On Nano Continuity

The purpose of this paper to propose a new class of functions called nano continuous functions and derive their characterizations in terms of nano closed sets, nano closure and nano interior. There is also an attempt to define nano-open maps, nano closed maps and nano homeomorphism Keywords: Nano topology, nano-open sets, nano closed sets, nano interior, nano closure, nano continuous functions, nano-open maps, nano closed maps, nano homeomorphism 2010 AMS Subject Classification:54B05,54C0

Topological geometry analysis for complex dynamic systems based on adaptive control method

Several models had been proposed for dynamic systems, and different criteria had been analyzed for such models such as Hamiltonian, synchronization, Lyapunov expansion, and stability. The geometry criteria play a significant part in analyzing dynamic systems and some study articles analyze the geometry of such topics. The synchronization and the complex-network control with specified topology; meanwhile, the exact topology may be unknown. In the present paper, and by making use of the adaptive control method, a proposed control method is developed to determine the actual topology. The basic idea in the proposed method is to receive evolution of the network-node

Generalized open sets in grill N-topology

[EN] The aim of this paper is to give a systematic development of grill N-topological spaces and discuss a few properties of local function. We build a topology for the corresponding grill by using the local function. Furthermore, we investigate the properties of weak forms of open sets in the grill N-topological spaces and discuss the relationships between them.Thivagar, ML.; Reilly, IL.; Dasan, MA.; Ramesh, V. (2017). Generalized open sets in grill N-topology. Applied General Topology. 18(2):289-299. doi:10.4995/agt.2017.6797SWORD28929918

Dynamic system linear models and Bayes classifier for time series classification in promoting sustainabilitys

Research purpose: The current work introduces a novel method for time series discriminant analysis (DA). Proposing a version for the Bayes classifier employing Dynamic Linear Models, which we denote by BCDLM This article explores the application of DLMs and the Bayes Classifier in time series classification to promote application in sustainability across diverse sectors. Method: This paper presents some computer simulation studies in which we generate four different scenarios corresponding to time series observations from various Dynamic Linear Models (DLMs). In Discriminant Analysis, we investigated strategies for estimating variance in models and compared the performance of the BCDLM with other common classifiers. Such datasets are composed of real-time series (data from SONY AIBO Robot and spectrometry of coffee types) and pseudo-time series (data from Swedish leaves adapted for time series). We also point out that algorithm was used to determine training and test sets in real-world applications. Results: Considering the real-time series examined in this paper, The results obtained indicate that the parametric approach developed represents a promising alternative for this class of DA problems, with observations of time series in a situation that is quite difficult in practice when we have series with large sizes with respect to the number of observations in the classes, even though more thorough studies are required. Conclusions: It concludes that the BCDLM performed comparably to the results of the classifiers 1NN, RDA, NBND and NBK and superior to the methods LDA and QDA. This offers a powerful combination for time series classification, enabling accurate predictions and informed decision-making in areas such as energy consumption, waste management, and resource allocation

Impact of Non-Linear Electronic Circuits and Switch of Chaotic Dynamics

Switch-mode power supply is an extremely non-linear system that can inevitably exhibit unpredictable behavior. These control laws may be insufficient for nonlinear systems because they are not robust when the requirements on the dynamic characteristics of the system are strict [10]. Control laws that are insensitive to parameter variations, disturbances, and nonlinearities must be used. In this paper, we have tested the method of the first harmonic, used to analyses servo controls with a nonlinear element, and to predict certain non-linear behaviors. It mainly allows predicting the limit cycles, but also the jump phenomena, the harmonics as well as the responses of non-linear systems to sinusoidal inputs. We apply this method for the prediction of limit cycles and the determination of their amplitude and frequency. We take as an example a Boost converter controlled by current [4]. This system is chaotic when the duty cycle is more significant than 0.5: we then eliminate the chaos by applying the slippery mode command (for the ripple of the output voltage, for the current ripple of the inductance and switching frequency) when the output is periodic (duty cycle less than or equal to 0.5). In this article, we assess that established approach provides the best outcomes: it appears that the preference between the classical mode and the sliding mode depends heavily on the variance domain of the parameters E, R, and Iref