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Academic literature on the topic 'Theorem on Partial'

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Published: 18 May 2024

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Journal articles on the topic "Theorem on Partial"

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ABBAS, MUJAHID, BASIT ALI, and GABRIELA PETRUSEL. "Fixed points of set-valued contractions in partial metric spaces endowed with a graph." Carpathian Journal of Mathematics 30, no. 2 (2014): 129–37. http://dx.doi.org/10.37193/cjm.2014.02.15.

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Hassen, Abbas and Vetro [H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and its App., 159 (2012), 3234–3242] introduced the concept of a partial Hausdorff-Pompeiu metric and proved Nadler’s theorem in this context. Employing the notion of a partial Hausdorff-Pompeiu metric, we investigate the existence of fixed points of set-valued mappings on partial metric spaces endowed with a graph. Our results extend some recent theorems in the literature.
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Karapınar, Erdal, Nabi Shobkolaei, Shaban Sedghi, and Mansour Vaezpour. "A common fixed point theorem for cyclic operators on partial metric spaces." Filomat 26, no. 2 (2012): 407–14. http://dx.doi.org/10.2298/fil1202407k.

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In this paper, we prove a common fixed point theorem for two self-mappings satisfying certain conditions over the class of partial metric spaces. In particular, the main theorem of this manuscript extends some well-known fixed point theorems in the literature on this topic.
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Pogromsky, Alexander Yu. "A partial synchronization theorem." Chaos: An Interdisciplinary Journal of Nonlinear Science 18, no. 3 (September 2008): 037107. http://dx.doi.org/10.1063/1.2959145.

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Lipasov, Pavel P., and Vladimir N. Shchennikov. "Stability with Respect to a Part of Variables under Constant Perturbations of the Partial Equilibrium Position of Differential Equation Nonlinear Systems." Mordovia University Bulletin 28, no. 3 (September 20, 2018): 344–51. http://dx.doi.org/10.15507/0236-2910.028.201803.344-351.

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Introduction. It is impossible to take into account all the forces acting in the process of mathematical modeling of dynamic processes. In order that mathematical models the most accurately describe the dynamic processes, they must include the terms that correspond the constant perturbations. These problems arise in applied tasks. In this paper we consider the case when the system allows for the partial equilibrium position. The aim of this work is to prove the stability theorem for the partial equilibrium position at constant perturbations, which are small at every instant. Materials and Methods. The research objects are nonlinear systems of differential equations that allow for a partial equilibrium position. Using the second Lyapunov method, there are proved the stability theorems for the constant perturbations of the partial equilibrium position, which are small at every instant. Results. Together with the introduction of stability for a part of the variables, it has become necessary to introduce stability for the part of phase variables under constant perturbations. The first stability theorem of the part of phase variables under constant perturbations was obtained by A. S. Oziraner. In this work, we prove a theorem of the stability of the constant perturbations of the partial equilibrium position, small at every instant. It should be noted that there is no stability theorems of constant perturbations for the partial equilibrium position. Thus, the theorem proved in this work is of a pioneer nature. Conclusions. The theorem 3 proved in the work is the development of the mathematical theory of stability. The results of this work are applicable in the mechanics of controlled motion, nonlinear system.
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Hannabou, Mohamed, Khalid Hilal, and Ahmed Kajouni. "Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems." Journal of Mathematics 2020 (November 12, 2020): 1–9. http://dx.doi.org/10.1155/2020/5729128.

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In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.
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Al-hawasy, Jamil Amir, and Safaa J. Mohammed Al-Qaisi. "The Continuous Classical Boundary Optimal Control of a Couple Nonlinear Elliptic Partial Differential Equations with State Constraints." Al-Mustansiriyah Journal of Science 30, no. 1 (August 15, 2019): 143. http://dx.doi.org/10.23851/mjs.v30i1.464.

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This paper is concerned with, the proof of the existence and the uniqueness theorem for the solution of the state vector of a couple of nonlinear elliptic partial differential equations using the Minty-Browder theorem, where the continuous classical boundary control vector is given. Also the existence theorem of a continuous classical boundary optimal control vector governing by the couple of nonlinear elliptic partial differential equation with equality and inequality constraints is proved. The existence of the uniqueness solution of the couple of adjoint equations associated with the considered couple of the state equations with equality and inequality constraints is studied. The necessary conditions theorem and the sufficient conditions theorem for optimality of the couple of nonlinear elliptic equations with equality and inequality constraints are proved using the Kuhn-Tucker-Lagrange multipliers theorems
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Ge, Zheng-Ming, and Jung-Kui Yu. "Pragmatical Asymptotical Stability Theorems on Partial Region and for Partial Variables with Applications to Gyroscopic Systems." Journal of Mechanics 16, no. 4 (December 2000): 179–87. http://dx.doi.org/10.1017/s1727719100001842.

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ABSTRACTFor a long time, all stability theorems are concerned with the stability of the zero solution of the differential equations of disturbed motion on the whole region of the neighborhood of the origin. But for various problems of dynamical systems, the stability is actually on partial region. In other words, the traditional mathematical model is unmatched with the dynamical reality and artificially sets too strict demand which is unnecessary. Besides, although the stability for many problems of dynamical systems may not be mathematical asymptotical stability, it is actual asymptotical stability — namely “pragmatical asymptotical stability” which can be introduced by the concept of probability. In order to fill the gap between the traditional mathematical model and dynamical reality of various systems, one pragmatical asymptotical stability theorem on partial region and one pragmatical asymptotical stability theorem on partial region for partial variables are given and applications for gyroscope systems are presented.
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Tarasenko, Stepan. "Sperner's Theorem." Modeling Control and Information Technologies, no. 5 (November 21, 2021): 87–89. http://dx.doi.org/10.31713/mcit.2021.27.

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In the course of this work the analysis of the proofs of the simple case of the Sperner Theorem was carried out, the approaches to the proof of the complicated case were proposed, the partial cases of multisets were considered, the theorem for these partial cases was proved, the generalized theorem was proved for some partial cases. (the number of n - element multisets of k - element multiset), developed a small program to graphically show this fact, proved the bimonotonicity of this function. Also, in the course of this work, one of the possible applications of this theorem was considered, namely, the «Procedure for secret distribution», but the applied potential of the theorem does not end there.
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Guo, Shuangjian, Xiaohui Zhang, Yuanyuan Ke, and Yizheng Li. "Enveloping actions and duality theorems for partial twisted smash products." Filomat 34, no. 10 (2020): 3217–27. http://dx.doi.org/10.2298/fil2010217g.

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In this paper, we first generalize the theorem about the existence of an enveloping action to a partial twisted smash product. Then we construct a Morita context between the partial twisted smash product and the twisted smash product related to the enveloping action. Finally, we present versions of the duality theorems of Blattner-Montgomery for partial twisted smash products.
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Góźdź, A., and M. Góźdź. "Spectral theorem and partial symmetries." Physics of Atomic Nuclei 75, no. 10 (October 2012): 1195–202. http://dx.doi.org/10.1134/s1063778812100055.

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Dissertations / Theses on the topic "Theorem on Partial"

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Sarkar, Koushik. "Topology of different metric spaces and fixed point theories." Thesis, University of North Bengal, 2021. http://ir.nbu.ac.in/handle/123456789/4380.

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Kreuger, Per. "Computational Issues in Calculi of Partial Inductive Definitions." Doctoral thesis, Decisions, Networks and Analytics lab, 1995. http://urn.kb.se/resolve?urn=urn:nbn:se:ri:diva-21196.

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We study the properties of a number of algorithms proposed to explore the computational space generated by a very simple and general idea: the notion of a mathematical definition and a number of suggested formal interpretations ofthis idea. Theories of partial inductive definitions (PID) constitute a class of logics based on the notion of an inductive definition. Formal systems based on this notion can be used to generalize Horn-logic and naturally allow and suggest extensions which differ in interesting ways from generalizations based on first order predicate calculus. E.g. the notion of completion generated by a calculus of PID and the resulting notion of negation is completely natural and does not require externally motivated procedures such as "negation as failure". For this reason, computational issues arising in these calculi deserve closer inspection. This work discuss a number of finitary theories of PID and analyzethe algorithmic and semantical issues that arise in each of them. There has been significant work on implementing logic programming languages in this setting and we briefly present the programming language and knowledge modelling tool GCLA II in which many of the computational prob-lems discussed arise naturally in practice.

Also published as SICS Dissertation no. SICS-D-19

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Aziz, Waleed. "Analytic and algebraic aspects of integrability for first order partial differential equations." Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1468.

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This work is devoted to investigating the algebraic and analytic integrability of first order polynomial partial differential equations via an understanding of the well-developed area of local and global integrability of polynomial vector fields. In the view of characteristics method, the search of first integrals of the first order partial differential equations P(x,y,z)∂z(x,y) ∂x +Q(x,y,z)∂z(x,y) ∂y = R(x,y,z), (1) is equivalent to the search of first integrals of the system of the ordinary differential equations dx/dt= P(x,y,z), dy/dt= Q(x,y,z), dz/dt= R(x,y,z). (2) The trajectories of (2) will be found by representing these trajectories as the intersection of level surfaces of first integrals of (1). We would like to investigate the integrability of the partial differential equation (1) around a singularity. This is a case where understanding of ordinary differential equations will help understanding of partial differential equations. Clearly, first integrals of the partial differential equation (1), are first integrals of the ordinary differential equations (2). So, if (2) has two first integrals φ1(x,y,z) =C1and φ2(x,y,z) =C2, where C1and C2 are constants, then the general solution of (1) is F(φ1,φ2) = 0, where F is an arbitrary function of φ1and φ2. We choose for our investigation a system with quadratic nonlinearities and such that the axes planes are invariant for the characteristics: this gives three dimensional Lotka– Volterra systems x' =dx/dt= P = x(λ +ax+by+cz), y' =dy/dt= Q = y(µ +dx+ey+ fz), z' =dz/dt= R = z(ν +gx+hy+kz), where λ,µ,ν 6= 0. v Several problems have been investigated in this work such as the study of local integrability and linearizability of three dimensional Lotka–Volterra equations with (λ:µ:ν)–resonance. More precisely, we give a complete set of necessary and sufficient conditions for both integrability and linearizability for three dimensional Lotka-Volterra systems for (1:−1:1), (2:−1:1) and (1:−2:1)–resonance. To prove their sufficiency, we mainly use the method of Darboux with the existence of inverse Jacobi multipliers, and the linearizability of a node in two variables with power-series arguments in the third variable. Also, more general three dimensional system have been investigated and necessary and sufficient conditions are obtained. In another approach, we also consider the applicability of an entirely different method which based on the monodromy method to prove the sufficiency of integrability of these systems. These investigations, in fact, mean that we generalized the classical centre-focus problem in two dimensional vector fields to three dimensional vector fields. In three dimensions, the possible mechanisms underling integrability are more difficult and computationally much harder. We also give a generalization of Singer’s theorem about the existence of Liouvillian first integrals in codimension 1 foliations in Cnas well as to three dimensional vector fields. Finally, we characterize the centres of the quasi-homogeneous planar polynomial differential systems of degree three. We show that at most one limit cycle can bifurcate from the periodic orbits of a centre of a cubic homogeneous polynomial system using the averaging theory of first order.
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Han, Zhi. "Applications of stochastic control and statistical inference in macroeconomics and high-dimensional data." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54401.

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This dissertation is dedicated to study the modeling of drift control in foreign exchange reserves management and design the fast algorithm of statistical inference with its application in high dimensional data analysis. The thesis has two parts. The first topic involves the modeling of foreign exchange reserve management as an drift control problem. We show that, under certain conditions, the control band policies are optimal for the discounted cost drift control problem and develop an algorithm to calculate the optimal thresholds of the optimal control band policy. The second topic involves the fast computing algorithm of partial distance covariance statistics with its application in feature screening in high dimensional data. We show that an O(n log n) algorithm for a version of the partial distance covariance exists, compared with the O(n^2) algorithm implemented directly accordingly to its definition. We further propose an iterative feature screening procedure in high dimensional data based on the partial distance covariance. This procedure enjoys two advantages over the correlation learning. First, an important predictor that is marginally uncorrelated but jointly correlated with the response can be picked by our procedure and thus entering the estimation model. Second, our procedure is robust to model mis- specification.
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Leahy, James-Michael. "On parabolic stochastic integro-differential equations : existence, regularity and numerics." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10569.

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In this thesis, we study the existence, uniqueness, and regularity of systems of degenerate linear stochastic integro-differential equations (SIDEs) of parabolic type with adapted coefficients in the whole space. We also investigate explicit and implicit finite difference schemes for SIDEs with non-degenerate diffusion. The class of equations we consider arise in non-linear filtering of semimartingales with jumps. In Chapter 2, we derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by Lévy driven stochastic differential equations (SDEs) with adapted coefficients in weighted Hölder norms using the Sobolev embedding theorem and the change of variable formula. As an application of some basic properties of flows of Weiner driven SDEs, we prove the existence and uniqueness of classical solutions of linear parabolic second order stochastic partial differential equations (SPDEs) by partitioning the time interval and passing to the limit. The methods we use allow us to improve on previously known results in the continuous case and to derive new ones in the jump case. Chapter 3 is dedicated to the proof of existence and uniqueness of classical solutions of degenerate SIDEs using the method of stochastic characteristics. More precisely, we use Feynman-Kac transformations, conditioning, and the interlacing of space inverses of stochastic flows generated by SDEs with jumps to construct solutions. In Chapter 4, we prove the existence and uniqueness of solutions of degenerate linear stochastic evolution equations driven by jump processes in a Hilbert scale using the variational framework of stochastic evolution equations and the method of vanishing viscosity. As an application, we establish the existence and uniqueness of solutions of degenerate linear stochastic integro-differential equations in the L2-Sobolev scale. Finite difference schemes for non-degenerate SIDEs are considered in Chapter 5. Specifically, we study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear SIDEs and show that the rate is of order one in space and order one-half in time.
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Melo, Gustavo Cavalcanti. "Funções parciais recursivas e funções parcialmente Turing-computáveis: uma prova de equivalência." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9586.

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In the thirties of the last century, several formal versions for the intuitive notion of algorithmic function were offered. Among them, the version of the recursive functions and the version of the Turing-computable functions. Posteriorly, such versions were extended in order to also include the partial algorithmic functions, giving rise, in this way, to the version of the partial recursive functions and to the version of the partially Turing-computable functions. In this context, this research, located into Computability Theory domain and built in the light of theoretical assumptions of Davis (1982), Mendelson (2009), Dias & Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), among others, is intended to rebuild the proof that the given formal versions referred to the intuitive notion of partial algorithmic function, despite being conceptually distinct, they are extensionally equivalents in the sense that they determine the same set of theoretical-numerical functions. As a part of this rebuilding, we shall prove, in na unprecedented way, using quintuples, that every partial recursive function is partially Turing-computable. In the literature, this theorem is proved by means of a set of quadruples. However, defining a lower cardinality set constructed by quintuples, it is possible to prove it in a smaller time interval, which representes a gain from the computational point of view. Besides presenting this alternative proof, posed by the Church-Turing thesis that the set of partial recursive functions includes all the partial algorithmic functions, we shall investigate if this set itself and its infinite subsets are or are not algorithmic. In this survey, we shall demonstrate, in arithmetical terms, with the aid of Rice‟s theorem, that although the set of partial recursive functions is algorithmic, all its subsets which are different from the empty set are not, among which are the set of recursive functions and the set of primitive recursive functions.
Na década de 30 do século passado, foram oferecidas várias versões formais para a noção intuitiva de função algorítmica. Dentre elas, a versão das funções recursivas e a versão das funções Turing-computáveis. Posteriormente, tais versões foram estendidas a fim de abranger também as funções parciais algorítmicas, dando origem, deste modo, à versão das funções parciais recursivas e à versão das funções parcialmente Turing-computáveis. Nesse contexto, esta pesquisa, situada dentro do domínio da Teoria da Computabilidade e construída à luz dos pressupostos teóricos de Davis (1982), Mendelson (2009), Dias e Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), entre outros, destina-se a reconstruir a prova de que as referidas versões formais dadas para a noção intuitiva de função parcial algorítmica, apesar de conceitualmente distintas, são extensionalmente equivalentes no sentido de que elas determinam o mesmo conjunto de funções numéricas. Como parte desta reconstrução, provaremos, de modo inédito, mediante o uso de quíntuplas, que toda função parcial recursiva é parcialmente Turing-computável. Na literatura especializada, esse teorema é provado por meio de um conjunto de quádruplas. Porém, definindo um conjunto de menor cardinalidade constituído por quíntuplas, é possível prová-lo em um intervalo menor de tempo, o que representa um ganho do ponto de vista computacional. Além de apresentar essa prova alternativa, posto pela Tese de Church-Turing que o conjunto das funções parciais recursivas contém todas as funções parciais algorítmicas, investigaremos se ele próprio e os seus infinitos subconjuntos são ou não algorítmicos. Nesta investigação, demonstraremos, em termos aritméticos, com o auxílio do Teorema de Rice, que embora o conjunto das funções parciais recursivas seja algorítmico, todos os seus subconjuntos diferentes do conjunto vazio não o são, dentre os quais estão o conjunto das funções recursivas e o conjunto das funções recursivas primitivas.
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Yue, Wen. "Absolute continuity of the laws, existence and uniqueness of solutions of some SDEs and SPDEs." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/absolute-continuity-of-the-laws-existence-and-uniqueness-of-solutions-of-some-sdes-and-spdes(2bc80de8-7c36-453f-a7c2-69fa4ee0e705).html.

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This thesis consists of four parts. In the first part we recall some background theory that will be used throughout the thesis. In the second part, we studied the absolute continuity of the laws of the solutions of some perturbed stochastic differential equaitons(SDEs) and perturbed reflected SDEs using Malliavin calculus. Because the extra terms in the perturbed SDEs involve the maximum of the solution itself, the Malliavin differentiability of the solutions becomes very delicate. In the third part, we studied the absolute continuity of the laws of the solutions of the parabolic stochastic partial differential equations(SPDEs) with two reflecting walls using Malliavin calculus. Our study is based on Yang and Zhang \cite{YZ1}, in which the existence and uniqueness of the solutions of such SPDEs was established. In the fourth part, we gave the existence and uniqueness of the solutions of the elliptic SPDEs with two reflecting walls and general diffusion coefficients.
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Barles, Guy. "Contribution à la théorie des solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications à des problèmes de contrôle optimal et de perturbations singulières." Paris 9, 1988. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1988PA090004.

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Nous présentons dans ce travail divers résultats concernant les équations de Hamilton-Jacobi du premier ordre ainsi que leurs applications à certains problèmes de contrôle optimal déterministe et de perturbations singulières. La première partie est consacrée à l'étude des solutions continues: nous donnons divers résultats d'existence, d'unicité et de régularité à la fois locale et globale). La deuxième partie décrit une étude systématique des solutions discontinues: elle fournit une approche générale très simple des problèmes de temps de sortie, de contrôle non-borne et de perturbations singulières, avec, en particulier, des applications dans le cadre des grandes déviations
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Santos, Renato Augusto Nascimento. "Existência de soluções para uma classe de problemas elípticos não quadráticos no infinito." Universidade Federal da Paraí­ba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7414.

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We study the deformation theorem using the condition introduced by Cerami [8]. Furthermore, we study the following Dirichlet problem: ( u = f(x; u); x 2 u = 0; x 2 @ where is a smooth and bounded domain in RN and f : R ! R is a Caratheodory function with subcritical growth. In the above problem, we use the condition of Cerami [8] again, to ensure the existence of non-trivial solution. For this purpose, we use General Minimax Theorem proved by Bartolo in [12].
Neste trabalho, estudamos o Teorema de Deformação usando a condição introduzida por Cerami [8]. Além disso, estudamos o seguinte problema de Dirichlet: ( u = f(x; u); x 2 u = 0; x 2 @ onde e um domínio suave e limitado em RN e f : R ! R é uma função de Caratheodory com crescimento subcrítico. No problema acima, utilizamos novamente a condição de Cerami [8], para garantir a existência de solução não-trivial, para este propósito, usaremos Teorema Geral de Minimax provado pelo Bartolo em [12].
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Safi, Mohammed. "Stabilité de Lyapunov de systèmes couplés impliquant une équation de transport." Thesis, Toulouse, ISAE, 2018. http://www.theses.fr/2018ESAE0022/document.

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L’objet de cette thèse est l’étude des propriétés de stabilité et contrôle pour des systèmes linéaires écrits à l’aide d’équations aux dérivées partielles (EDP) ou d’équations à retard. Nous souhaitons exploiter dans cette thèse les liens qui existent entre ces deux classes de systèmes de dimension infinie afin de développer une nouvelle approche permettant leur analyse. En effet dans plusieurs applications, il est possible de choisir l’un ou l’autre de ces deux types de systèmes pour modéliser la dynamique considérée. Par exemple, les phénomènes de congestion dans un réseau routier peuvent être modélisés à l’aide d’EDP de type transport [JKC], mais aussi par un modèle à retard distribué [MMN] ou encore à retard discret [SN]. On peut également renvoyer aux travaux de Krstic [K] sur la formulation d’un système à retard comme un système EDP. Ces deux classes de systèmes sont des cas particuliers de systèmes de dimension infinie, et contrairement aux cas de systèmes de dimension finie, on parle de fonctions d’état plutôt que vecteur d’état. Cela implique que l’analyse associée est plus délicate et fait appel à des outils dédiés. Dans le cadre de la thèse, l’étudiant se focalisera sur les approches basées sur une extension du théorème de Lyapunov pour les systèmes de dimension infinie utilisant des fonctionnelles spécifiques. Comme pour la modélisation, l’analyse de stabilité des systèmes à retard ou de type EDP peut être menée à l’aide de fonctionnelles de Lyapunov très similaires. Nous souhaitons que cette thèse tire parti des travaux existants dans les deux communautés sur les systèmes à retards et de type EDP pour développer une approche novatrice et unifiée pour l’analyse et le contrôle de systèmes de dimension infinie. Pour cela, le candidat s’appuiera sur ses acquis en automatique et en mathématiques ainsi que sur l’expertise des deux encadrants. Plusieurs contributions sont attendues durant la thèse. Dans un premier temps, il sera question d’étendre des résultats récents [SG1,2] développés pour l’analyse de stabilité des systèmes à retards au cas de systèmes régis par des EDP. Ces premiers résultats auront vocation à servir de base pour l’étude de la synthèse de commandes robustes dans le cadre d’applications telles que le contrôle de trafic routier [MMN], le contrôle de vibration [RBPA], etc… Cette thèse en automatique requiert plusieurs compétences parmi lesquelles des connaissances sur la théorie de Lyapunov pour les systèmes avec ou sans retard, sur les inégalités matricielles linéaires tout en s’appuyant sur les outils de mathématiques appliquées pour l’étude des équations aux dérivées partielles (algèbre linéaire, analyse fonctionnelle, espaces de Hilbert, de Sobolev)
The purpose of this thesis is the study of stability and control properties for linear systems described by partial differential equations (PDE) or delay differential equations. We wish to use in this thesis the relationship between these two classes of infinite-dimensional systems in view of developing a new paradigm for their analysis. Indeed, in many applications, it is possible to choose one or the other of these two classes of systems to model the dynamics of the system under consideration. For example, traffic flow can be modeled using PDE type of transportation [JKC], but also by a distributed delay model [SMP] or discrete delay [SN]. We may also refer to the work of Krstic [K] on the formulation of a delay system as an PDE system. These two classes of systems are special cases of infinite dimensional systems, unlike the case of finite-dimensional systems, we better called state functions rather than the state vector. This implies that the analysis is more delicate and refers to the use of dedicated tools. As part of the thesis, the student will focus on approaches based on an extension of Lyapunov theorem for infinite dimensional systems using specific functional. As for the modeling process, the stability analysis of delayed or PDE type systems can be conducted using very similar Lyapunov functionals. We hope that this thesis builds on existing work in the two communities on delay systems and PDE to develop an innovative and unified approach to the analysis and control of infinite dimensional systems. To do so, the candidate will build on its skills in automatic and mathematics as well as the on from expertise of both supervisors. Several contributions are expected during the thesis . Initially, we aim at extedning recent results [SG13,14] developed in the context of the stability analysis of delay systems to the case of systems governed by PDE. These first results will provide the basis for the design of robust control laws for various applications including traffic control, vibration control, etc ... Cette thèse portera sur l’étude des propriétés de stabilité et de contrôle des systèmes linéaires de dimension infinie, plus particulièrement écrits à l’aide d’EDP ou d’équations à retard. L’intérêt naturel pour l’étude de cette classe de systèmes à la frontière entre mathématiques appliquées et automatique connaît un succès grandissant de part la large gamme d’applications en contrôle pouvant être décrites par ces modèles : en ingénierie, biologie, informatique… L’émulation scientifique entre systèmes à retard et systèmes de type EDP permettra en outre à cette thèse de tirer parti des méthodes et outils propres à chacun des ces domaines. This PhD proposal in automatic control requires several skills including knowledge on Lyapunov theory for systems with or without delay , on linear matrix inequalities while relying on mathematical tools applied in the study of partial differential equations ( linear algebra functional analysis , Hilbert spaces , Sobolev)
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Books on the topic "Theorem on Partial"

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1963-, Zhang Tusheng, and Zhao Huaizhong 1964-, eds. The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations. Providence, R.I: American Mathematical Society, 2008.

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Zwiers, J. Compositionality, concurrency, and partial correctness: Proof theories for networks of processes and their relationship. Berlin: Springer-Verlag, 1989.

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Jean-Yves, Chemin, Danchin Raphaël, and SpringerLink (Online service), eds. Fourier Analysis and Nonlinear Partial Differential Equations. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Ghandehari, Mostafa. Ray optics on surfaces. Arlington: Dept. of Mathematics, University of Texas at Arlington, 1997.

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Krantz, Steven G. The Implicit Function Theorem: History, Theory, and Applications. New York, NY: Springer New York, 2013.

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Compositionality, concurrency, and partial correctness: Proof theories for networks of processes and their relationship. Berlin: Springer-Verlag, 1989.

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A new approach to the local embedding theorem of CR-structures for n [greater than or equal to] 4 (the local solvability for the operator [overbarred partial] B in the abstract sense). Providence, R.I: American Mathematical Society, 1987.

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Hoehnke, Hans-Jürgen. Partial algebras and their theories. New York: Springer, 2005.

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Vasilʹevich, Fedori︠u︡k Mikhail, ed. Partial differential equations. Berlin: Springer, 1999.

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Partial stability and control. Boston: Birkhauser, 1998.

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Book chapters on the topic "Theorem on Partial"

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Arnold, Vladimir I. "Spherical Functions. Maxwell’s Theorem. The Removable Singularities Theorem." In Lectures on Partial Differential Equations, 105–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05441-3_11.

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Ebert, Marcelo R., and Michael Reissig. "Holmgren’s Uniqueness Theorem." In Methods for Partial Differential Equations, 49–55. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66456-9_5.

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Georgiev, Svetlin G., and Khaled Zennir. "The Cauchy–Kovalevskaya Theorem." In Multiplicative Partial Differential Equations, 242–56. Boca Raton: Chapman and Hall/CRC, 2023. http://dx.doi.org/10.1201/9781003440116-7.

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Ebert, Marcelo R., and Michael Reissig. "The Cauchy-Kovalevskaja Theorem." In Methods for Partial Differential Equations, 37–48. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66456-9_4.

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Ferguson, Thomas S. "Partial Converses to Theorem 1." In A Course in Large Sample Theory, 8–12. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-4549-5_2.

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DiBenedetto, Emmanuele. "Quasi-Linear Equations and the Cauchy—Kowalewski Theorem." In Partial Differential Equations, 29–50. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4899-2840-5_2.

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DiBenedetto, Emmanuele. "Quasi-Linear Equations and the Cauchy–Kowalewski Theorem." In Partial Differential Equations, 17–35. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4552-6_2.

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Costa, Peter J. "The Hartman–Grobman Theorem." In Select Ideas in Partial Differential Equations, 173–98. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-031-02434-4_9.

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Talenti, Giorgio. "An Embedding Theorem." In Partial Differential Equations and the Calculus of Variations, 919–24. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4684-9196-8_39.

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Talenti, Giorgio. "An Embedding Theorem." In Partial Differential Equations and the Calculus of Variations, 919–24. Boston, MA: Birkhäuser Boston, 1989. http://dx.doi.org/10.1007/978-1-4615-9831-2_18.

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Conference papers on the topic "Theorem on Partial"

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Falkensteiner, Sebastian, Cristhian Garay-López, Mercedes Haiech, Marc Paul Noordman, Zeinab Toghani, and François Boulier. "The fundamental theorem of tropical partial differential algebraic geometry." In ISSAC '20: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3373207.3404040.

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Jianyi Jing, Lequan Min, and Geng Zhao. "Partial generalized synchronization theorem of discrete systems with applications in encryption scheme." In 2007 5th International Conference on Communications, Circuits and Systems. IEEE, 2007. http://dx.doi.org/10.1109/icccas.2007.6247594.

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Ben-David, Shalev, and Eric Blais. "A Tight Composition Theorem for the Randomized Query Complexity of Partial Functions: Extended Abstract." In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2020. http://dx.doi.org/10.1109/focs46700.2020.00031.

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Ševček, Tomáš. "The Consumer Surplus Line Integral Revisited." In EDAMBA 2022: 25th International Scientific Conference for Doctoral Students and Post-Doctoral Scholars. Bratislava: University of Economics in Bratislava, 2023. http://dx.doi.org/10.53465/edamba.2022.9788022550420.453-461.

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The consumer surplus line integral is a concept which has helped shed some light upon the consumer’s welfare changes due to changes in product prices and/or changes in the consumer’s income. The main objective of this article is to derive the consumer surplus line integral making use of the divergence theorem as well as Green’s theorem. This approach enables the interested reader to come up with other line integrals with the same value. To our knowledge, this is one of the very first direct applications of the two theorems in economics. A partial objective is to summarize the fundamental ideas, definitions and theorems from a branch of vector calculus dealing with curves and line integrals. Therefore, the target audience of the article consists of not only economists studying the consumer’s surplus, but also of quantitative-minded economists seeking for new research methods.
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Nguyen, Thanh H., Arunesh Sinha, and He He. "Partial Adversarial Behavior Deception in Security Games." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/40.

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Learning attacker behavior is an important research topic in security games as security agencies are often uncertain about attackers' decision making. Previous work has focused on developing various behavioral models of attackers based on historical attack data. However, a clever attacker can manipulate its attacks to fail such attack-driven learning, leading to ineffective defense strategies. We study attacker behavior deception with three main contributions. First, we propose a new model, named partial behavior deception model, in which there is a deceptive attacker (among multiple attackers) who controls a portion of attacks. Our model captures real-world security scenarios such as wildlife protection in which multiple poachers are present. Second, we introduce a new scalable algorithm, GAMBO, to compute an optimal deception strategy of the deceptive attacker. Our algorithm employs the projected gradient descent and uses the implicit function theorem for the computation of gradient. Third, we conduct a comprehensive set of experiments, showing a significant benefit for the attacker and loss for the defender due to attacker deception.
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Lian, Ren-Zun, and Long Li. "Partial-Structure-Oriented Work-Energy Theorem (PS-WET) Governing Multi-Coil Wireless Power Transfer (WPT) Phenomenon." In 2022 IEEE MTT-S International Microwave Workshop Series on Advanced Materials and Processes for RF and THz Applications (IMWS-AMP). IEEE, 2022. http://dx.doi.org/10.1109/imws-amp54652.2022.10106950.

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Lian, Ren-Zun, and Long Li. "Characteristic Mode Analysis for Metallic Yagi–Uda Transmitting Antennas Based on Partial-Structure-Oriented Work-Energy Theorem." In 2022 IEEE 8th International Conference on Computer and Communications (ICCC). IEEE, 2022. http://dx.doi.org/10.1109/iccc56324.2022.10065888.

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Nakhaie Jazar, G., M. Mahinfalah, J. Christopherson, A. Khazaei, and G. Nazari. "Periodicity Conditions for Third-Order Nonlinear With Application to Wave Propagation in Relaxing Media." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35090.

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It is known that wave propagation in nonlinear continues media, such as acoustic waves in solids, water waves, and solitary waves in arteries, can be reduced to a third order ordinary differential equations. They can be cast in a general third order ODE as x‴‴‴+f(t,x,x′,x″)=0. However, having an ODE as a reduced model for a phenomenon expressible by a partial differential equation lacks a proof to grantee for having a periodic solution. A third-order existence theorem has been proven to establish the sufficient conditions of periodicity for the above general third-order ODE. However, the equation is too general. In this paper we examine the following more specific equation x‴‴‴+g1(x′)x″+g2(x)x′+g(x,x′,t)=e(t). and prove a new theorem to establish the sufficient condition for its periodicity. To obtain the periodicity conditions, the Schauder’s fixed-point theorem is implemented. A numerical method is also developed for rapid convergence.
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Xu, Shugen, Weiqiang Wang, and Yan Liu. "A New Approach to Elastodynamic Response of Cylindrical Shell Based on Generalized Solution Structure Theorem for Wave Equation." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-25233.

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In this paper, a generalized solution structure theorem has been provided. It can be use to solve the wave equation about the structural response of cylinder under the dynamic pressure. This new approach also can be used to solve a batch of partial differential equations with the similar form. A detailed derivation process has been given to show how the solution is obtained. Finally, a practical example is presented, and all the elastodynamic response data at any point during dynamic pressure can be acquired conveniently.
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Marsden, Gary C., F. Kiamilev, S. Esener, and Sing H. Lee. "Optical Matrix Encoding for Constraint Satisfaction." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/optcomp.1989.mc2.

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Many Artificial Intelligence problems, such as theorem proving, computer vision, and expert systems, can be seen as constraint satisfaction problems1,2,3. In such problems, constraints are given on any possible solution. Most often, the problem is either explicitly stated in terms of allowed partial solutions or can be converted to such a representation. The objective is to find one or more solutions satisfying all constraints simultaneously, or the determination that no such solution exists. A simplistic approach to solving constraint satisfaction problems is to generate all possible solutions, then test each against the constraints to see if indeed they are satisfied. The process of backtracking provides a marginal improvement by testing increasingly larger partial solutions. Consistent Labelling is a more efficient procedure which eliminates allowed partial solutions that conflict with one another 2. A problem is represented in a constraint network. Arc and path Consistent Labelling eliminate allowed partial solutions that are inconsistent over the smallest closed loops. The remaining allowed partial solutions can then be used in an efficient backtracking search. Using Consistent Labelling on larger loops, it is possible to obtain solutions to constraint satisfaction problems without backtracking4.
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Reports on the topic "Theorem on Partial"

1

Bao, Gang, and William W. Symes. A Trace Theorem for Solutions of Linear Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, September 1989. http://dx.doi.org/10.21236/ada455263.

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Katz, Lawrence. Efficiency Wage Theories: A Partial Evaluation. Cambridge, MA: National Bureau of Economic Research, April 1986. http://dx.doi.org/10.3386/w1906.

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Molinari, Francesca, Arie Beresteanu, and Ilya Molchanov. Partial identification using random set theory. Institute for Fiscal Studies, December 2010. http://dx.doi.org/10.1920/wp.cem.2010.4010.

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Hatfield, John William, and Gerard Padró Miquel. A Political Economy Theory of Partial Decentralization. Cambridge, MA: National Bureau of Economic Research, December 2008. http://dx.doi.org/10.3386/w14628.

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Chung, Sung G., and Thomas F. George. Generalization of Levinson's Theorem to Particle-Matter Interactions. Fort Belvoir, VA: Defense Technical Information Center, January 1987. http://dx.doi.org/10.21236/ada176501.

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Shafi, Qaisar, Steven Barr, Thomas Gaisser, and Todor Stanev. Particle Theory & Cosmology. Office of Scientific and Technical Information (OSTI), March 2015. http://dx.doi.org/10.2172/1213669.

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Sage, M. (Problems in particle theory). Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/6366633.

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Mansouri, F., P. Suranyi, and L. C. R. Wijewardhana. Research in particle theory. Office of Scientific and Technical Information (OSTI), October 1991. http://dx.doi.org/10.2172/6095761.

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Mansouri, F., P. Suranyi, and L. C. R. Wijewardhana. Research in particle theory. Office of Scientific and Technical Information (OSTI), October 1992. http://dx.doi.org/10.2172/7073633.

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Mansouri, F., P. Suranyi, L. Wijewardhana, and L. Witten. Research in particle theory. Office of Scientific and Technical Information (OSTI), December 1989. http://dx.doi.org/10.2172/5149404.

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