Authors:Khizra Bukhsh; Awais Younus, Aiman Mukheimer, Thabet Abdeljawad Abstract: The paper presents a detailed analysis of control and observation of generalized Caputo proportional fractional time-invariant linear systems. The focus is on identifying controllable states and observable systems within the controllable subspace, null space, and unobservable subspace of the proposed system. The necessary conditions for the controllable subspace and the necessary and sufficient conditions for observability criteria are firmly established. The controllable subspace is treated geometrically as the set of controllable states, while the observable system is characterized by a zero unobservable subspace. The results are reinforced by examples and will immensely benefit future studies on fractional-order control systems. PubDate: Sat, 15 Jun 2024 00:00:00 +030
Authors:Vijay Gupta; Ruchi Gupta Abstract: There are different methods available in literature to construct a new operator. One of the methods to construct an operator is the composition method. It is known that Baskakov operators can be achieved by composition of Post Widder $P_n$ and Sz\'asz-Mirakjan $S_n$ operators in that order, which is a discretely defined operator. But when we consider different order composition namely $S_n\circ P_n$, we get another different operator. Here we study such and we establish some convergence estimates for the composition operators $S_n\circ P_n$, along with difference with other operators. Finally we found the difference between two compositions by considering numeric values. PubDate: Sat, 15 Jun 2024 00:00:00 +030
Authors:Danilo Costarellı; Anna Rita Sambucını Abstract: The aim of this paper is to compare the fuzzy-type algorithm for image rescaling introduced by Jurio et al., 2011, quoted in the list of references, with some other existing algorithms such as the classical bicubic algorithm and the sampling Kantorovich (SK) one. Note that the SK algorithm is a recent tool for image rescaling and enhancement that has been revealed to be useful in several applications to real world problems, while the bicubic algorithm is widely known in the literature. A comparison among the abovementioned algorithms (all implemented in the MatLab programming language) was performed in terms of suitable similarity indices such as the Peak-Signal-to-Noise-Ratio (PSNR) and the likelihood index $S$. PubDate: Sat, 15 Jun 2024 00:00:00 +030
Authors:Mitsuo Izuki; Takahiro Noi, Yoshihiro Sawano, Hirokazu Tanaka Abstract: Funahashi established that the space of two-layer feedforward neural networks is dense in the space of all continuous functions defined over compact sets in $n$-dimensional Euclidean space. The purpose of this short survey is to reexamine the proof of Theorem 1 in Funahashi \cite{Funahashi}. The Tietze extension theorem, whose proof is contained in the appendix, will be used. This paper is based on harmonic analysis, real analysis, and Fourier analysis. However, the audience in this paper is supposed to be researchers who do not specialize in these fields of mathematics. Some fundamental facts that are used in this paper without proofs will be collected after we present some notation in this paper. PubDate: Sat, 15 Jun 2024 00:00:00 +030
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