We develop a novel method to completely solve the 3-term partial exponential Diophantine equation that represents a generalization of the standard discrete logarithm problem. Our method not only reveals the internal structure of the equation's solution and yields a numerical algorithm to solve it systematically, but also provides an alternative approach to the discrete logarithm problem.
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http://dx.doi.org/10.1016/j.heliyon.2024.e24766 | DOI Listing |
Phys Rev E
May 2024
College of Physics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.
In this study, we explore the quantum critical phenomena in generalized Aubry-André models, with a particular focus on the scaling behavior at various filling states. Our approach involves using quantum fidelity susceptibility to precisely identify the mobility edges in these systems. Through a finite-size scaling analysis of the fidelity susceptibility, we are able to determine both the correlation-length critical exponent and the dynamical critical exponent at the critical point of the generalized Aubry-André model.
View Article and Find Full Text PDFRes Number Theory
May 2024
University of Salzburg, Hellbrunnerstrasse 34/I, A-5020 Salzburg, Austria.
In this paper, we consider the Diophantine equation for given integers , with , whereas varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions (, ) , then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of .
View Article and Find Full Text PDFThis research is intended to address a robust cooperative control problem of heterogeneous uncertain nonlinear high-order fully actuated multiagent systems (HUN-HOFAMASs). A nonlinear HOFA system model is used to describe the multiagent systems (MASs) with heterogeneous uncertain nonlinear dynamics, which is called the HUN-HOFAMASs. A predictive terminal sliding-mode control-based robust cooperative control scheme is presented to address this problem.
View Article and Find Full Text PDFWe develop a novel method to completely solve the 3-term partial exponential Diophantine equation that represents a generalization of the standard discrete logarithm problem. Our method not only reveals the internal structure of the equation's solution and yields a numerical algorithm to solve it systematically, but also provides an alternative approach to the discrete logarithm problem.
View Article and Find Full Text PDFISA Trans
April 2024
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, China; Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen 518055, China. Electronic address:
This research focuses on a cooperative control problem for networked multi-agent systems (NMASs) under time-variant communication constraints (containing time-variant communication delays and time-variant data losses) in the forward and feedback channels. From the perspective of high-order fully actuated (HOFA) system theory, a HOFA system model is adopted to describe the NMAS, which is called the networked HOFA multi-agent system (NHOFAMAS). Because of complicated working scenarios over the network, the states of NMASs are immeasurable and the communication constraints are always present, such that an observer-based HOFA predictive control (OB-HOFAPC) method is designed to implement the cooperative control when existing the immeasurable states and time-variant communication constraints.
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