• Title/Summary/Keyword: Boundedness

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WEAK HERZ-TYPE HARDY SPACES WITH VARIABLE EXPONENTS AND APPLICATIONS

  • Souad Ben Seghier
    • Journal of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.33-69
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    • 2023
  • Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝn → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

Performance measurement of safety-critical systems based on ordinary differential equations and Petri nets: A case study of nuclear power plant

  • Nand Kumar Jyotish;Lalit Kumar Singh;Chiranjeev Kumar
    • Nuclear Engineering and Technology
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    • v.55 no.3
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    • pp.861-869
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    • 2023
  • This article proposes a novel approach to measure the performance of Safety-Critical Systems (SCS). Such systems contain multiple processing nodes that communicate with each other is modeled by a Petri nets (PN). The paper uses the PN for the performance evaluation of SCS. A set of ordinary differential equations (ODEs) is derived from the Petri net model that represent the state of the system, and the solutions can be used to measure the system's performance. The proposed method can avoid the state space explosion problem and also introduces new metrics of performance, along with their measurement: deadlock, liveness, stability, boundedness, and steady state. The proposed technique is applied to Shutdown System (SDS) of Nuclear Power Plant (NPP). We obtained 99.887% accuracy of performance measurement, which proves the effectiveness of our approach.

EPIDEMIC SEIQRV MATHEMATICAL MODEL AND STABILITY ANALYSIS OF COVID-19 TRANSMISSION DYNAMICS OF CORONAVIRUS

  • S.A.R. BAVITHRA;S. PADMASEKARAN
    • Journal of applied mathematics & informatics
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    • v.41 no.6
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    • pp.1393-1407
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    • 2023
  • In this study, we propose a dynamic SEIQRV mathematical model and examine it to comprehend the dynamics of COVID-19 pandemic transmission in the Coimbatore district of Tamil Nadu. Positiveness and boundedness, which are the fundamental principles of this model, have been examined and found to be reliable. The reproduction number was calculated in order to predict whether the disease would spread further. Existing arrangements of infection-free, steady states are asymptotically stable both locally and globally when R0 < 1. The consistent state arrangements that are present in diseases are also locally steady when R0 < 1 and globally steady when R0 > 1. Finally, the numerical data confirms our theoretical study.

Implementation of Robust Adaptive Controller with Switching Action for Direct Drive Manipulators

  • Kim, Eung-Seok;Lim, Mee-Seub;Kim, Kwon-Ho;Kim, Kwang-Bae
    • Journal of Electrical Engineering and information Science
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    • v.1 no.1
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    • pp.39-44
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    • 1996
  • In this paper, adaptive controller with switching action is designed for rigid body robot manipulators to ensure the uniform stability of the manipulator system without a priori knowledge of the unmodeled dynamics. It will be shown that the parameter estimates are bounded independent of the other closed-loop signals boundedness, and also shown that the tracking error belongs to the normalized error bound via mathematical analisys. The robustness and performance of the proposed adaptive controller is investigated for the two-link direct drive manipulator actuated by VRM(Variable Reluctance Motor).

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MULTIPLICITY RESULTS OF CRITICAL LOCAL EQUATION RELATED TO THE GENUS THEORY

  • Mohsen Alimohammady;Asieh Rezvani;Cemil Tunc
    • Communications of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.1045-1061
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    • 2023
  • Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation $$\{-div[a(x,{\mid}{\nabla}u{\mid}){\nabla}u]\,=\,{\mu}(b(x){\mid}u{\mid}^{s(x)-2}-{\mid}u{\mid}^{r(x)-2})u\;in\;{\Omega},\\u\,=0\,on\;{\partial}{\Omega},$$ where Ω⊆ ℝN is a bounded domain, µ is a positive real parameter, p, r and s are continuous real functions on ${\bar{\Omega}}$ and a(x, ξ) is of type |ξ|p(x)-2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |∇u|)∇u = g(x)|∇u|p(x)-2∇u, where g ∈ L(Ω) and g(x) ≥ 0 and the case $a(x,\,{\mid}{\nabla}u{\mid}){{\nabla}u}\,=\,(1\,+\,{\nabla}u{\mid}^2)^{\frac{p(x)-2}{2}}{\nabla}u$ such that p(x) ≡ p.

Lp-boundedness (1 ≤ p ≤ ∞) for Bergman Projection on a Class of Convex Domains of Infinite Type in ℂ2

  • Ly Kim Ha
    • Kyungpook Mathematical Journal
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    • v.63 no.3
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    • pp.413-424
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    • 2023
  • The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ ℂ2, for 1 < p < ∞, the Bergman projection 𝓟 is bounded from Lp(Ω, dV ) to the Bergman space Ap(Ω); from L(Ω) to the holomorphic Bloch space BlHol(Ω); and from L1(Ω, P(z, z)dV) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.

A method to analyze the flyability of airplane trajectories with specified engine power

  • Gilles Labonte;Vincent Roberge;Mohammed Tarbouchi
    • Advances in aircraft and spacecraft science
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    • v.10 no.5
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    • pp.473-494
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    • 2023
  • This article introduces a formalism for the analysis of airplane trajectories on which the motion is determined by specifying the power of the engines. It explains a procedure to solve the equations of motion to obtain the value of the relevant flight parameters. It then enumerates the constraints that the dynamical abilities of the airplane impose on the amount of fuel used, the speed, the load factor, the lift coefficient, the positivity and upper boundedness of the power available. Examples of analysis are provided to illustrate the method proposed, with rectilinear and circular trajectories. Two very different types of airplanes are used in the examples: a Silver Fox-like small UAV and a common Cessna 182 Skylane.

PREVENTION STRATEGIES TO CONTROL AN EPIDEMIC USING A SEIQHRV MODEL

  • Mohit Soni;Rajesh Kumar Sharma;Shivram Sharma
    • The Pure and Applied Mathematics
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    • v.31 no.2
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    • pp.131-158
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    • 2024
  • This study investigates the impact of precautionary measures, such as isolating exposed individuals, wearing masks, and maintaining physical distance, on preventing infectious disease. A deterministic SEIQHRV epidemic model is employed for this purpose. The model's positivity, boundedness, disease-free, and endemic equilibrium points are identified. A sensitivity test assesses the impact of preventive measures on infected classes. Results show that a basic reproduction number less than unity drives disease eradiction, while a higher unity value encourages the adoption of preventive measures.

An Integration Type Adaptive Compensator for a Class of Linearly Parameterized Systems (선형 파라미터화된 시스템에 대한 적분형 적응보상기)

  • Yoo Byung-Kook;Yang Keun-Ho
    • Journal of the Institute of Convergence Signal Processing
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    • v.6 no.2
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    • pp.82-88
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    • 2005
  • A compensation scheme for a class of linearly parameterized systems is presented. The compensator consists of a typical linearizing control and an adaptive observer with integration type update law, which is based on Speed Gradient (SG) algorithm.. Instead of the intermediate functions of the compensation schemes suggested by other researchers, the proposed compensator is designed with some design functions which guarantee the growth, convexity, attainability, and pseudo gradient conditions in the update law. The scheme achieves the asymptotic stability of the tracking error and the boundedness of the estimation errors. A numerical example is given to demonstrate the validity of the proposed design.

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A Direct Adaptive Fuzzy Control of Nonlinear Systems with Application to Robot Manipulator Tracking Control

  • Cho, Young-Wan;Seo, Ki-Sung;Lee, Hee-Jin
    • International Journal of Control, Automation, and Systems
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    • v.5 no.6
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    • pp.630-642
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    • 2007
  • In this paper, we propose a direct model reference adaptive fuzzy control (MRAFC) for MIMO nonlinear systems whose structure is represented by the Takagi-Sugeno fuzzy model. The adaptive law of the MRAFC estimates the approximation error of the fuzzy logic system so that it provides asymptotic tracking of the reference signal for the systems with uncertain or slowly time-varying parameters. The developed control law and adaptive law guarantee the boundedness of all signals in the closed-loop system. In addition, the plant state tracks the state of the reference model asymptotically with time for any bounded reference input signal. To verify the validity and effectiveness of the MRAFC scheme, the suggested analysis and design techniques are applied to the tracking control of robot manipulator and simulation studies are carried out. In the control design, the MRAFC is combined with feedforward PD control to make the actual joint trajectories of the robot manipulator with system uncertainties track the desired reference joint position trajectories asymptotically stably.