A new approach for designing self-organizing systems and application to adaptive control

There is tremendous interest in the design of intelligent machines capable of autonomous learning and skillful performance under complex environments. A major task in designing such systems is to make the system plastic and adaptive when presented with new and useful information and stable in response to irrelevant events. A great body of knowledge, based on neuro-physiological concepts, has evolved as a possible solution to this problem. Adaptive resonance theory (ART) is a classical example under this category. The system dynamics of an ART network is described by a set of differential equations with nonlinear functions. An approach for designing self-organizing networks characterized by nonlinear differential equations is proposed

Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given

Comparison of a manual and an automated tracking method for Tibetan Plateau vortices

Tibetan Plateau vortices (TPVs) are mesoscale cyclones originating over the Tibetan Plateau (TP) during the extended summer season (April-September). Most TPVs stay on the TP while a small number can move off the TP to the east. TPVs are known to be one of the main precipitation-bearing systems on the TP and moving-off TPVs have been associated with heavy precipitation and flooding downstream of the TP (e.g. Sichuan province, Yangtze River Valley). Identifying and tracking TPVs is difficult both due to their comparatively small horizontal extent (400 – 800 km) and the limited availability of soundings over the TP, which, in turn, constitutes a challenge for short-term predictions of TPV-related impacts and for the climatological study of TPVs. In this study, (i) manual tracking (MT) results using radiosonde data from a network over and downstream of the TP are compared with (ii) results obtained by an automated tracking (AT) algorithm applied to ERA-Interim reanalysis. Ten MT-TPV cases are selected based on method (i) and matched to and compared with the corresponding AT-TPVs identified with method (ii). Conversely, ten AT-TPVs are selected and compared with the corresponding MT-TPVs. In general, the comparison shows good results in cases where the underlying data are in good agreement, but considerable differences are also seen in some cases and explained in terms of differences in the tracking methods, data availability/coverage and disagreement between sounding and ERA-Interim data. Recommendations are given for future efforts in TPV detection and tracking, including in an operational weather forecasting context

Newton-Kantorovičův konvergenční teorém Halleovy metody v Banachově prostoru

A Newton-Kantorovich convergence theorem of a new modified Halleys method family is established in a Banach space to solve nonlinear operator equationsV článku je stanoven Newton-Kantorovičův konvergenční teorém modifikované Halleovy metody pro řešení operátorových rovni

Effect of aggregates on the magnetization property of ferrofluids: A model of gaslike compression

The effect of field-induced aggregation of particles on the magnetization property of ferrofluids is investigated. From the viewpoint of energy, magnetizability of ferrofluids is more complicated than predicted by Langevin theory because the aggregation, i.e., the transition of ferrofluid microstructure, would consume the energy of the applied magnetic field. For calculating the effect of aggregates on the magnetization of ferrofluids, a model of gaslike compression (MGC) is proposed to simulate the evolution of the aggregate structure. In this model, the field-induced colloidal particles aggregating in ferrofluids is equivalent to the "gas of the particles" being compressed by the applied magnetic field. The entropy change of the ferrofluid microstructure is proportional to the particle volume fraction in field-induced aggregates phivH. On the basis of the known behavior of ferrofluid magnetization and the aggregate structure determined from the present experiments, phivH is obtained and found to depend on the aggregating characteristic parameter of ferrofluid particles γ in addition to the particle volume fraction in ferrofluids phiv and the strength of applied magnetic field H. The effect of the nonmagnetic surface layer of ferrofluid particles is also studied. The theory of MGC conforms to our experimental results better than Langevin theory

Semilokální konvergenční teorém inverzní Jarratovy metody za nové Holderovy podmínky

Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem