Relevant bibliographies by topics / Weierstrass theorem -The Catalan

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Academic literature on the topic 'Weierstrass theorem -The Catalan'

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Published: 4 June 2025
Last updated: 15 July 2025

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Journal articles on the topic "Weierstrass theorem -The Catalan"

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Mohammed, Ghanim. "A SHORT ELEMENTARY PROOF OF THE BEAL CONJECTURE WITH DEDUCTION OF THE FERMAT LAST THEOREM." GLOBAL JOURNAL OF ADVANCED ENGINEERING TECHNOLOGIES AND SCIENCES 8, no. 1 (2021): 1–16. https://doi.org/10.5281/zenodo.4568087.

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The present short paper, which is an amelioration of my previous article “confirmation of the Beal-Brun-Tijdeman-Zagier conjecture” published by the GJETS in 20/11/2019 [15], confirms the Beal’s conjecture, remained open since 1914 and saying that:       The proof uses elementary tools of mathematics, such as the L’Hôpital rule, the Bolzano-Weierstrass theorem, the intermediate value theorem and the growth properties of certain elementary functions. The proof uses also the Catalan-Mihailescu theorem [18] [19] and some methods developed in my paper on the Fermat last theorem [14] published by the GJAETS in 10/12/2018. The particular case of the Fermat last theorem is deduced
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Laville, Guy, and Ivan Ramadanoff. "Stone-Weierstrass theorem." Banach Center Publications 37, no. 1 (1996): 189–94. http://dx.doi.org/10.4064/-37-1-189-194.

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Nesterenko, Yu V. "Lindemann–Weierstrass Theorem." Moscow University Mathematics Bulletin 76, no. 6 (2021): 239–43. http://dx.doi.org/10.3103/s0027132221060073.

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Wu, Hueytzen J. "New Stone-Weierstrass Theorem." Advances in Pure Mathematics 06, no. 13 (2016): 943–47. http://dx.doi.org/10.4236/apm.2016.613071.

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Portilla, Ana, Yamilet Quintana, José M. Rodrı́guez, and Eva Tourı́s. "Weierstrass’ theorem with weights." Journal of Approximation Theory 127, no. 1 (2004): 83–107. http://dx.doi.org/10.1016/j.jat.2004.01.003.

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Rao, N. V. "The Stone-Weierstrass Theorem Revisited." American Mathematical Monthly 112, no. 8 (2005): 726. http://dx.doi.org/10.2307/30037574.

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Rao, N. V. "The Stone-Weierstrass Theorem Revisited." American Mathematical Monthly 112, no. 8 (2005): 726–29. http://dx.doi.org/10.1080/00029890.2005.11920244.

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Niemiec, Piotr. "Strengthened Stone-Weierstrass type theorem." Opuscula Mathematica 31, no. 4 (2011): 645. http://dx.doi.org/10.7494/opmath.2011.31.4.645.

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Martínez-Legaz, Juan Enrique. "On Weierstrass extreme value theorem." Optimization Letters 8, no. 1 (2012): 391–93. http://dx.doi.org/10.1007/s11590-012-0587-0.

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Prolla, J. B. "On the Weierstrass-Stone Theorem." Journal of Approximation Theory 78, no. 3 (1994): 299–313. http://dx.doi.org/10.1006/jath.1994.1080.

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Dissertations / Theses on the topic "Weierstrass theorem -The Catalan"

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Rivard-Cooke, Martin. "An Analog of the Lindemann-Weierstrass Theorem for the Weierstrass p-Function." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31722.

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This thesis aims to prove the following statement, where the Weierstrass p-function has algebraic invariants and complex multiplication by Q(alpha): "If beta_1,..., beta_n are algebraic numbers which are linearly independent over Q(alpha), then p(beta_1),...,p(beta_n) are algebraically independent over Q." This was proven by Philippon in 1983, and the proof in this thesis follows his ideas. The difference lies in the strength of the tools used, allowing certain arguments to be simplified. This thesis shows that the above result is equivalent to imposing the restriction (beta_1,...,beta_n)=(1,beta,...,beta^{n-1}), where n=[Q(alpha,beta):Q(alpha)]. The core of the proof consists of developing height estimates, constructing representations for morphisms between products of elliptic curves, and finding height and degree estimates on large families of polynomials which are small at a point in Q(alpha,beta,g_2,g_3)(p(1),p'(1),...,p(beta^{n-1}),p'(beta^{n-1})). An application of Philippon's zero estimate (1986) and his criterion of algebraic independence (1984) is then used to obtain the main result.
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Sheppard, Barnaby. "On generalisations of the Stone-Weierstrass theorem to Jordan structures." Thesis, University of Reading, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301909.

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The main theorem of the thesis asserts that if B is a JB*-subtriple of a JB*triple A such that B separates oe(An U {O}, then if A or B is postliminal, A=B. The main theorem and many of the other key results of the thesis are generalisations of the results of Kaplansky (1951) and Glimm (1960) on the Stone-Weierstrass conjecture for C* -algebras. We first prove a Stone-Weierstrass theorem for postliminal JB-algebras. This plays an essential role in the proof of the main theorem and is also important in the proof of our second main result, the Glimm-Stone-Weierstrass theorem for JB-algebras. Vital to the Glimm-Stone-Weierstrass proof, we show that if A is a universally reversible prime and antiliminal JB-algebra, then S(A) C P(A). Conversely, if A is universally reversible and of dimension greater than one, S(A) C P(A) implies A is prime and antiliminal. The C* -algebra version of this theorem is due to Tomiyama and Takesaki (1961). By means of the universal enveloping C*-algebra functor, we show that if , the Stone-Weierstrass conjecture is true for C* -algebras then it is true for JB-algebras. Employing a similar technique we prove Stone-Weierstrass theorems for semi-finite JW-algebras and type I JW-algebras, building on results of Akemann (1969- 70). The crucial result of the thesis reduces the Stone-Weierstrass separation condition for JB*-triples locally to that of JB*-algebras. Using this in conjunction with the Stone-Weierstrass theorem for postliminal JB-algebras is an essential part of the proof of the main theorem
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Elallam, Abderrahim. "Constructions & Optimization in Classical Real Analysis Theorems." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/etd/3901.

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This thesis takes a closer look at three fundamental Classical Theorems in Real Analysis. First, for the Bolzano Weierstrass Theorem, we will be interested in constructing a convergent subsequence from a non-convergent bounded sequence. Such a subsequence is guaranteed to exist, but it is often not obvious what it is, e.g., if an = sin n. Next, the H¨older Inequality gives an upper bound, in terms of p ∈ [1,∞], for the the integral of the product of two functions. We will find the value of p that gives the best (smallest) upper-bound, focusing on the Beta and Gamma integrals. Finally, for the Weierstrass Polynomial Approximation, we will find the degree of the approximating polynomial for a variety of functions. We choose examples in which the approximating polynomial does far worse than the Taylor polynomial, but also work with continuous non-differentiable functions for which a Taylor expansion is impossible.
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Redpath, Stuart Frederick. "Universal approximation properties of feedforward artificial neural networks." Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1015869.

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In this thesis we summarise several results in the literature which show the approximation capabilities of multilayer feedforward artificial neural networks. We show that multilayer feedforward artificial neural networks are capable of approximating continuous and measurable functions from Rn to R to any degree of accuracy under certain conditions. In particular making use of the Stone-Weierstrass and Hahn-Banach theorems, we show that a multilayer feedforward artificial neural network can approximate any continuous function to any degree of accuracy, by using either an arbitrary squashing function or any continuous sigmoidal function for activation. Making use of the Stone-Weirstrass Theorem again, we extend these approximation capabilities of multilayer feedforward artificial neural networks to the space of measurable functions under any probability measure.
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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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<p>This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of N<sub>q</sub>(g) is now known.</p><p>At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.</p><p> </p>
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Arruda, Rafael Lucas de [UNESP]. "Teorema de Riemann-Roch e aplicações." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/86493.

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Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-25Bitstream added on 2014-06-13T20:28:17Z : No. of bitstreams: 1 arruda_rl_me_sjrp.pdf: 624072 bytes, checksum: 23ddd00e27d1ad781e2d1cec2cb65dee (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica<br>The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve
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Heinz, Sebastian. "Preservation of quasiconvexity and quasimonotonicity in polynomial approximation of variational problems." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2008. http://dx.doi.org/10.18452/15808.

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Die vorliegende Arbeit beschäftigt sich mit drei Klassen ausgewählter nichtlinearer Probleme, die Forschungsgegenstand der angewandten Mathematik sind. Diese Probleme behandeln die Minimierung von Integralen in der Variationsrechnung (Kapitel 3), das Lösen partieller Differentialgleichungen (Kapitel 4) und das Lösen nichtlinearer Optimierungsaufgaben (Kapitel 5). Mit deren Hilfe lassen sich unterschiedlichste Phänomene der Natur- und Ingenieurwissenschaften sowie der Ökonomie mathematisch modellieren. Als konkretes Beispiel werden mathematische Modelle der Theorie elastischer Festkörper betrachtet. Das Ziel der vorliegenden Arbeit besteht darin, ein gegebenes nichtlineares Problem durch polynomiale Probleme zu approximieren. Um dieses Ziel zu erreichen, beschäftigt sich ein großer Teil der vorliegenden Arbeit mit der polynomialen Approximation von nichtlinearen Funktionen. Den Ausgangspunkt dafür bildet der Weierstraßsche Approximationssatz. Auf der Basis dieses bekannten Satzes und eigener Sätze wird als Hauptresultat der vorliegenden Arbeit gezeigt, dass im Übergang von einer gegebenen Funktion zum approximierenden Polynom wesentliche Eigenschaften der gegebenen Funktion erhalten werden können. Die wichtigsten Eigenschaften, für die dies bisher nicht bekannt war, sind: Quasikonvexität im Sinne der Variationsrechnung, Quasimonotonie im Zusammenhang mit partiellen Differentialgleichungen sowie Quasikonvexität im Sinne der nichtlinearen Optimierung (Theoreme 3.16, 4.10 und 5.5). Schließlich wird gezeigt, dass die zu den untersuchten Klassen gehörenden nichtlinearen Probleme durch polynomiale Probleme approximiert werden können (Theoreme 3.26, 4.16 und 5.8). Die dieser Approximation zugrunde liegende Konvergenz garantiert sowohl eine Approximation im Parameterraum als auch eine Approximation im Lösungsraum. Für letztere werden die Konzepte der Gamma-Konvergenz (Epi-Konvergenz) und der G-Konvergenz verwendet.<br>In this thesis, we are concerned with three classes of non-linear problems that appear naturally in various fields of science, engineering and economics. In order to cover many different applications, we study problems in the calculus of variation (Chapter 3), partial differential equations (Chapter 4) as well as non-linear programming problems (Chapter 5). As an example of possible applications, we consider models of non-linear elasticity theory. The aim of this thesis is to approximate a given non-linear problem by polynomial problems. In order to achieve the desired polynomial approximation of problems, a large part of this thesis is dedicated to the polynomial approximation of non-linear functions. The Weierstraß approximation theorem forms the starting point. Based on this well-known theorem, we prove theorems that eventually lead to our main result: A given non-linear function can be approximated by polynomials so that essential properties of the function are preserved. This result is new for three properties that are important in the context of the considered non-linear problems. These properties are: quasiconvexity in the sense of the calculus of variation, quasimonotonicity in the context of partial differential equations and quasiconvexity in the sense of non-linear programming (Theorems 3.16, 4.10 and 5.5). Finally, we show the following: Every non-linear problem that belongs to one of the three considered classes of problems can be approximated by polynomial problems (Theorems 3.26, 4.16 and 5.8). The underlying convergence guarantees both the approximation in the parameter space and the approximation in the solution space. In this context, we use the concepts of Gamma-convergence (epi-convergence) and of G-convergence.
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Arruda, Rafael Lucas de. "Teorema de Riemann-Roch e aplicações /." São José do Rio Preto : [s.n.], 2011. http://hdl.handle.net/11449/86493.

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Orientador: Parham Salehyan<br>Banca: Eduardo de Sequeira Esteves<br>Banca: Jéfferson Luiz Rocha Bastos<br>Resumo: O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica<br>Abstract: The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve<br>Mestre
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Chen, Bo-Lin, and 陳柏霖. "Uncomputability of the Bolzano–Weierstrass theorem." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/rgw66n.

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碩士<br>元智大學<br>資訊工程學系<br>104<br>The Bolzano–Weierstrass theorem says that any bounded sequence of real numbers has a converging subsequence. But it does not tell us how to calculate a converging subsequence of real numbers. Neither does it tell us how to calculate a value that is the limit of a converging subsequence. We show the nonexistence of an algorithm that, given a Turing machine M that outputs a binary string, and ϵ>0, outputs a real number which differs from the limit of a converging subsequence of {0.M(1^n )}_(n=1)^∞ by at most ε in absolute value.
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Miller, Daniel J. "A preparation theorem for Weierstrass systems." 2003. http://www.library.wisc.edu/databases/connect/dissertations.html.

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Books on the topic "Weierstrass theorem -The Catalan"

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Weierstrass-Stone, the theorem. P. Lang, 1993.

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Mann, Peter. The Stationary Action Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0007.

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This crucial chapter focuses on the stationary action principle. It introduces Lagrangian mechanics, using first-order variational calculus to derive the Euler–Lagrange equation, and the inverse problem is described. The chapter then considers the Ostrogradsky equation and discusses the properties of the extrema using the second-order variation to the action. It then discusses the difference between action functions (of Dirichlet boundary conditions) and action functionals of the extremal path. The different types of boundary conditions (Dirichlet vs Neumann) are elucidated. Topics discussed include Hessian conditions, Douglas’s theorem, the Jacobi last multiplier, Helmholtz conditions, Noether-type variation and Frenet–Serret frames, as well as concepts such as on shell and off shell. Actions of non-continuous extremals are examined using Weierstrass–Erdmann corner conditions, and the action principle is written in the most general form as the Hamilton–Suslov principle. Important applications of the Euler–Lagrange formulation are highlighted, including protein folding.
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Book chapters on the topic "Weierstrass theorem -The Catalan"

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Abhyankar, Shreeram. "Weierstrass preparation theorem." In Mathematical Surveys and Monographs. American Mathematical Society, 1990. http://dx.doi.org/10.1090/surv/035/16.

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Viola, Carlo. "The Weierstrass Factorization Theorem." In UNITEXT. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41345-7_2.

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Krall, Allan M. "The Stone-Weierstrass Theorem." In Applied Analysis. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4748-1_6.

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Murty, M. Ram, and Purusottam Rath. "The Lindemann–Weierstrass Theorem." In Transcendental Numbers. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0832-5_4.

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Ullrich, David. "The Weierstrass factorization theorem." In Complex Made Simple. American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/097/14.

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Groenewegen, G. L. M., and A. C. M. van Rooij. "The Stone-Weierstrass Theorem." In Spaces of Continuous Functions. Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-201-4_3.

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Bernard, Sophie. "Formalization of the Lindemann-Weierstrass Theorem." In Interactive Theorem Proving. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66107-0_5.

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Bilu, Yuri F., Yann Bugeaud, and Maurice Mignotte. "The Theorem of Thaine." In The Problem of Catalan. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10094-4_12.

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Bilu, Yuri F., Yann Bugeaud, and Maurice Mignotte. "Gauss Sums and Stickelberger’s Theorem." In The Problem of Catalan. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10094-4_7.

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Shalit, Orr Moshe. "Introduction and the Stone-Weierstrass theorem." In A First Course in Functional Analysis. Chapman and Hall/CRC, 2017. http://dx.doi.org/10.1201/9781315367132-1.

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Conference papers on the topic "Weierstrass theorem -The Catalan"

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Panahian Fard, Saeed, and Zarita Zainuddin. "Triangular type-2 fuzzy neural networks version of the Stone-Weierstrass theorem." In 2013 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2013. http://dx.doi.org/10.1109/fskd.2013.6816185.

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Cordero-Dávila, Alberto, Jorge González-García, and Diego Gabriel Reyes-Olguín. "Spot diagram borders are always caustic curves and/or marginal rays: Proof applied by means of the Weierstrass theorem." In Latin America Optics and Photonics Conference. Optica Publishing Group, 2022. http://dx.doi.org/10.1364/laop.2022.w4a.22.

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Weierstrass theorem and different Zernike polynomials are used to prove that for any optical system with general exit pupil affected by any aberrations, the borders of all leaving rays are curves caustic and/or marginal rays.
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BRIEM, EGGERT. "A STONE-WEIERSTRASS THEOREM FOR FUNCTION SPACES THAT DO NOT CONTAIN THE CONSTANT FUNCTIONS." In Proceedings of the Sixth Conference. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704450_0007.

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