Results 61 to 70 of about 4,000,497 (331)

On the Stability of Quadratic Functional Equations [PDF]

Abstract and Applied Analysis, 2008
Let X, Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx + y) + f(kx-y) = 2k2f(x) + 2f(y) for all x, y ∈ X if and only if the mapping f : X → Y satisfies f(x + y) + f(x-y) = 2f(x) + 2f(y) for all x, y ∈ X. Furthermore, the Hyers‐Ulam‐Rassias stability of the above functional equation in Banach spaces is proven.
Lee, Jung Rye, An, Jong Su, Park, Choonkil   +2 more
openaire   +3 more sources

Algebraic treatment of the Pais-Uhlenbeck oscillator and its PT-variant

, 2019
The algebraic method enables one to study the properties of the spectrum of a quadratic Hamiltonian through the mathematical properties of a matrix representation called regular or adjoint.
Fernández, Francisco M.
core   +1 more source

A Q‐Learning Algorithm to Solve the Two‐Player Zero‐Sum Game Problem for Nonlinear Systems

International Journal of Adaptive Control and Signal Processing, Volume 39, Issue 3, Page 566-581, March 2025.
A Q‐learning algorithm to solve the two‐player zero‐sum game problem for nonlinear systems. ABSTRACT This paper deals with the two‐player zero‐sum game problem, which is a bounded L2$$ {L}_2 $$‐gain robust control problem. Finding an analytical solution to the complex Hamilton‐Jacobi‐Issacs (HJI) equation is a challenging task.
Afreen Islam, Anthony Siming Chen, Guido Herrmann   +2 more
wiley   +1 more source

The GUP and quantum Raychaudhuri equation

Nuclear Physics B, 2018
In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation.
Elias C. Vagenas, Lina Alasfar, Salwa M. Alsaleh, Ahmed Farag Ali   +3 more
doaj   +1 more source

On the integer solutions of quadratic equations [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal), 2004
The main purpose of the paper is to present an algorithm that decides whether an arbitrary quadratic equation with rational coefficients ( in arbitrarily many unknowns) has a solution in positive integers. The algorithm given is in fact more general, and gives further information: it considers integral solutions restricted to lie in the region bounded ...
Grunewald, F, Segal, D
openaire   +1 more source

Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation

, 2018
We prove uniqueness theorems concerning the functional inequalities in connection with an n -dimensional cubic-quadratic-additive equation m ∑ i=1 ci f ( ai1x1 +ai2x2 + · · ·+ainxn ) = 0 by applying the direct method.
Yang-Hi Lee, Soon-Mo Jung, M. Rassias
semanticscholar   +1 more source

Quadratic equations over free groups are NP-complete

, 2008
We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP ...
A. G. Myasnikov, A.I. Mal’cev, A.Yu. Ol’shanskiĭ, I. G. Lysënok, J.P. McCammond, L.P. Comerford Jr., M.R. Garey, N. W. M. Touikan, O. Kharlampovich, R.I. Grigorchuk, R.I. Grigorchuk, V. Diekert   +11 more
core   +2 more sources

Optimized Time–Frequency Analysis for Induction Motor Fault Detection Using Hybrid Differential Evolution and Deep Learning Techniques

International Journal of Adaptive Control and Signal Processing, EarlyView.
Workflow of the parameter optimization process for ITSC fault detection, applying Differential Evolution optimization and the Smooth Pseudo Wigner‐Ville Distribution for signal processing. The optimized parameters are then used in the failure identification pipeline, which combines the signal processing with a YOLO‐based architecture for fault severity
Rafael Martini Silva, Avyner Lorran de Oliveira Vitor, Marcelo Favoretto Castoldi, Alessandro Goedtel, Wesley Angelino Souza   +4 more
wiley   +1 more source

On the Geodesic Form of Non-Relativistic Dynamic Equations

, 1999
It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$.
Mangiarotti, L., Sardanashvily, G.
core   +2 more sources

Data‐Driven Distributed Safe Control Design for Multi‐Agent Systems

International Journal of Adaptive Control and Signal Processing, EarlyView.
This paper presents a data‐driven control barrier function (CBF) technique for ensuring safe control of multi‐agent systems (MASs) with uncertain linear dynamics. A data‐driven quadratic programming (QP) optimization is first developed for CBF‐based safe control of single‐agent systems using a nonlinear controller. This approach is then extended to the
Marjan Khaledi, Bahare Kiumarsi
wiley   +1 more source