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Dissertations / Theses on the topic 'Orlicz spaces'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Al-Rashed, Maryam Houmod Ali. "Noncommutative Orlicz spaces." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434998.

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2

Cazacu, Constantin Dan. "Twisted sums of Orlicz spaces /." free to MU campus, to others for purchase, 1998. http://wwwlib.umi.com/cr/mo/fullcit?p9901223.

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3

Szab?o, L?aszl?o. "On ergodic and Martingale theorems in Orlicz spaces /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683756124057.

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4

Doto, James William. "Conditional uniform convexity in Orlicz spaces and minimization problems." Thesis, Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/27352.

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El-Mabrouk, Khalifa. "Semilinear perturbations of harmonic spaces and Martin-Orlicz capacities an approach to the trace of moderate U-functions /." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964456435.

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6

Lai, Wei-Kai. "The radon-nikodym property for the Wittstock and Fremlin tensor products of orlicz sequence spaces and banach lattices /." Full text available from ProQuest UM Digital Dissertations, 2008. http://0-proquest.umi.com.umiss.lib.olemiss.edu/pqdweb?index=0&did=1850496461&SrchMode=1&sid=1&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1277325845&clientId=22256.

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7

Capolli, Marco. "Selected Topics in Analysis in Metric Measure Spaces." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/288526.

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The thesis is composed by three sections, each devoted to the study of a specific problem in the setting of PI spaces. The problem analyzed are: a C^m Lusin approximation result for horizontal curves in the Heisenberg group, a limit result in the spirit of Burgain-Brezis-Mironescu for Orlicz-Sobolev spaces in Carnot groups and the differentiability of Lipschitz functions in Laakso spaces.

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Capolli, Marco. "Selected Topics in Analysis in Metric Measure Spaces." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/288526.

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The thesis is composed by three sections, each devoted to the study of a specific problem in the setting of PI spaces. The problem analyzed are: a C^m Lusin approximation result for horizontal curves in the Heisenberg group, a limit result in the spirit of Burgain-Brezis-Mironescu for Orlicz-Sobolev spaces in Carnot groups and the differentiability of Lipschitz functions in Laakso spaces.

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9

Carvalho, Marcos Leandro Mendes. "Equações diferenciais parciais elípticas multivalentes: crescimento crítico, métodos variacionais." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3686.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-25T14:36:31Z No. of bitstreams: 2 Tese - Marcos Leandro Mendes Carvalho - 2013.pdf: 2450216 bytes, checksum: 78d3d3298d2050e0e82310644ecda305 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-25T14:39:40Z (GMT) No. of bitstreams: 2 Tese - Marcos Leandro Mendes Carvalho - 2013.pdf: 2450216 bytes, checksum: 78d3d3298d2050e0e82310644ecda305 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)

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10

Kumar, Vishvesh. "Harmonic analysis on Orlicz spaces for certain hypergroups and on discrete hypergroups arising from semigroups with emphasis on Ramsey theory." Thesis, IIT Delhi, 2019. http://eprint.iitd.ac.in:80//handle/2074/8075.

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MENESES, João Paulo Formiga de. "Existência de múltiplas soluções positivas para uma classe de problemas elípticos quaselineares." Universidade Federal de Campina Grande, 2016. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1425.

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Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-13T18:38:15Z No. of bitstreams: 1 JOÃO PAULO FORMIGA DE MENESES - DISSERTAÇÃO PPGMAT 2016..pdf: 1613708 bytes, checksum: 5f49f16ec6b9bdf21a073af08bdf1006 (MD5)<br>Made available in DSpace on 2018-08-13T18:38:15Z (GMT). No. of bitstreams: 1 JOÃO PAULO FORMIGA DE MENESES - DISSERTAÇÃO PPGMAT 2016..pdf: 1613708 bytes, checksum: 5f49f16ec6b9bdf21a073af08bdf1006 (MD5) Previous issue date: 2016-11-25<br>Neste trabalho, utilizando sub e supersoluções e métodos variacionais sobre espaços de Orlicz-Sobolev, estudamos a existência

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Silva, Ailton Rodrigues da. "Existência, multiplicidade e concentração de soluções positivas para uma classe de problemas quasilineares em espaços de Orlicz-Sobolev." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9258.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-15T12:49:10Z No. of bitstreams: 1 arquivototal.pdf: 1323834 bytes, checksum: 530efbd6b56f11c5cc1b4369c8c44888 (MD5)<br>Made available in DSpace on 2017-08-15T12:49:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1323834 bytes, checksum: 530efbd6b56f11c5cc1b4369c8c44888 (MD5) Previous issue date: 2016-02-29<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>In this work we establish existence, multiplicity and concentration of positive solutions for the following class of problem 8<: 􀀀d

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13

Carvalho, Gilson Mamede de. "Equações de Schrödinger quaselineares com potenciais singulares ou se anulando no infinito." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9254.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-15T11:35:55Z No. of bitstreams: 1 arquivototal.pdf: 1290749 bytes, checksum: 9377b99ec1efcaa5be2f62cc2aae83ac (MD5)<br>Made available in DSpace on 2017-08-15T11:35:55Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1290749 bytes, checksum: 9377b99ec1efcaa5be2f62cc2aae83ac (MD5) Previous issue date: 2016-07-19<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>In this work, we study existence of standing wave solution for a class of quasilinear Schrödinger equations involving potentials that

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14

Zghal, Mohamed Khalil. "Inégalités de type Trudinger-Moser et applications." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1077/document.

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Cette thèse porte sur quelques inégalités de type Trudinger-Moser et leurs applications à l'étude des injections de Sobolev qu'elles induisent dans les espaces d'Orlicz et à l'analyse d'équations aux dérivées partielles non linéaires à croissance exponentielle.Le travail qu'on présente ici se compose de trois parties. La première partie est consacrée à la description du défaut de compacité de l'injection de Sobolev 4D dans l'espace d'Orlicz dansle cadre radial.L'objectif de la deuxième partie est double. D'abord, on caractérise le défaut de compacité de l'injection de Sobolev 2D dans les diffé

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15

Ben, Ayed Inès. "Etude d'injections de Sobolev critiques dans les espaces d'Orlicz et applications." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1133.

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Dans cette thèse, on s'est attaché d'une part à d'écrire le défaut de compacité de l'injection de Sobolev critique dans les différentes classes d'espaces d'Orlicz, et d'autre part à étudier l'équation de Klein-Gordon avec une non-linéarité exponentielle. Ce travail se divise en trois parties. L'objectif de la première partie est de caractériser le défaut de compacité de l'injection de Sobolev de $H^2_{rad}(R^4)$ dans l'espace d'Orlicz $mathcal{L}(R^4)$.Le but de la deuxième partie est double : tout d'abord, on a décrit le défaut de compacité de l'injection de Sobolev de $H^1(R^2)$ dans les dif

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16

Tomková, Iva. "PERLA Ústí nad Orlicí." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-354977.

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The object of the study is urban planning - architectural design strategy of conversion and revitalization of the factory PEARL 01 in Usti nad Orlici. The area of the site is about 3 hectares, an area eight times larger than the actual main square in the town. Most of the land is owned by the city. Current status of the area does not match the aesthetic or functional demands placed on this space, which is intended for expansion of the city center, whose current capacity does not match the needs of even the size of the city. Textile industry and Perla itself played an important role in the hist

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Annová, Denisa. "PERLA Ústí nad Orlicí." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-354956.

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The subject of the diploma thesis is to design reclamation of brownfield PERLA 01 in Ústí nad Orlicí. The construction program consists conversion of existing building to assembly hall, gallery, tourist centre, sheltered workshop, rentable space, office building. New building is Start up centre. The project design a character of public space and a new square.

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18

Vlček, Marek. "Vysokoškolská kolej Hradec Králové, nábřeží Orlice." Master's thesis, Vysoké učení technické v Brně. Fakulta architektury, 2019. http://www.nusl.cz/ntk/nusl-401803.

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The diploma project is resolving the possibilities of designing contemporary buildings into the historical context of city centre. The emphasis is aimed on urban integration of new volumes into the present city structure and its genius loci. The result of the design should be buildings with specific character and clear dispositions using quality materials. The area is located near the city centre of Hradec Králové and is defined by the streets Comenius, I.Herrmann and Hradecká. It is directly adjacent to the historic city center. In the middle of the area is flowing The Orlice River, which div

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19

Livovská, Lucia. "Hotel při ČPP aréně v Hradci Králové, nábřeží Orlice." Master's thesis, Vysoké učení technické v Brně. Fakulta architektury, 2019. http://www.nusl.cz/ntk/nusl-401802.

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The diploma project is resolving the possibilities of designing contemporary buildings into the historical context of city centre. The emphasis is aimed on urban integration of new volumes into the present city structure and its genius loci. The result of the design should be buildings with specific character and clear dispositions using quality materials. The area is located near the city centre of Hradec Králové and is defined by the streets Comenius, I.Herrmann and Hradecká. It is directly adjacent to the historic city center. In the middle of the area is flowing The Orlice River, which div

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20

Charpentier, Stéphane. "Opérateurs de composition sur les espaces de fonctions holomorphes de plusieurs variables complexes : universalité dans les espaces de Banach et de Fréchet." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14104/document.

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Dans la première partie de ma thèse, il est démontré, dans les espaces de Banach et de Fréchet de suites, un résultat d'existence d'un sous-espace fermé de dimension infinie dont les éléments non-nuls sont des séries universelles.La deuxième partie est consacrée à l'étude des opérateurs de composition sur des espaces de fonctions holomorphes de plusieurs variables complexes. Dans un premier temps, le spectre et la dynamique des opérateurs de composition hyperboliques sur les espaces de Hardy de la boule sont décrits complètement.Dans un second temps, la continuité et la compacité des opérateur

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21

SONG, YUKUN SONG. "Stochastic Integrals with Respect to Tempered $\alpha$-Stable Levy Process." Case Western Reserve University School of Graduate Studies / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=case1501506513936836.

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22

Ghawadrah, Ghadeer. "Théorie descriptive des ensembles et espaces de Banach." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066078/document.

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Cette thèse traite de la théorie descriptive des ensembles et de la géométrie des espaces de Banach. La première partie consiste en l’étude de la complexité descriptive de la famille des espaces de Banach avec la propriété d’approximation bornée, respectivement la propriété π, dans l’ensemble des sous-espaces fermés de C(Δ), où Δ est l’ensemble de Cantor. Ces familles sont boréliennes. En outre, nous montrons que si alpha<br>This thesis deals with the descriptive set theory and the geometry of Banach spaces.The first chapter consists of the study of the descriptive complexity of the set of Ban

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23

Issa, Samar. "Méthodes variationnelles : Applications à l'analyse d'image et au modèle de Frenkel-Kontorova." Phd thesis, Université de La Rochelle, 2011. http://tel.archives-ouvertes.fr/tel-00808646.

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Cette thèse est décomposée en deux parties. La première est consacrée à l'étude de la restauration d'image et la seconde partie est consacrée à l'étude d'un modèle de Frenkel-Kontorova par des méthodes issues du calcul variationnel et des équations aux dérivées partielles. Au chapitre 1, nous présentons les questions essentielles que nous traiterons dans cette thèse, puis on fait des rappels sur les définitions et quelques propriétés d'espace des fonctions à variations bornées BV , l'espace d'Orlicz et le modèle de Frenkel-Kontorova. Au chapitre 2, nous montrons que les problèmes de minimisati

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24

Giri, Chinmay Kumar. "Orlicz Function Spaces and Composition Operator." Thesis, 2013. http://ethesis.nitrkl.ac.in/5436/1/411MA2075.pdf.

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In our dissertation we present here the salient features from the theory of Orlicz function spaces, LÖ(Ù), generated by the Young’s function Ö on an arbitrary ó−finite measurable spaces Ù. We will discussed these are the Banach spaces equipped with the equivalent orlicz and gauge norms.Finally we study the Composition operators Cô between Orlicz spaces LÖ(Ù) generated by measurable and non-singular transformations ô from Ù into itself. We also investigate the Boundedness and compactness of the composition operators on the Orlicz spaces by using different types of Ä2 conditions of the orlicz fu

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25

Teymurazyan, Rafayel. "Obstacle type problems in Orlicz-Sobolev spaces." Doctoral thesis, 2013. http://hdl.handle.net/10451/8648.

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Tese de doutoramento, Matemática (Física Matemática e Mecânica dos Meios Contínuos), Universidade de Lisboa, Faculdade de Ciências, 2013<br>This thesis consists of four chapters. In the first chapter we study the regularity of solutions for a class of elliptic problems in Orlicz-Sobolev spaces. In particular, we see that bounded weak solutions of Au := 􀀀div 􀀀 a(x; jruj)ru _ = f(x); x 2 ; where Ω ⊂ Rn is a bounded domain, for an appropriate a and f are C1 α regular. Using Lewy-Stampacchia inequalities for one obstacle problem we derive C1 α regularity results (both locally and up to the boundar

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26

Offwood, Theresa Maria. "No free lunch and risk measures on Orlicz spaces." Thesis, 2012. http://hdl.handle.net/10539/11942.

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The importance of Orlicz spaces in the study of mathematics of nance came to the for in the 2000's when Frittelli and his collaborators connected the theory of utility functions to Orlicz spaces. In this thesis, we look at how Orlicz spaces play a role in nancial mathematics. After giving an overview of scalar-valued Orlicz spaces, we look at the rst fundamental theorem of asset pricing in an Orlicz space setting. We then give a brief summary of scalar risk measures, followed by the representation result for convex risk measures on Orlicz hearts. As an example of a risk measure, we t

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27

Wróblewska-Kamińska, Aneta. "An application of Orlicz spaces in partial differential equations." Doctoral thesis, 2012. http://depotuw.ceon.pl/handle/item/138.

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Our purpose is to investigate mathematical properties of some systems of nonlinear partial differential equations where the nonlinear term is monotone and its behaviour - coercivity/growth conditions are given with the help of some general convex function defining Orlicz spaces. Our first result is the existence of weak solutions to unsteady flows of non-Newtonian incompressible nonhomogeneous (with non-constant density) fluids with nonstandard growth conditions of the stress tensor. We are motivated by the problem of anisotropic behaviour of fluids which are also characterised by rapid shear

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28

Zecca, Gabriella. "On the L^p-solvability of the Dirichlet problem and generalizations in Orlicz spaces." Tesi di dottorato, 2008. http://www.fedoa.unina.it/3509/1/tesiGZecca.pdf.

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29

Dhara, Raj Narayan. "Existence and regularity theory in weighted Sobolev spaces and applications." Doctoral thesis, 2016. https://depotuw.ceon.pl/handle/item/2051.

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In the thesis we discuss several questions related to the study of degenerate, possibly nonlinear PDEs of elliptic type. At first we discuss the equivalent conditions between the validity of weighted Poincar\'e inequalities, structure of the functionals on weighted Sobolev spaces, isoperimetric inequalities and the existence and uniqueness of solutions to the degenerate nonlinear elliptic PDEs with nonhomogeneous boundary condition, having the form:\begin{eqnarray}\label{eqn:abs}\left\{\begin{array}{lll}{\rm div} \left( \rho (x)|\nabla u|^{p-2}\nabla u\right) =x^*,\\~~~~~~~~~~~~u-w \in W^{1,p}

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30

El-Mabrouk, Khalifa [Verfasser]. "Semilinear perturbations of harmonic spaces and Martin-Orlicz capacities : an approach to the trace of moderate U-functions / vorgelegt von Khalifa El Mabrouk." 2002. http://d-nb.info/964456435/34.

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31

Buriánková, Eva. "Chování jednorozměrných integrálních operátorů na prostorech funkcí." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-346973.

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In this manuscript we study the action of one-dimensional integral operators on rearrangement-invariant Banach function spaces. Our principal goal is to characterize optimal target and optimal domain spaces corresponding to given spaces within the category of rearrangement-invariant Banach function spaces as well as to establish pointwise estimates of the non-increasing rearrangement of a given operator applied on a given function. We apply these general results to proving optimality relations between special rearrangement-invariant spaces. We pay special attention to the Laplace transform, wh

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32

Naik, S. "Multipliers between Orlicz sequence space." Thesis, 2014. http://ethesis.nitrkl.ac.in/6292/1/E-74.pdf.

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Let $ M,N $ be Orlicz functions and let $ D(l_M,l_N) $ be the space of all diagonal operators (that is multipliers) acting between the Orlicz sequence spaces $ l_M $ and $ l_N $. We prove that the space of multipliers $ D(l_M,l_N) $ coincides with (and is isommorphic to) the Orlicz sequence space $ l_{M_{N}^*} $, where $ M_{N}^* $ is the Orlicz function defined by $ M_N^*( \lambda )=\text{sup} \lbrace N( \lambda x)-M(x),x\in(0,1) \rbrace $ .

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33

Skrzypczak, Iwona. "Hardy–type inequalities and nonlinear eigenvalue problems." Doctoral thesis, 2013.

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Naszym celem jest wprowadzenie nowej metody konstruowania nier´owno´sci typu Hardy’ego. Konstruujemy je znaj¸ac rozwi¸azania u zagadnie´n p oraz A– harmonicznych. Wyprowadzamy nier´owno´sci typu Caccioppoli dla u. Jako wniosek z nich otrzymujemy wa˙zone nier´owno´sci typu Hardy’ego dla funkcji Lipschitzowskich o zwartym no´sniku.

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34

Skříšovský, Emil. "Stlačitelné Navier-Stokes-Fourierovy rovnice pro adiabatický koeficient blízko jedničky." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-405891.

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In the present thesis we study the compressible Navier-Stokes-Fourier sys- tem. This is a system of partial differential equations describing the evolutionary problem for an adiabatic flow of a heat conducting compressible viscous fluid in a bounded domain. Here we consider the problem in two dimensions with zero Dirichlet boundary conditions for velocity. The cold pressure term in the pressure law for the momentum equation is here considered in the form pC(ϱ) ∼ ϱ logα (1+ϱ) for some α > 0, for which we need to work on the scale of Orlicz spaces in order to obtain useful estimates and in those

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Kleprlík, Luděk. "Vlastnosti slabě diferencovatelných funkcí a zobrazení." Doctoral thesis, 2014. http://www.nusl.cz/ntk/nusl-342351.

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We study the optimal conditions on a homeomorphism f : Ω → Rn which guarantee that the composition u◦f is weakly differentiable and its weak derivative belongs to the some function space. We show that if f has finite distortion and q-distortion Kq = |Df|q /Jf is integrable enough, then the composition operator Tf (u) = u ◦ f maps functions from W1,q loc into space W1,p loc and the well-known chain rule holds. To prove it we characterize when the inverse mapping f−1 maps sets of measure zero onto sets of measure zero (satisfies the Luzin (N−1 ) con- dition). We also fully characterize condition

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Zindulka, Mikuláš. "Bázové posloupnosti v Banachových prostorech." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448170.

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An ordering on bases in Banach spaces is defined as a natural generalization of the notion of equivalence. Its theory is developed with emphasis on its behavior with respect to shrinking and boundedly-complete bases. We prove that a bounded operator mapping a shrinking basis to a boundedly-complete one is weakly compact. A well-known result concerning the factorization of a weakly compact operator through a reflexive space is then reinterpreted in terms of the ordering. Next, we introduce a class of Banach spaces whose norm is constructed from a given two-dimensional norm N. We prove that any

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Takáč, Jakub. "Interpolace logaritmicky konvexních kombinací operátorů." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-448302.

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We study the behaviour of logarithmically convex combinations of operators given by Tf = |S1f| 1 θ |S2f|1− 1 θ , where S1, S2 are some (usually quasi-linear) operators acting on spaces of measurable functions and θ ∈ (1, ∞) is a parameter. We develop two, quite different in nature, interpolation theories, each of which enables us to obtain a rather com- prehensive information about the behavior of such operators on function spaces. The first one is completely general and is based on abstract interpolation and Calderón spaces. We illustrate the theoretical results by a wide variety of examples

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38

Klawe, Filip. "Mathematical analysis of thermo-visco-elastic models." Doctoral thesis, 2015.

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Our research is directed to quasi-static evolution of thermo-visco-elastic models. We assume that the material is subject to two kinds of mechanical deformations: elastic and inelastic. Moreover, our analysis captures the influence of the temperature on visco-elastic properties of the body. The subject of this dissertation is to study a thermodynamically consistent models which describe such type of phenomena related to Mróz model, Norton-Hoff-type model and model with growth conditions in Orlicz spaces. The proofs base on two level Galerkin approximation. We present the construction of approx

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Musil, Vít. "Klasické operátory harmonické analýzy v Orliczových prostorech." Doctoral thesis, 2018. http://www.nusl.cz/ntk/nusl-392438.

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Classical operators of harmonic analysis in Orlicz spaces V'ıt Musil We deal with classical operators of harmonic analysis in Orlicz spaces such as the Hardy-Littlewood maximal operator, the Hardy-type integral operators, the maximal operator of fractional order, the Riesz potential, the Laplace transform, and also with Sobolev-type embeddings on open subsets of Rn or with respect to Frostman measures and, in particular, trace embeddings on the boundary. For each operator (in case of embeddings we consider the identity operator) we investigate the question of its boundedness from an Orlicz spa

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Musil, Vít. "Poloha Orliczova prostoru a optimalita." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340763.

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Given a rearrangement-invariant Banach function space Y (Ω), we consider the problem of the existence of an optimal (largest) domain Or- licz space LA (Ω) satisfying the Sobolev embedding Wm LA (Ω) !Y (Ω). We present a complete solution of this problem within the class of Marcinkiewicz endpoint spaces which covers several important examples.

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Le, Van Dinh. "The broken circuit complex and the Orlik - Terao algebra of a hyperplane arrangement." Doctoral thesis, 2016. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2016021714257.

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My thesis is mostly concerned with algebraic and combinatorial aspects of the theory of hyperplane arrangements. More specifically, I study the Orlik-Terao algebra of a hyperplane arrangement and the broken circuit complex of a matroid. The Orlik-Terao algebra is a useful tool for studying hyperplane arrangements, especially for characterizing some non-combinatorial properties. The broken circuit complex, on the one hand, is closely related to the Orlik-Terao algebra, and on the other hand, plays a crucial role in the study of many combinatorial problem: the coefficients of the characteristic

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