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Academic literature on the topic 'Möbiu'

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Published: 11 March 2023

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Journal articles on the topic "Möbiu"

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Hu, Zejun, and Haizhong Li. "Classification of Möbius Isoparametric Hypersurfaces in 4." Nagoya Mathematical Journal 179 (2005): 147–62. http://dx.doi.org/10.1017/s0027763000025629.

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AbstractLet Mn be an immersed umbilic-free hypersurface in the (n + 1)-dimensional unit sphere n+1, then Mn is associated with a so-called Möbius metric g, a Möbius second fundamental form B and a Möbius form Φ which are invariants of Mn under the Möbius transformation group of n+1. A classical theorem of Möbius geometry states that Mn (n ≥ 3) is in fact characterized by g and B up to Möbius equivalence. A Möbius isoparametric hypersurface is defined by satisfying two conditions: (1) Φ ≡ 0; (2) All the eigenvalues of B with respect to g are constants. Note that Euclidean isoparametric hyper-surfaces are automatically Möbius isoparametric, whereas the latter are Dupin hypersurfaces.In this paper, we prove that a Möbius isoparametric hypersurface in 4 is either of parallel Möbius second fundamental form or Möbius equivalent to a tube of constant radius over a standard Veronese embedding of ℝP2 into 4. The classification of hypersurfaces in n+1 (n ≥ 2) with parallel Möbius second fundamental form has been accomplished in our previous paper [6]. The present result is a counterpart of Pinkall’s classification for Dupin hypersurfaces in 4 up to Lie equivalence.
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Buyalo, S. "Möbius and sub-Möbius structures." St. Petersburg Mathematical Journal 28, no. 5 (July 25, 2017): 555–68. http://dx.doi.org/10.1090/spmj/1463.

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Bayad, Abdelmejid, Daeyeoul Kim, and Yan Li. "Arithmetical properties of double Möbius-Bernoulli numbers." Open Mathematics 17, no. 1 (February 17, 2019): 32–42. http://dx.doi.org/10.1515/math-2019-0006.

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Abstract Given positive integers n, n′ and k, we investigate the Möbius-Bernoulli numbers Mk(n), double Möbius-Bernoulli numbers Mk(n,n′), and Möbius-Bernoulli polynomials Mk(n)(x). We find new identities involving double Möbius-Bernoulli, Barnes-Bernoulli numbers and Dedekind sums. In part of this paper, the Möbius-Bernoulli polynomials Mk(n)(x), can be interpreted as critical values of the following Dirichlet type L-function $$\begin{array}{} \displaystyle L_{HM}(s;n,x):=\sum_{d|n} \sum_{m= 0}^\infty \frac{\mu(d)}{(md+x)^s} \, \, \text{(for Re} (s) \gt 1), \end{array} $$ which has analytic continuation to the whole s-complex plane, where μ is the Möbius function.
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Balakan, Gülcan, and Oğuzhan Demirel. "The Formulas of Möbius-Bretschneider and Möbius-Cagnoli in the Poincaré Disc Model of Hyperbolic Geometry." Al-Mustansiriyah Journal of Science 32, no. 1 (February 21, 2021): 31. http://dx.doi.org/10.23851/mjs.v32i1.932.

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Wang, Changping. "Möbius geometry for hypersurfaces in S4." Nagoya Mathematical Journal 139 (September 1995): 1–20. http://dx.doi.org/10.1017/s0027763000005274.

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Our purpose in this paper is to study Möbius geometry for those hypersurfaces in S4 which have different principal curvatures at each point. We will give a complete local Möbius invariant system for such hypersurface in S4 which determines the hypersurface up to Möbius transformations. And we will classify the so-called Möbius homogeneous hypersurfaces in S4.
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Wang, Changping. "Surfaces in Möbius geometry." Nagoya Mathematical Journal 125 (March 1992): 53–72. http://dx.doi.org/10.1017/s0027763000003895.

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Our purpose in this paper is to give a basic theory of Möbius differential geometay. In such geometry we study the properties of hypersurfaces in unit sphere Sn which are invariant under the Möbius transformation group on Sn.Since any Möbius transformation takes oriented spheres in Sn to oriented spheres, we can regard the Möbius transformation group Gn as a subgroup MGn of the Lie transformation group on the unit tangent bundle USn of Sn. Furthermore, we can represent the immersed hypersurfaces in Sn by a class of Lie geometry hypersurfaces (cf. [9]) called Möbius hypersurfaces. Thus we can use the concepts and the techniques in Lie sphere geometry developed by U. Pinkall ([8], [9]), T. Cecil and S. S. Chern [2] to study the Möbius differential geometry.
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Li, Feng Jiang, and Jian Bo Fang. "Complete hypersurfaces with constant Möbius scalar curvature." International Journal of Mathematics 27, no. 08 (July 2016): 1650063. http://dx.doi.org/10.1142/s0129167x16500634.

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Let [Formula: see text] be an umbilical free hypersurface in the unit sphere [Formula: see text]. Four basic invariants of [Formula: see text], under the Möbius transformation group of [Formula: see text] are the Möbius metric [Formula: see text], the Möbius second fundamental form [Formula: see text], the Blaschke tensor [Formula: see text] and the Möbius form [Formula: see text]. In this paper, we study complete hypersurfaces with constant normalized Möbius scalar curvature [Formula: see text] and vanishing Möbius form [Formula: see text]. By computing the Laplacian of the funtion [Formula: see text], where the trace-free Blaschke tensor [Formula: see text], and applying the well known generalized maximum principle of Omori–Yau, we obtain the following result: [Formula: see text] must be either Möbius equivalent to a minimal hypersurface with constant Möbius scalar curvature, when [Formula: see text]; [Formula: see text] in [Formula: see text], when [Formula: see text]; the pre-image of the stereographic projection [Formula: see text] of the circular cylinder [Formula: see text] in [Formula: see text], when [Formula: see text]; or the pre-image of the projection [Formula: see text] of the hypersurface [Formula: see text] in [Formula: see text], when [Formula: see text].
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Alden, J. W. "Möbius." Nature 515, no. 7526 (November 2014): 304. http://dx.doi.org/10.1038/515304a.

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Sun, Jiancai. "Contragredient Modules and Invariant Bilinear Forms on Möbius Nonlocal Vertex Algebras." Algebra Colloquium 20, no. 03 (July 4, 2013): 403–16. http://dx.doi.org/10.1142/s1005386713000370.

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We study contragredient modules for Möbius nonlocal vertex algebras and characterize the space of all invariant bilinear forms on Möbius nonlocal vertex algebras. Finally, Möbius weak quantum vertex algebras of Zamolodchikov-Faddeev type are studied as examples.
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Muhammad, Guntur Maulana, Iden Rainal Ihsan, and Roni Priyanda. "Sifat Preservasi Lingkaran dan Garis Pada Transformasi Möbius." Jambura Journal of Mathematics 4, no. 2 (June 1, 2022): 200–208. http://dx.doi.org/10.34312/jjom.v4i2.13497.

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This article discusses Möbius transformation from the point of view of algebra to describe one of its geometric properties, i.e. preserving circles and lines in complex planes. In simple terms, this preservation means that Möbius transformation maps a collection of circles and lines (back) into a collection of circles and lines. In general, the discussion begins with an explanation of the definition of the Möbius transformation in the complex plane. The discussion continues on defining the basic mapping and direct affine transformation. These two concepts are used to prove the existence of the preservation properties of circles and lines in the Möbius transformation. It can be shown that the Möbius transformation can be expressed as a composition of the direct affine transform and the inverse. It can also be shown that the direct affine transform and the inverse both have the property of preserving circles and lines in the complex plane. Thus, it can be concluded that in this study the Möbius transformation has the property of preserving circles and lines in the complex plane.
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Dissertations / Theses on the topic "Möbiu"

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DI, GRAVINA LUCA MARIA. "Some questions about the Möbius function of finite linear groups." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/371474.

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La funzione di Möbius definita per insiemi parzialmente ordinati localmente finiti è un classico strumento di analisi combinatoria. Si tratta di una generalizzazione della funzione di Möbius nota in teoria dei numeri e ha varie applicazioni pure in teoria dei gruppi, dalla caratteristica di Eulero di complessi di sottogruppi fino allo studio di aspetti algebrici in automi cellulari. Nella prima parte della tesi richiamiamo alcune informazioni elementari per strutture d'ordine che sono legate alla funzione di Möbius, e ne presentiamo le principali proprietà, quali ad esempio la formula di inversione di Möbius e i teoremi di Crapo. Inoltre analizziamo alcuni legami importanti con argomenti di teoria dei gruppi, al fine di motivare il nostro interesse nei confronti della funzione di Möbius di gruppi lineari finiti. Nella seconda parte, lavoriamo su questi gruppi per studiarne la funzione di Möbius e otteniamo risultati originali che si rivelano utili per calcolarla, nota la struttura di alcuni particolari reticoli di sottospazi associati ai sottogruppi. Vediamo in dettaglio il caso in cui abbiamo un reticolo di sottospazi distributivo. In seguito mostriamo un esempio di sottogruppo del gruppo lineare generale, tale che il reticolo di sottospazi associato al sottogruppo non è distributivo. In questo modo osserviamo che i nostri ragionamenti hanno una validità più ampia e possono essere applicati a situazioni differenti, sotto determinate condizioni. Nell'ultima parte della tesi, colleghiamo i risultati ottenuti in precedenza ad alcune questioni aperte che riguardano gruppi profiniti finitamente generati e gruppi finiti almost-simple, presentando un approccio originale al problema. Benché poi questo problema non venga completamente risolto, otteniamo degli utili risultati parziali che possono essere sviluppati in futuro.
The Möbius function of locally finite partially ordered sets is a classical tool in enumerative combinatorics. It is a generalization of the number-theoretic Möbius function and it has several applications in group theory, from the Euler characteristic of subgroup complexes to algebraic aspects of cellular automata. In the first part of the thesis, we recall some basic notions about the order structures which are related to the Möbius function, and we present its main properties, such as the Möbius inversion formula and Crapo's theorems. Moreover, we investigate some relevant connections with group-theoretical topics to motivate our interest in the Möbius function of finite linear groups. In the second part, we work on these groups to obtain information about their Möbius function, and our original results are useful to compute it if we know the structure of some special subspace lattices related to subgroups. We study in detail the case of distributive subspace lattices. Then we show an example of a subgroup in the general linear group, such that the subspace lattice associated to the subgroup is non-distributive. In this way, we see that our arguments can also be applied to different situations, under certain conditions. In the last part of the thesis, we connect the previously obtained results to an open question about finitely generated profinite groups and finite almost-simple groups, introducing an original approach to the problem. Although we do not completely answer to this last question, we get some useful partial results.
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Graziani, Lorenzo. "Un groviglio di mondi. Studio sul pluralismo fisico, metafisico e letterario postmoderno." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/260546.

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The main goal of this PhD dissertation is to explore the relation between postmodern poetics and some features of other theories developed at the same time in various areas of knowledge – mainly metaphysics, physics and sociology. If we can say that the modern paradigm was born with the question of how a multiplicity of different points of view could coexist, the postmodern paradigm seems to arise with the awareness that a systematic legitimation of differences cannot be based on a sole foundation that leads to a complete inclusion. For this reason, we argue that the concept of possible world is not only a useful heuristic metaphor adopted in different areas of the artistic and scientific postmodern culture, but it can put in constructive conversation different areas of knowledge which are usually thought to be more isolated and refractory to mutual influence than they actually are. Precisely because of the diverse usages and meanings that the term ‘world’ acquires in different contexts, the ontological commitment toward possible worlds varies significantly. They can be godly concepts, fictional scenarios, real sums of individuals that are isolated from each other, or ideal set of objects that are associated with different and mutually exclusive frames of reference and cultural coordinates. To shed a light on these matters is the main goal of the first book, entitled "What is a possible world?". The second book, entitled "Entangled worlds: the postmodernist literature", is committed to explore the topology of the possible worlds projected by postmodernist texts; in fact, the paradoxical topology that emerges from these texts appears to be inherently connected with a vast range of issues concerning our world.
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Cipolone, Anthony Dominic-Paul. "Möbius: for Orchestra." ScholarWorks@UNO, 2006. http://scholarworks.uno.edu/td/472.

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Möbius: for Orchestra attempts to explore an alternative use of the material that typically appears in the development section of a piece composed in sonata form. By using the modified themes in the recapitulation rather than disregarding them entirely, the A-B-A' form of the basic sonata becomes more of an A-B-(A'+B'). Much like the mathematical function this piece is named after – a loop whose ending is never identical to its beginning and whose mirror-image lacks symmetry – the listener is brought to a new ending with familiar, non-repeated material. Many times throughout the piece, the listener will hear up to three tonal centers at once, though differences in range, color, texture and dynamics give the effect of a single tonal center with a certain amount of unease. Ostinatos and long notes also help to dissuade the ear from settling on a comfortable sound, ending with uncertainty, much like it began.
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Santos, Marcus Vinicio de Jesus. "Transformação de Möbius." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/6499.

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The aim of this work is the study of arbitrary mobius transformations by means of simple complex transformations, namely: the Translation, the Rotation, the Homotetia (Contraction and Dilatation) and Inversion. The results obtained were applied in circles and straight line. At the end, we give the the alternative of studying mobius transformations via matrices.
O objetivo deste trabalho é estudar transformações de Möbius arbitrárias por meio de transformações complexas mais simples, a saber: a Translação, a Rotação, a Homotetia (Contração e Dilatação) e a Inversão. Os resultados obtidos foram aplicados em círculos e retas. No final, damos a alternativa de estudar transformações de Möbius via matrizes.
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Duran, Franciéli [UNESP]. "Transformações de Möbius e inversões." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/94367.

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O objetivo deste trabalho é estudar Transformações de Möbius arbitrárias por meio de transformações mais simples. Um estudo detalhado de inversão geométrica é realizado com o objetivo de estudar a inversão complexa. Apresentamos o comportamento das Transformações de Möbius no in nito e as classi camos em elíptica, hiperbólica, loxodrômica e parabólica
The aim of this work is the study of arbitrary Möbius transformations by use of simpler ones. A detailed study of geometric inversions is done to well understand complex inversions. We present the behavior of Möbius transformations at in nity and classify them as elliptic, hyperbolic, loxodromic, and parabolic
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Duran, Franciéli. "Transformações de Möbius e inversões /." Rio Claro, 2013. http://hdl.handle.net/11449/94367.

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Orientador: Thiago de Melo
Banca: Valderlei Marcos do Nascimento
Banca: Márcio de Jesus Soares
Resumo: O objetivo deste trabalho é estudar Transformações de Möbius arbitrárias por meio de transformações mais simples. Um estudo detalhado de inversão geométrica é realizado com o objetivo de estudar a inversão complexa. Apresentamos o comportamento das Transformações de Möbius no in nito e as classi camos em elíptica, hiperbólica, loxodrômica e parabólica
Abstract: The aim of this work is the study of arbitrary Möbius transformations by use of simpler ones. A detailed study of geometric inversions is done to well understand complex inversions. We present the behavior of Möbius transformations at in nity and classify them as elliptic, hyperbolic, loxodromic, and parabolic
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Ramirez, Aguirre Josimar Joao. "Ortogonalidade da Função de Möbius." reponame:Repositório Institucional da UnB, 2014. http://repositorio.unb.br/handle/10482/17013.

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Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2014.
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Nesta dissertação de Mestrado apresentamos uma nova prova do Teorema de Davenport (1937), e a prova de Terence Tao que a conjectura de Chowla implica a conjectura de Sarnak. Na primeira parte do trabalho apresentamos a teoria básica das L-funcões bem como uma variação método de Vinogradov, usando as identidades de Vaughan. Em seguida, usamos estas ferramentas para mostrar o Teorema de Davenport. A principal referência desta parte são os capítulos 5 e 13 do livro Analitic Number Theory de Henryk Iwaniec e Emmanuel Kowalski, [9]. A prova que a Conjectura de Chowla implica na Conjectura de Sarnak é baseada em princípio de grandes desvios, obtido por uma variação do método do segundo momento. A exposição é inspirada na primeira parte do artigo de Peter Sarnak, intitulado Three Lectures on the Mobius Function Randomness and Dynamics, [16]. _______________________________________________________________________________ ABSTRACT
In this Master's thesis we present a new proof of Davenport's Theorem (1937), and the Terence Tao's proof that Chowla conjecture implies Sarnak's conjecture. In the _rst part of this work we present the basic theory of L-functions and a variation of the Vinogradov's method using the Vaughan's identities. Then we use these tools to prove Davenport's Theorem. This section is based on chapters 5 and 13 of the reference Analytic Number Theory by Henryk Iwaniec and Emmanuel Kowalski, [9]. The Chowla's Conjecture implies Sarnak's Conjecture is based on a principle of large deviations obtained by variation of the second moment method. The exposition is inspired on the _rst part of Peter Sarnak's article entitled Three Lectures on the Mobius Function Randomness and Dynamics, [16].
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Vieira, Nelson Felipe Loureiro. "Transformações de Möbius em RO." Master's thesis, Universidade de Aveiro, 2005. http://hdl.handle.net/10773/2880.

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Mestrado em Matemática
O principal objectivo deste trabalho texto consiste em estudar a influência das transformações Möbius, em vários aspectos da análise de Clifford. No capítulo zero introduziremos as definições e resultados preliminares, necessários para boa compreensão do texto; encerraremos este capítulo com o problema de Dirichlet na bola unitária em C. O primeiro capítulo é dedicado ao problema de Dirichlet para o caso da bola unitária em R0,n. Serão obtidas as generalizações dos resultados apresentados no capítulo zero para o caso complexo. No capítulo seguinte serão introduzidas as coordenadas projectivas e algumas definições associadas. Com este tipo de coordenadas, estabeleceremos um isomorfismo entre (R ) 2x2 e R . Com base nesta relação, estabeleceremos uma descrição matricial das superfícies esféricas, a qual conduzirá a uma conveniente representação matricial das transformações Möbius – dita representação de Vahlen. Na secção final deste capítulo será feita uma caracterização do grupo de Clifford (1,n+1) em termos destas matrizes. p,q p+1,q+1 No terceiro e último capítulo estudaremos a métrica diferencial invariante sob a acção das transformações de Möbius. Finalmente, concluiremos com o estudo do comportamento dos operadores de Laplace e de Dirac sob a acção das transformações de Möbius. ABSTRACT: The main objective of this work is to study the influence of the Möbius transformations in some aspects of Clifford analysis. In the preliminary chapter we introduce some definitions and preliminary results which are necessary for a good comprehension of the present text; we finish this chapter with the Dirichlet problem over the complex unit ball. The first chapter is dedicated to the study of the Dirichlet problem in the ndimensional unit ball. We will obtain the generalizations of the results presented in the complex case. In the next chapter we will introduce projective coordinates and some associated definitions. With this kind of coordinates we will establish an isomorphism between (Rp,q)2x2 and Rp+1,q+1. With this relation we will also establish a matricial description of the unit sphere which implies a convenient matricial representation of Möbius transformation - usually called Vahlen representation. In the final section we will characterized the Clifford group Γ(1,n+1) in terms of these matrices. In the third chapter we will study the invariant differential metric under the action of Möbius transformation. Finally, we will study the behaviour of Laplace and Dirac operator under the action of Möbius transformations.
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Inoue, Mitsunori. "Studies on Möbius Aromaticity of Hexaphyrins." 京都大学 (Kyoto University), 2011. http://hdl.handle.net/2433/142391.

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ALMEIDA, Múcio Brandão Vaz de. "Alterações ortopédicas na seqüência de Möbius." Universidade Federal de Pernambuco, 2006. https://repositorio.ufpe.br/handle/123456789/3110.

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Introdução: A Seqüência de Möbius (SM) consiste de paralisia congênita do VI e VII nervos cranianos, podendo apresentar em sua etiologia associação com o uso do misoprostol como abortivo. O objetivo deste estudo foi descrever as anomalias ortopédicas em portadores dessa seqüência, além de investigar possível associação de tais alterações entre os casos esporádicos e aqueles cujas mães usaram misoprostol durante o primeiro trimestre da gravidez. Métodos: Foram analisados 42 portadores da SM, atendidos na Associação de Assistência à Criança Deficiente Pernambuco, no período de 1999 a 2005. Vinte e cinco eram do gênero feminino e 17 do masculino. A idade no momento da pesquisa variou de 8 meses a 15 anos e 11 meses; média de 6 anos e 1 mês de idade. O diagnóstico da doença foi estabelecido por equipe multidisciplinar, incluindo neuropediatra, oftalmologista, ortopedista e psicólogo. As mães dos investigados foram interrogadas quanto ao uso do misoprostol durante a gravidez. O estudo foi do tipo observacional, sendo descrito os achados ortopédicos de uma série de casos. Foi introduzido componente analítico para investigar se a freqüência de anomalias do aparelho locomotor estava ou não associada ao uso de misoprostol. Resultados: Das 42 mães destes pacientes, 25 (59,5%) utilizaram o misoprostol como abortivo durante o primeiro trimestre de gestação. Dezessete (40,5%) mães negaram ter usado abortivos durante a gestação. Houve acometimento do VI e VII nervos cranianos em todos os pacientes. O IX e o X nervos cranianos estiveram acometidos em 17 (40,5%) pacientes. A associação com Síndrome de Poland foi vista em um paciente, e com paralisia cerebral em quatro. Trinta e quatro (80,9%) pacientes apresentaram alguma deformidade ortopédica, sendo o pé torto a mais comum. Conclusão: Anomalias ortopédicas foram observadas na grande maioria dos pacientes incluídos no estudo, sendo o pé torto congênito a mais encontrada. Não houve diferença estatisticamente significante entre a freqüência de anomalias ortopédicas em portadores da Seqüência de Möbius filhos de mães que usaram misoprostol, quando comparadas com os casos esporádicos
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Books on the topic "Möbiu"

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Möbius. Pamplona]: Museo Universidad de Navarra, 2016.

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Möbius, Jürgen. Jürgen Möbius. Bönen: DruckVerlag Kettler, 1999.

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Chen, Nanxian. Möbius inversion in physics. Singapore: World Scientific, 2010.

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Fauvel, John, Raymond Flood, and Robin Wilson, eds. Möbius und sein Band. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-6203-5.

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Richard, Kwakkel, ed. De ring van Möbius. Amsterdam: Sijthoff, 2010.

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Paul, Watzlawick, ed. Gödelsatz, Möbius-Schleife, Computer-Ich. Wien: F. Deuticke, 1986.

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Fosdick, Roger, and Eliot Fried, eds. The Mechanics of Ribbons and Möbius Bands. Dordrecht: Springer Netherlands, 2016. http://dx.doi.org/10.1007/978-94-017-7300-3.

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Dür, Arne. Möbius Functions, Incidence Algebras and Power Series Representations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0077472.

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Möbius, Klaus. Der Architekt Klaus Möbius: Staatstheater Mainz : Kleines Haus. Berlin: H. Schmidt, 1998.

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Toth, Gabor. Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0061-8.

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Book chapters on the topic "Möbiu"

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Röschel, O. "Möbius Mechanisms." In Advances in Robot Kinematics, 375–82. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4120-8_39.

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Berman, David, Hugo Garcia-Compean, Paulius Miškinis, Miao Li, Daniele Oriti, Steven Duplij, Steven Duplij, et al. "Möbius Strip." In Concise Encyclopedia of Supersymmetry, 249. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_329.

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Berman, David, Hugo Garcia-Compean, Paulius Miškinis, Miao Li, Daniele Oriti, Steven Duplij, Steven Duplij, et al. "Möbius Transformation." In Concise Encyclopedia of Supersymmetry, 249. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_330.

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Rivera-Serrano, Carlos M., and Barry M. Schaitkin. "Möbius Syndrome." In Encyclopedia of Otolaryngology, Head and Neck Surgery, 1703–7. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-23499-6_680.

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Rovenski, Vladimir. "Möbius Transformations." In Modeling of Curves and Surfaces with MATLAB®, 159–97. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-71278-9_4.

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Stewart, Ian. "Möbius’ Vermächtnis." In Möbius und sein Band, 153–202. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-6203-5_6.

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Hariri, Parisa, Riku Klén, and Matti Vuorinen. "Möbius Transformations." In Springer Monographs in Mathematics, 25–48. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-32068-3_3.

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Balakrishnan, V. "Möbius Transformations." In Mathematical Physics, 623–43. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39680-0_27.

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Reshetnyak, Yu G. "Möbius Transformations." In Stability Theorems in Geometry and Analysis, 63–105. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8360-2_2.

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Chen, Harold. "Möbius Syndrome." In Atlas of Genetic Diagnosis and Counseling, 1–12. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4614-6430-3_159-2.

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Conference papers on the topic "Möbiu"

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Poddar, Ajay K., Ulrich L. Rohde, and Shiban K. Koul. "Möbius-Graphene and Möbius-Metamaterial VCO." In 2016 IEEE MTT-S International Microwave and RF Conference (IMaRC). IEEE, 2016. http://dx.doi.org/10.1109/imarc.2016.7939613.

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Bittner, Stefan, Yalei Song, Yann Monceaux, Kimhong Chao, Hector M. Reynoso de la Cruz, Clement Lafargue, Dominique Decanini, et al. "Möbius strip microlasers." In 2021 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC). IEEE, 2021. http://dx.doi.org/10.1109/cleo/europe-eqec52157.2021.9542455.

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Klimenko, Stanislav, Gregory M. Nielson, Lialia Nikitina, and Igor Nikitin. "Adventures of Möbius band." In the eighteenth annual symposium. New York, New York, USA: ACM Press, 2002. http://dx.doi.org/10.1145/513400.513436.

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Soluk, Patricia, James Greenwood-Lee, Julie Peschke, Angela Beltaos, Vive Kumar, Ken Munyikwa, Shauna Babiuk, and Shauna Rechseidler-Zenteno. "Building Educational Resilience in Mathematics Delivery and Assessment." In Tenth Pan-Commonwealth Forum on Open Learning. Commonwealth of Learning, 2022. http://dx.doi.org/10.56059/pcf10.616.

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Abstract:
Mathematics is a foundational subject in education. Learning outcomes in mathematics build on previous competencies and students are well-served by real-time intervention and feedback. However, contemporary math education is limited by technology, scalable learning, shareable experiences (both teaching and learning), and accessible modes of practice. Most assessment platforms do not have the functionality to support symbols and equations. During the pandemic we have diverted assessments in high enrolment mathematics courses from paper to electronic delivery. We developed randomized examinations for Introductory Statistics and Introduction to Calculus I and we developed an entire course with assessment using OERs (open educational resources) for Business Mathematics. Our team developed highly interactive, traceable, and intervenable content in math problem solving using the Möbius (https://digitaled.com/mobius) platform. We enabled an LTI integration of the platform into our LMS (learning management system) to provide seamless access for students. Möbius promotes cognitive learning through a powerful math engine, student feedback, analytics, and interactive STEM (science, technology, engineering, math) curriculum content. We are serving 3,000 learners with effective assessment and have relieved faculty and staff of administering and marking alternative examinations through a long pandemic. We have seen improvements in student feedback, increased accessibility, reduced administrative burden, and enhanced exam security. Möbius is a truly scalable and cost-effective platform for math educators and students that provides more efficient and effective management of educational delivery.
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Coen, Stéphane, Gang Xu, Liam Quinn, Bruno Garbin, Gian-Luca Oppo, Nathan Goldman, Stuart G. Murdoch, Miro Erkintalo, and Julien Fatome. "Nonlinear topological protection of spontaneous symmetry breaking in a driven Kerr resonator." In CLEO: Applications and Technology. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_at.2022.jm3a.3.

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A two-mode Kerr cavity with a π-phase defect exhibits a virtual Möbius topology and enables spontaneous symmetry breaking with unprecedented robustness. Experiments performed with homogeneous and localized states confirm our predictions.
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Lipman, Yaron, and Thomas Funkhouser. "Möbius voting for surface correspondence." In ACM SIGGRAPH 2009 papers. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1576246.1531378.

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Mitchel, Thomas W., Noam Aigerman, Vladimir G. Kim, and Michael Kazhdan. "Möbius Convolutions for Spherical CNNs." In SIGGRAPH '22: Special Interest Group on Computer Graphics and Interactive Techniques Conference. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3528233.3530724.

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HAYASHI, M., T. SUZUKI, H. EBISAWA, and K. KUBOKI. "SUPERCONDUCTING STATES ON A MÖBIUS STRIP." In Proceedings of the 1st International Symposium on TOP2005. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772879_0006.

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"ROBUST ILC DESIGN USING MÖBIUS TRANSFORMATIONS." In 2nd International Conference on Informatics in Control, Automation and Robotics. SciTePress - Science and and Technology Publications, 2005. http://dx.doi.org/10.5220/0001172601410146.

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Björklund, Andreas, Thore Husfeldt, Petteri Kaski, and Mikko Koivisto. "Fourier meets möbius: fast subset convolution." In the thirty-ninth annual ACM symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1250790.1250801.

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Reports on the topic "Möbiu"

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Emmanuele, Daniela. Force Free Möbius Motions of the Circle. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-27-2012-59-65.

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Deryagina, Madina, and Ilia Mednykh Mednykh. On the Jacobian Group for Möbius Ladder and Prism Graphs. GIQ, 2014. http://dx.doi.org/10.7546/giq-15-2014-117-126.

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