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Rozprawy doktorskie na temat „Optimal Transportation”

Autor: Grafiati
Data publikacji: 4 czerwca 2021
Data aktualizacji: 14 marca 2023

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1

Giddings, Robin Douglas. "Mesh movement via optimal transportation." Thesis, University of Reading, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.515757.

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Cavalletti, Fabio. "Optimal transportation in geodesic spaces." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4213.

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Zhang, Xiaoning. "Optimal road pricing in transportation networks /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?CIVL%202003%20ZHANG.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2003.<br>Includes bibliographical references (leaves 230-240). Also available in electronic version. Access restricted to campus users.
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Figalli, Alessio. "Optimal transportation and action-minimizing measures." Doctoral thesis, Lyon, École normale supérieure (sciences), 2007. http://www.theses.fr/2007ENSL0422.

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Figalli, Alessio. "Optimal transportation and action-minimizing measures." Doctoral thesis, Scuola Normale Superiore, 2007. http://hdl.handle.net/11384/85683.

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Bonnotte, Nicolas. "Unidimensional and Evolution Methods for Optimal Transportation." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00946781.

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In dimension one, optimal transportation is rather straightforward. The easiness with which a solution can be obtained in that setting has recently been used to tackle more general situations, each time thanks to the same method. First, disintegrate your problem to go back to the unidimensional case, and apply the available 1D methods to get a first result; then, improve it gradually using some evolution process.This dissertation explores that direction more thoroughly. Looking back at two problems only partially solved this way, I show how this viewpoint in fact allows to go even further.The
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Nenna, Luca. "Numerical Methods for Multi-Marginal Optimal Transportation." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLED017/document.

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Dans cette thèse, notre but est de donner un cadre numérique général pour approcher les solutions des problèmes du transport optimal (TO). L’idée générale est d’introduire une régularisation entropique du problème initial. Le problème régularisé correspond à minimiser une entropie relative par rapport à une mesure de référence donnée. En effet, cela équivaut à trouver la projection d’un couplage par rapport à la divergence de Kullback-Leibler. Cela nous permet d’utiliser l’algorithme de Bregman/Dykstra et de résoudre plusieurs problèmes variationnels liés au TO. Nous nous intéressons particuli
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Jeong, Young-Sik. "Optimal military transportation in a Korean wartime theater." Thesis, Monterey California. Naval Postgraduate School, 2006. http://hdl.handle.net/10945/2439.

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Due to their high dependency on highway transportation, Republic of Korea's (ROK's) military and industry suffer from congestion, shortfall of means (convoys in the military case), high cost and increase in environmental damage. Our research develops an optimization model to guide TOK's military planning using multi-modal transportation. We apply our Military Logistics Transportation Model (MLTM) to a realistic scenario. MLTM provides guidance on the optimal frequency of transportation services and the optimal routes for the freight. By comparing the solution of MLTM with current practice
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Lai, Ming Fai. "Optimal assignment of ferry fleet for waterborne transportation /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?CIVL%202002%20LAI.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002.<br>Includes bibliographical references (leaves 60-61). Also available in electronic version. Access restricted to campus users.
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Bardelloni, Mauro. "The decomposition of optimal transportation problems with convex cost." Doctoral thesis, SISSA, 2014. http://hdl.handle.net/20.500.11767/3902.

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Caravenna, Laura. "The Disintegration Theorem and Applications to Optimal Mass Transportation." Doctoral thesis, SISSA, 2009. http://hdl.handle.net/20.500.11767/4622.

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Wiking, Josefin. "Alternative cost-optimal pathways for the transport sector of Cyprus." Thesis, KTH, Energisystemanalys, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-179032.

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This thesis investigates the possible future pathways for the road transportation sector of Cyprus, in a time horizon from the year 2013 to 2040. The road transportation sector of Cyprus is the most energy consuming sector in the country, completely dependent on the use of diesel and gasoline. In order to comply with the renewable energy target for the transportation sector set by the European Union, Cyprus needs to transform its road transportation sector. The software MESSAGE (Model for Energy Supply Strategy Alternatives and their General Environmental Impact) is used to model the road tran
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Wan, Kam Hung. "Optimal integrated transit network design /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?CIVL%202002%20WAN.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002.<br>Includes bibliographical references (leaves 92-95). Also available in electronic version. Access restricted to campus users.
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14

Georgiadis, Vasilis. "Optimal capital structure of deep sea foreign freight transportation companies." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90803.

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Thesis: S.M. in Engineering and Management, Massachusetts Institute of Technology, Engineering Systems Division, System Design and Management Program, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (page 46).<br>This thesis aims to understand the optimal leverage range for shipping companies (maritime foreign freight transportation companies - SIC 4412), through data analysis. This study confirms that in a traditional industry like shipping, the Market value-leverage curve is very similar to the theoretical curve, as proposed by traditional capital struct
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15

Edwards, Derek L. "Designing optimal demand-responsive transportation feeder systems and comparing performance in heterogeneous environments." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/52230.

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The goal of this research is to develop a method of objectively comparing and optimizing the performance of demand-responsive transportation systems in heterogeneous environments. Demand-responsive transportation refers to modes of transportation that do not follow fixed routes or schedules, including taxis, paratransit, deviated-route services, ride sharing as well as other modes. Heterogeneous environments are transportation environments in which streets do not follow regular patterns, passenger behavior is difficult to model, and transit schedules and layouts are non-uniform. An example
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16

Antos, Justin David. "Paying for public transportation : the optimal, the actual, and the possible." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40101.

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Thesis (M.C.P.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 2007.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>:June 2007."<br>Includes bibliographical references (p. 110-121).<br>Passenger transportation poses challenges to American cities in the form of air pollution, traffic congestion, auto collisions, and barriers to mobility. Public transit has the potential to be part of a solution to these urban problems, yet transit agencies across the country cl
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Çelikbilek, Can. "Determining the Optimal Transportation Method in Due-Date Driven Manufacturing Environments." Ohio University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1312312985.

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Dong, Wenjie. "Self-organizing and optimal control for nonlinear systems." Diss., [Riverside, Calif.] : University of California, Riverside, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3359894.

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Thesis (Ph. D.)--University of California, Riverside, 2009.<br>Includes abstract. Title from first page of PDF file (viewed January 27, 2010). Includes bibliographical references (p. 82-87). Issued in print and online. Available via ProQuest Digital Dissertations.
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19

Tan, Xiaolu. "Stochastic control methods for optimal transportation and probabilistic numerical schemes for PDEs." Palaiseau, Ecole polytechnique, 2011. https://theses.hal.science/docs/00/66/10/86/PDF/These_TanXiaolu.pdf.

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Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) non-linéaires dégénérées, ainsi que pour des problèmes de contrôle d'EDP non-linéaires résultants d'un nouveau problème de transport optimal. Toutes ces questions sont motivées par des applications en mathématiques financières. La thèse est divisée en quatre parties. Dans une première partie, nous nous intéressons à la condition nécessaire et suffisante de la monotonie du thêta-schéma de différences finies pour l'équation de diffusion en dimension un. Nous donnons la formule explicite dans le cas de
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Wang, Hao. "The Hot Optimal Transportation Meshfree (HOTM) Method for Extreme Multi-physics Problems." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1607533458323004.

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Abou-Senna, Hatem. "Microscopic Assessment of Transportation Emissions on Limited Access Highways." Doctoral diss., University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5090.

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On-road vehicles are a major source of transportation carbon dioxide (CO2) greenhouse gas emissions in all the developed countries, and in many of the developing countries in the world. Similarly, several criteria air pollutants are associated with transportation, e.g., carbon monoxide (CO), nitrogen oxides (NOx), and particulate matter (PM). The need to accurately quantify transportation-related emissions from vehicles is essential. Transportation agencies and researchers in the past have estimated emissions using one average speed and volume on a long stretch of roadway. With MOVES, there
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22

Uraz, Emre. "Offshore Wind Turbine Transportation & Installation Analyses Planning Optimal Marine Operations for Offshore Wind Projects." Thesis, Högskolan på Gotland, Institutionen för kultur, energi och miljö, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-217007.

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Transportation and installation of offshore wind turbines (Tower, Nacelle and Rotor) is a complete process conducted over several phases, usually in sequence. There are several factors that can turn this process into a challenge. These factors can either be due to offshore site conditions or the technical limitations of the installation vessels. Each project has its own characteristic parameters and requires a unique optimum solution. This paper identifies the dynamics of the installation process and analyzes the effects of each phase on the progression of events.The challenges in wind turbine
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23

Santhanam, Ramesh T. "An inventory model with two truckload transportation and quantity discounts." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001349.

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Guo, Gaoyue. "Continuous-time Martingale Optimal Transport and Optimal Skorokhod Embedding." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX038/document.

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Cette thèse présente trois principaux sujets de recherche, les deux premiers étant indépendants et le dernier indiquant la relation des deux premières problématiques dans un cas concret.Dans la première partie nous nous intéressons au problème de transport optimal martingale dans l’espace de Skorokhod, dont le premier but est d’étudier systématiquement la tension des plans de transport martingale. On s’intéresse tout d’abord à la semicontinuité supérieure du problème primal par rapport aux distributions marginales. En utilisant la S-topologie introduite par Jakubowski, on dérive la semicontinu
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25

Lu, Xin Yang. "Geometric and regularity properties of solutions of evolution problems associated to some distance related functionals." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85726.

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von, Nessi Gregory Thomas, and greg vonnessi@maths anu edu au. "Regularity Results for Potential Functions of the Optimal Transportation Problem on Spheres and Related Hessian Equations." The Australian National University. Mathematical Sciences Institute, 2008. http://thesis.anu.edu.au./public/adt-ANU20081215.120059.

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In this thesis, results will be presented that pertain to the global regularity of solutions to boundary value problems having the general form \begin{align} F\left[D^2u-A(\,\cdot\,,u,Du)\right] &= B(\,\cdot\,,u,Du),\quad\text{in}\ \Omega^-,\notag\\ T_u(\Omega^-) &= \Omega^+, \end{align} where $A$, $B$, $T_u$ are all prescribed; and $\Omega^-$ along with $\Omega^+$ are bounded in $\mathbb{R}^n$, smooth and satisfying notions of c-convexity and c^*-convexity relative to one another (see [MTW05] for definitions). In particular, the case where $F$ is a quotient of symmetric functions of the eigen
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De, Philippis Guido. "Regularity of optimal transport maps and applications." Doctoral thesis, Scuola Normale Superiore, 2012. http://hdl.handle.net/11384/85688.

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Oliveira, Aline Duarte de. "O teorema da dualidade de Kantorovich para o transporte de ótimo." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2011. http://hdl.handle.net/10183/32470.

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Abordaremos a teoria do transporte otimo demonstrando o teorema da dualidade de Kantorovich para uma classe ampla de funções custo. Tal resultado desempenha um papel de suma importância na teoria do transporte otimo. Uma ferramenta importante utilizada e o teorema da dualidade de Fenchel-Rockafellar, aqui enunciado e demonstrado em bastante generalidade. Demonstramos tamb em o teorema da dualidade de Kantorovich-Rubinstein, que trata do caso particular da função custo distância.<br>We analyze the optimal transport theory proving the Kantorovich duality theorem for a wide class of cost function
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Liu, Liang. "Probabilistic Assessment and Optimal Life-Cycle Management Considering Climate Change and Cost-Benefit Analysis: Applications to Bridge Networks and Ships." Thesis, Lehigh University, 2021. http://pqdtopen.proquest.com/#viewpdf?dispub=28156457.

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The continuous operation of civil and marine structures is essential for maintaining the flow of people and goods. However, structures are exposed to extreme or progressive events during their service time. The uncertainties associated with the occurrence and the magnitude of extreme events (e.g. flooding and scour) may change, leading to unprecedented loading conditions, while the progressive events (e.g. corrosion and fatigue) may jeopardize the structural capacity to resist loads. In order to maintain or improve the structural capacity, repair and maintenance actions need to be applied to s
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Kryvobok, Valeria, Валерія Кривобок, Микита Глущенко, Nikita Hlushchenko, and Huang Chenfan. "Method for calculating the optimal number of loading and uploading points of the airport cargo warehouse." Thesis, National Aviation University, 2021. https://er.nau.edu.ua/handle/NAU/51160.

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1. Transport terminals: purpose, attributes, functions. URL: https://dsl-ua.com/en/2019/06/24/ru-transportnyie-terminalyi-naznachenie-atributyi-funktsii/ 2. Calculation of parameters of service systems for passenger and freight transportation. URL:http://repo.ssau.ru/bitstream/Metodicheskie-materialy/Raschet-parametrov-sistem-obsluzhivaniya-passazhirskih-i-gruzovyh-perevozok-Elektronnyi-resurs-ucheb-posobie.pdf 3. Transportation of perishing goods. URL:https://files.stroyinf.ru/Data2/1/4293826/4293826395.htm#i483584<br>The cargo complex of the airport is a warehouse of temporary storage of c
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Palmgren, Myrna. "Optimal Truck Scheduling : Mathematical Modeling and Solution by the Column Generation Principle." Doctoral thesis, Linköping : Linköpings universitet, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-3590.

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Feyeux, Nelson. "Transport optimal pour l'assimilation de données images." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAM076/document.

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Pour prédire l'évolution d'un système physique, nous avons besoin d'initialiser le modèle mathématique le représentant, donc d'estimer la valeur de l'état du système au temps initial. Cet état n'est généralement pas directement mesurable car souvent trop complexe. En revanche, nous disposons d'informations du système, prises à des temps différents, incomplètes, mais aussi entachées d'erreurs, telles des observations, de précédentes estimations, etc. Combiner ces différentes informations partielles et imparfaites pour estimer la valeur de l'état fait appel à des méthodes d'assimilation de donné
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Singh, Archit. "Electric Road Systems : A feasibility study investigating a possible future of road transportation." Thesis, KTH, Energiteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-194242.

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The transportation sector is a vital part of today’s society and accounts for 20 % of our global total energy consumption. It is also one of the most greenhouse gas emission intensive sectors as almost 95 % of its energy originates from petroleum-based fuels. Due to the possible harmful nature of greenhouse gases, there is a need for a transition to more sustainable transportation alternatives. A possible alternative to the conventional petroleum-based road transportation is implementation of Electric Road Systems (ERS) in combination with electric vehicles (EVs). ERS are systems that enable d
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Valenti, Giammarco. "Cooperative ADAS and driving, bio-inspired and optimal solutions." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/336890.

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Mobility is a topic of great interest in research and engineering since critical aspects such as safety, traffic efficiency, and environmental sustainability still represent wide open challenges for researchers and engineers. In this thesis, at first, we address the cooperative driving safety problem both from a centralized and decentralized perspective. Then we address the problem of optimal energy management of hybrid vehicles to improve environmental sustainability, and finally, we develop an intersection management systems for Connected Autonomous Vehicle to maximize the traffic efficiency
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Bam, Prayag. "Development and Implementation of Network Level Trade-off Analysis tool in Transportation Asset Management." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1512227253641838.

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Gao, Lijun. "Information Points and Optimal Discharging Speed: Effects on the Saturation Flow at Signalized Intersections." University of Toledo / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1430482821.

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Sgarioto, Daniel Emmanuel, and s9908712@student rmit edu au. "Non-linear Dynamic Modelling and Optimal Control of Aerial Tethers for Remote Delivery and Capture of Payloads." RMIT University. Aerospace, Mechanical and Manufacturing Engineering, 2006. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20070209.144754.

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Many potentially useful applications that broadly fall under the umbrella of payload transportation operations have been proposed for aerial towed-cable (ATC) systems, namely the precise capture and delivery of payloads. There remain outstanding issues concerning the dynamics and control of ATC systems that are inhibiting the near-term demonstration of these applications. The development of simplified representations of ATC systems that retain the important dynamics, yet are simple enough for use in control system development is limited. Likewise, little research exists into the development of
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Mandad, Manish. "Approximation robuste de surfaces avec garanties." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4156/document.

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Cette thèse comprend deux parties indépendantes.Dans la première partie nous contribuons une nouvelle méthode qui, étant donnée un volume de tolérance, génère un maillage triangulaire surfacique garanti d’être dans le volume de tolérance, sans auto-intersection et topologiquement correct. Un algorithme flexible est conçu pour capturer la topologie et découvrir l’anisotropie dans le volume de tolérance dans le but de générer un maillage de faible complexité.Dans la seconde partie nous contribuons une nouvelle approche pour calculer une fonction de correspondance entre deux surfaces. Tandis que
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Preux, Anthony. "Transport optimal et équations des gaz sans pression avec contrainte de densité maximale." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS435/document.

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Dans cette thèse, nous nous intéressons aux équations des gaz sans pression avec contrainte de congestion qui soulèvent encore de nombreuses questions. La stratégie que nous proposons repose sur des précédents travaux sur le mouvement de foule dans le cadre de l'espace de Wasserstein, et sur un modèle granulaire avec des collisions inélastiques.Elle consiste en l'étude d'un schéma discrétisé en temps dont les suites doivent approcher les solutions de ces équations.Le schéma se présente de la manière suivante : à chaque pas de temps, le champ des vitesses est projeté sur un ensemble lui permett
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Lepoultier, Guilhem. "Transport numérique de quantités géométriques." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112202/document.

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Une part importante de l’activité en calcul scientifique et analyse numérique est consacrée aux problèmes de transport d’une quantité par un champ donné (ou lui-même calculé numériquement). Les questions de conservations étant essentielles dans ce domaine, on formule en général le problème de façon eulérienne sous la forme d’un bilan au niveau de chaque cellule élémentaire du maillage, et l’on gère l’évolution en suivant les valeurs moyennes dans ces cellules au cours du temps. Une autre approche consiste à suivre les caractéristiques du champ et à transporter les valeurs ponctuelles le long d
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Bouras, Ikram. "Fixed charge network design problem with user-optimal flows." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS136.

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Cette thèse s'adresse à la classe des problèmes de conception de réseaux bi-niveaux. Nous nous sommes intéressés à l'étude des applications des différents domaines et au développement d'algorithmes exacts pour la résolution des problème de réseaux bi-niveau correspondants. En particulier, nous avons étudié le problème de conception de réseau bi-niveau dans lequel le ``leader" sélectionne une partie du réseau à activer, puis, dans le deuxième niveau, la solution doit être optimale pour un problème de flot dans le sous-réseau sélectionné. Dans cette thèse, trois applications de ce problème sont
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Caillaud, Corentin. "Asymptotical estimates for some algorithms for data and image processing : a study of the Sinkhorn algorithm and a numerical analysis of total variation minimization." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX023.

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Cette thèse traite de problèmes discrets d'optimisation convexe et s'intéresse à des estimations de leurs taux de convergence. Elle s'organise en deux parties indépendantes.Dans la première partie, nous étudions le taux de convergence de l'algorithme de Sinkhorn et de certaines de ses variantes. Cet algorithme apparaît dans le cadre du Transport Optimal (TO) par l'intermédiaire d'une régularisation entropique. Ses itérations, comme celles de ses variantes, s'écrivent sous la forme de produits composante par composante de matrices et de vecteurs positifs. Pour les étudier, nous proposons une no
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Sergent, Aaronn. "Optimal Sizing and Control of Battery Energy Storage Systems for Hybrid-Electric, Distributed-Propulsion Regional Aircraft." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1595519141013663.

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Souza, Estefano Alves de. "O problema de Monge-Kantorovich para duas medidas de probabilidade sobre um conjunto finito." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-04052009-162654/.

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Apresentamos o problema do transporte ótimo de Monge-Kantorovich com duas medidas de probabilidade conhecidas e que possuem suporte em um conjunto de cardinalidade finita. O objetivo é determinar condições que permitam construir um acoplamento destas medidas que minimiza o valor esperado de uma função de custo conhecida e que assume valor nulo apenas nos elementos da diagonal. Apresentamos também um resultado relacionado com a solução do problema de Monge-Kantorovich em espaços produto finitos quando conhecemos soluções para o problema nos espaços marginais.<br>We present the Monge-Kantorovich
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45

Динда, К. П. "Оцінка логістичного сервісу у проектах перевезення вантажу". Thesis, Сумський державний університет, 2016. http://essuir.sumdu.edu.ua/handle/123456789/47978.

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46

Fan, Zongyue. "A Lagrangian Meshfree Simulation Framework for Additive Manufacturing of Metals." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1619737226226133.

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Shibutani, Satomi. "Transportation of separate waste fractions in an underground waste transportation system." Thesis, KTH, Industriell ekologi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-58630.

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Today waste management has entered a new stage. Since wastes still contain natural materials and energy that can be extracted, it should be treated in effective ways, for example, for energy recovery or material recycling. Many countries and the municipalities have therefore made waste treatment strategies in accordance with for example, EU directives or governmental regulations. In such circumstances, Envac is one of waste management companies in Sweden, which collects different kinds of waste fractions through an underground pipe system by means of air pressure. In Hammarby sjöstad in Stockh
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Santambrogio, Filippo. "Variational problems in transport theory with mass concentration." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85701.

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Pass, Brendan. "Structural Results on Optimal Transportation Plans." Thesis, 2011. http://hdl.handle.net/1807/31893.

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In this thesis we prove several results on the structure of solutions to optimal transportation problems. The second chapter represents joint work with Robert McCann and Micah Warren; the main result is that, under a non-degeneracy condition on the cost function, the optimal is concentrated on a $n$-dimensional Lipschitz submanifold of the product space. As a consequence, we provide a simple, new proof that the optimal map satisfies a Jacobian equation almost everywhere. In the third chapter, we prove an analogous result for the multi-marginal optimal transportation problem; in this contex
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Li, Bo. "The Optimal Transportation Method in Solid Mechanics." Thesis, 2009. https://thesis.library.caltech.edu/5193/1/Thesis_Bo_Li.pdf.

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This dissertation is concerned with the development of a robust and efficient meshless method, the Optimal Transportation Method (OTM), for general solid flows involving extremely large deformation, fast, transient loading and hydrodynamic phenomena. This method is a Lagrangian particle method through an integration of optimal transportation theory with meshless interpolation and material point integrations. The theoretical framework developed in this thesis generalized the Benamou-Brenier differential formulation of optimal transportation problems and leads to a multi-field variational charac
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