelerated convergence method by N.N. Bogolyubova, Yu.A. Mitropolsky, A.M. Samoylenko. The result can be applied to construct a conditionally periodic solution of specific differential systems.

The great convergence? Mortality in Ireland and Europe, 1956–2014

Background Until recently, Irish age-standardized mortality rates (ASMRs) were amongst the highest in the EU-15. This study examines changes in ASMRs in Ireland from 1956 to 2014. Methods Using data from the World Health Organization Mortality Database, we compare ASMRs in Ireland to other EU-15 countries from 1956 to 2014. ASMRS are used to plot the relative ranking of Ireland within the EU-15, and illustrate trends in which Ireland diverged with, and converged to, the EU-15 average. ASMRS are estimated across sex, age groups (15–64 and 65+ years) and cause of death. Results Between 1956 and 1999, ASMRs in Ireland were amongst the highest in the EU-15. ASMRs in Ireland saw slower improvements during this period as compared to other EU-15 countries. However, post-2000, a sharp reduction in Irish ASMRs resulted in an accelerated convergence to the EU-15 average. As a consequence of improvements in ASMRs between 2000 and 2014, there were an estimated 15 300 fewer deaths in 2014. The majority of these averted deaths were due to lower mortality rates for diseases of the circulatory system and respiratory system. Conclusions Rather than converging to the EU-15 average during the latter half of the 20th century, there was a divergence in ASMRs between Ireland and the EU-15. However, in recent years, Ireland experienced accelerated improvements in mortality rates with large reductions in mortality observed for diseases of the circulatory system and respiratory system, especially amongst older people.