Institute of Mathematics AS CR, v. v. i.
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A new characterization of projective special unitary group PSU
No full textsummary:Projective special unitary groups , where is a prime, is uniquely determined by its order and the size of one conjugacy class
Collections of school leaving examination mathematics problems from 1879-1934
No full textsummary:Článek informuje o sbírkách maturitních úloh z matematiky, které byly vydány v období Rakousko-Uherska a v období tzv. první republiky v letech 1918-1939. Je uvedeno celkem pět sbírek s ukázkami úloh a jejich řešení
Solving elastodynamic problems of 2D quasicrystals in inhomogeneous media
No full textsummary:Initial value problem for three dimensional (3D) elastodynamic system in two dimensional (2D) inhomogeneous quasicrystals is considered. An analytical method is studied for the solution of this problem. The system is written in terms of Fourier images of displacements with respect to lateral variables. The resulting problem is reduced to integral equations of the Volterra type. Finally, using Paley Wiener theorem it is shown that the solution of the initial value problem can be found by the inverse Fourier transform. A numerical example is considered for the comparison of the exact solution with the computed solution obtained by using the method
Solving inverse nodal problem with frozen argument by using second Chebyshev wavelet method
No full textsummary:We consider the inverse nodal problem for Sturm-Liouville (S-L) equation with frozen argument. Asymptotic behaviours of eigenfunctions, nodal parameters are represented in two cases and numerical algorithms are produced to solve the given problems. Subsequently, solution of inverse nodal problem is calculated by the second Chebyshev wavelet method (SCW), accuracy and effectiveness of the method are shown in some numerical examples
Neural network-based fault diagnosis and fault-tolerant control for nonlinear systems with output measurement noise
Get PDFsummary:In this article, the problems of fault diagnosis (FD) and fault-tolerant control (FTC) are investigated for a class of nonlinear systems with output measurement noise. Due to the influence of measurement noise in the output sensor, the output observation error cannot be accurately obtained, which causes obstacles to the accuracy of FD. To address this issue, an output filter and disturbance estimator are constructed to decrease the negative effects of measurement noise and observer gain disturbances, and a novel non-fragile neural observer is designed to estimate the unknown states. A new evaluation function is also introduced to detect faults. Then, a novel neural FTC controller is proposed in the presence of faults, to ensure that all the closed-loop system signals are semiglobally uniformly ultimately bounded (SGUUB). The effectiveness of the proposed methodology is verified via numerical simulation of a one-link robot system
On the characterization of certain additive maps in prime -rings
No full textsummary:Let be a noncommutative prime ring equipped with an involution `', and let be the maximal symmetric ring of quotients of . Consider the additive maps and . We prove the following under some inevitable torsion restrictions. (a) If and are fixed positive integers such that for all and for all , then . (b) If for all , then . Furthermore, we characterize Jordan left -centralizers in semiprime rings admitting an anti-automorphism . As applications, we find the structure of generalized Jordan -derivations in prime rings and generalize as well as improve all the results of A. Abbasi, C. Abdioglu, S. Ali, M. R. Mozumder (2022)
An effective global path planning algorithm with teaching-learning-based optimization
Get PDFsummary:Due to the widespread use of mobile robots in various applications, the path planning problem has emerged as one of the important research topics. Path planning is defined as finding the shortest path starting from the initial point to the destination in such a way as to get rid of the obstacles it encounters. In this study, we propose a path planning algorithm based on a teaching-learning-based optimization (TLBO) algorithm with Bezier curves in a static environment with obstacles. The proposed algorithm changes the initially randomly selected control points step by step to obtain shorter Bezier curves that do not hit obstacles. We also improve the genetic algorithm-based path planning algorithm. Experimental results show that they provide better paths than other existing algorithms