equation resolution
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2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Meriem Hamdoun ◽  
Mohamed Ben Abdallah ◽  
Mounir Ayadi ◽  
Frédéric Rotella ◽  
Irène Zambettakis

AbstractThe two degree of freedom ball balancing table (BBT) is a well-known didactic tool used to evaluate the effectiveness and performances of many control algorithms for dynamic systems. The present paper proposes to control the ball position of the BBT system via a linear feedback controller based on a functional observer. The parameters of the linear functional observer are determined by applying the direct method which requires neither a Sylvester equation resolution nor canonical transformations. The use of a digital controller has motivated the elaboration of the equations in the discrete time case. In this work, the BBT is tested in real-time to evaluate the proposed controller performances when stabilizing a ball on a reference point. This paper is a continuity of the previous work [12], in which only simulation results have been carried out.


Radiation ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 5-17
Author(s):  
Joël Daouk ◽  
Batoul Dhaini ◽  
Jérôme Petit ◽  
Céline Frochot ◽  
Muriel Barberi-Heyob ◽  
...  

Photodynamic therapy (PDT) is a promising therapeutic strategy for cancers where surgery and radiotherapy cannot be effective. PDT relies on the photoactivation of photosensitizers, most of the time by lasers to produced reactive oxygen species and notably singlet oxygen. The major drawback of this strategy is the weak light penetration in the tissues. To overcome this issue, recent studies proposed to generate visible light in situ with radioactive isotopes emitting charged particles able to produce Cerenkov radiation. In vitro and preclinical results are appealing, but the existence of a true, lethal phototherapeutic effect is still controversial. In this article, we have reviewed previous original works dealing with Cerenkov-induced PDT (CR-PDT). Moreover, we propose a simple analytical equation resolution to demonstrate that Cerenkov light can potentially generate a photo-therapeutic effect, although most of the Cerenkov photons are emitted in the UV-B and UV-C domains. We suggest that CR-PDT and direct UV-tissue interaction act synergistically to yield the therapeutic effect observed in the literature. Moreover, adding a nanoscintillator in the photosensitizer vicinity would increase the PDT efficacy, as it will convert Cerenkov UV photons to light absorbed by the photosensitizer.


Author(s):  
Ngoc Thuy Pham

This paper presents a novel structure combining the port-controlled Hamiltonian (PCH) and Backstepping (BS) nonlinear control for the vector control of the six-phase induction motor (SPIM). In this new scheme, to improve the outer loop’s robustness, the BS technique using the integral tracking errors action is proposed in the speed and flux controllers design. The advantage of this proposed control law is not to increase the complexity of differential equation resolution due to being not increased system states numbers. To enhance more the performance of SPIM drives (SPIMD), port-controlled Hamiltonian (PCH) scheme is used in the inner current loop controllers. In this proposed PCH current controller, the stabilization of controller is achieved via system passivity. In that, the interconnection and damping matrix functions of PCH system are shaped so that the physical (Hamiltonian) system structure is preserved at the closed loop level and the closed loop energy function is equal to the difference between the physical energy of the system and the energy supplied by the controller. The proposed control design is based on combination PCH and BS techniques improve significantly performance and robustness. The proposed speed control scheme is validated by Matlab-Simulink software.


Author(s):  
Maysa Leite Almeida ◽  
Renato Borges Guerra

Neste trabalho apresentamos de forma sucinta os resultados de uma pesquisa de mestrado que teve como objeto o estudo da resolução de equações redutíveis à equação do primeiro grau, sob a perspectiva teórico-metodológica da TAD – Teoria Antropológica do Didático. Nessa investigação engendrou-se um  Percurso de Estudo e Pesquisa (PEP), que nos levou ao encontro de quatro diferentes práticas de resolução de equações do primeiro grau em diferentes épocas. As análises dessas práticas foram realizadas pelo contraste com o Modelo Epistemológico de Referência (MER) adotado, construído para colocar em evidência as propriedades operatórias enquanto regras para resolver equações do primeiro grau. O MER foi construído utilizando as noções de anéis e corpos, mais especificamente, do corpo dos inteiros módulo . Resultados neste percurso nos apontam que as técnicas históricas estão mais próximas das propriedades operatórias e são preferíveis frente a algumas técnicas atuais.


Author(s):  
Francisco Casesnoves

Analytical-convoluted and numerical Gaussian models have been used in recent decades for radiotherapy treatment planning software/calculations, to perform accurately radiation dose delivery –numerical, analytical, or numerical-analytical. The objective of this evoluted-contribution was to obtain an exact dose delivery, 3D analytical-integral-equation solution, for the triple Gaussian model of wedge filters, since previous/initial 2D approximations of other authors, although correct, were not completely exact. Additionally, to set conceptual and mathematical-geometrical differences between the beam modification created by Multi-Leaf Collimator and Wedge Filters, either standard or Conformal. Ever the precision, from mathematical theory algorithms to real laboratory measurements, a series of simulations are presented. The generic triple Gaussian model of Ulmer and Harder sets an Attenuation Exponential Factor, AEF, well approximated in 2 variables, namely, u and z. This evoluted contribution of the research contribution was specially focused on numerical methods and approximation analysis of the integral equation resolution –with extent details about numerical data, Appendix 3. In this paper we set a detailed spatial-spherical geometry discussion/proof towards the determination of a 3D integral form of the delivery dose in water. In other words, with an AEF for magnitude-values of variables u,v, and z. Simulations, based on these new determinations were shown with sharp presentation of the numerical-computational software and functional programming series development. Computing encode techniques are explained with some practical examples for numerical radiotherapy calculus.


2017 ◽  
Vol 8 (6) ◽  
Author(s):  
E. Thiébaut ◽  
C. Goupil ◽  
F. Pesty ◽  
Y. D’Angelo ◽  
G. Guegan ◽  
...  

2014 ◽  
Vol 1065-1069 ◽  
pp. 1547-1550
Author(s):  
Qi Qi Ma ◽  
Yan Chun Wang

Enping sag is located in the west of Zhu 1 sag of Pearl River Mouth Basin. In order to verify the reservoir spreading of Enping sag in Pearl River Mouth Basin and provide the reliable basis for reserves prediction. In this paper, according to the actual seismic data extracting the theoretical seismic model, applying spectral method to construct the acoustic wave equation, and then, deducing the partial differential equation resolution of absorbing boundary condition. Through the forward modeling summarized the seismic response characteristics of oil layer, and making a forward modeling with actual parameters of wells model. Finally obtained the expected effect.


2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Hugues Murray ◽  
Patrick Martin

Based on a 1D Poissons equation resolution, we present an analytic model of inversion charges allowing calculation of the drain current and transconductance in the Metal Oxide Semiconductor Field Effect Transistor. The drain current and transconductance are described by analytical functions including mobility corrections and short channel effects (CLM, DIBL). The comparison with the Pao-Sah integral shows excellent accuracy of the model in all inversion modes from strong to weak inversion in submicronics MOSFET. All calculations are encoded with a simple C program and give instantaneous results that provide an efficient tool for microelectronics users.


Author(s):  
Sylvie Boldo ◽  
François Clément ◽  
Jean-Christophe Filliâtre ◽  
Micaela Mayero ◽  
Guillaume Melquiond ◽  
...  

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