Article
Engineering, Electrical & Electronic
S. Radhika, F. Albu, A. Chandrasekar
Summary: This brief proposes two novel adaptive filters suitable for impulsive noise environments and investigates their stability condition and steady-state analysis. Additionally, a variable scheme is proposed to address the tradeoff between performance and error. Simulation results demonstrate the improved performance of the proposed algorithms.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2022)
Article
Computer Science, Artificial Intelligence
Zhongbo Sun, Gang Wang, Long Jin, Chao Cheng, Bangcheng Zhang, Junzhi Yu
Summary: This paper revisits and redesigns noise-suppressing zeroing neural network models for online solving time-varying matrix square roots problems from a control viewpoint framework. The developed models globally converge to the theoretical solutions without noise and exponentially converge in the presence of noise. Numerical results demonstrate the efficiency and superiority of the developed models for real-time solutions with inherent tolerance to noise.
EXPERT SYSTEMS WITH APPLICATIONS
(2022)
Article
Computer Science, Artificial Intelligence
Changxin Mo, Dimitrios Gerontitis, Predrag S. Stanimirovie
Summary: This paper investigates the time-varying tensor square root problem and proposes a new finite-time convergent Zhang neural network model. The existence and uniqueness of the solution are discussed, and numerical examples confirm the reliability and superiority of the proposed model.
Article
Computer Science, Information Systems
Gang Wang, Yongbai Liu, Yingyi Sun, Junzhi Yu, Zhongbo Sun
Summary: In this study, a noise-suppression zeroing neural dynamics (NSZND) model is developed from the control perspective to solve the time-varying or time-invariant cube root problem with different disturbances. The model achieves superior solving accuracy compared to other models and is extended to solve the tensor cube root problem and generate different fractals in the complex domain.
INFORMATION SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Wenqi Wu, Bing Zheng
Summary: In this article, two new Zhang neural network models, TZNN and VZNN, are proposed to solve time-varying linear equations and inequalities systems (LEIESs). These models do not require an additional relaxation vector, thereby reducing the computational cost. Experimental results demonstrate the efficiency and effectiveness of these models in solving LEIESs problems.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics
Baseer Gul, Muhammad Arif, Reem K. Alhefthi, Daniel Breaz, Luminita-Ioana Cotirla, Eleonora Rapeanu
Summary: Geometric function theory, a subfield of complex analysis, has witnessed increased research in recent years. The contributions of different subclasses of analytic functions associated with innovative image domains, using subordination notions, have become of significant interest. The present research introduces a novel subclass of starlike functions, denoted as S-sinh lambda*, and investigates its geometric nature in the open unit disk U. By finding sharp upper bounds of the coefficients alpha(n) for n = 2,3,4,5, and proving a lemma related to the image domain, the radius problems of various known classes, including S*(beta) and kappa(beta), are discussed. Several geometrically known classes and functions defined as ratios are also investigated. A new representation of functions in this class for a specific range of lambda is obtained.
Article
Mathematics, Applied
B. V. Rajarama Bhat, Chaitanya Gopalakrishna
Summary: This study provides new characterizations for detecting the non-existence of square roots for self-maps on arbitrary sets. It proves the density of continuous self-maps with no square roots in the space of all continuous self-maps for various topological spaces. The study also shows that every continuous self-map on a space homeomorphic to the unit cube in R-m with a fixed point on the boundary can be approximated by iterative squares of continuous self-maps.
ERGODIC THEORY AND DYNAMICAL SYSTEMS
(2023)
Article
Automation & Control Systems
Laura Menini, Corrado Possieri, Antonio Tornambe
Summary: The technical communique proposes a locally convergent continuous-time model for the Durand-Kerner method to determine all roots of a time-varying polynomial simultaneously. The effectiveness of this method is demonstrated through its application to a benchmark example.
Article
Mathematics
Javad Golzarpoor, Dilan Ahmed, Stanford Shateyi
Summary: In this paper, an improved mid-point method is proposed for finding the square root of a matrix and its inverse. Numerical simulations demonstrate the effectiveness and accuracy of the method for matrices of various sizes.
Article
Mathematics, Applied
Sumedh B. Thool, Yogesh J. Bagul, Ramkrishna M. Dhaigude, Christophe Chesneau
Summary: In this paper, new simple bounds are established for the quotients of inverse trigonometric and inverse hyperbolic functions. Polynomial bounds using even quadratic functions and exponential bounds are provided. Graph validation is also performed.
Article
Physics, Multidisciplinary
M. Coskun, M. Erturk
Summary: In this study, a new set of Bessel type functions was developed by inserting different hyperbolic cosine functions into the radial part of generalized Bessel functions, to improve the performance of basis sets in Hartree-Fock-Roothaan calculations. The results showed that the new basis sets outperformed conventional approaches in terms of accuracy.
Article
Computer Science, Interdisciplinary Applications
Tommaso Buvoli, Michael Minion
Summary: Parareal is a parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration, leading to significantly reduced computational time compared to serial time-stepping methods. This paper explores the use of exponential integrators within the Parareal iteration to solve non-diffusive equations. Numerical experiments and linear analysis are conducted to evaluate the stability and convergence properties of the exponential Parareal iteration. Results demonstrate that the exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators for certain non-diffusive equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Mathematics, Interdisciplinary Applications
Asifa Tassaddiq, Muhammad Tanveer, Muhammad Azhar, Muhammad Arshad, Farha Lakhani
Summary: In this article, an escape criteria using DK-iteration, complex sine function, and complex exponential function is established to analyze the dynamical behavior of specific fractals such as Julia set and Mandelbrot set. By generalizing existing algorithms, beautiful fractals for m=2, 3, and 4 are visualized. The image generation time using different input parameter values is also computed.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Interdisciplinary Applications
Xiaoqi Sun
Summary: This paper investigates the exponential stability in mean square for stochastic static neutral neural networks with varying delays. By using the Lyapunov functional method and stochastic analysis technique, the paper obtains the sufficient conditions to guarantee the exponential stability in mean square for the neural networks and extends some results of related literature.
COMPUTERS AND CONCRETE
(2022)
Article
Engineering, Electrical & Electronic
Alireza Naeimi Sadigh, Hadi Zayyani
Summary: In this paper, an improved version of the proportionate robust diffusion recursive least exponential hyperbolic cosine algorithm is proposed. The step-size parameter of this algorithm is optimally selected by minimizing the squared norm of the error vector. Theoretical analysis is performed to study the mean-square convergence, mean-square steady-state, and forgetting factor parameter selection, and simulation experiments demonstrate that the improved algorithm outperforms the original algorithm and other state-of-the-art algorithms in terms of convergence speed.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)