Relevant bibliographies by topics / Germs of real analytic functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Germs of real analytic functions'

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Published: 24 April 2022

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Journal articles on the topic "Germs of real analytic functions"

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Dudziński, Piotr. "Topological invariants of germs of real analytic functions." Glasgow Mathematical Journal 39, no. 1 (1997): 85–89. http://dx.doi.org/10.1017/s0017089500031943.

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Let f: (ℝn, 0)→ (ℝ,0) be a germ of a real analytic function. Let L and F(f) denote the link of f and the Milnor fibre of fc respectively, i. e., L = {x ∈ Sn−1 | f(x) = 0}, , where 0 ≤ ξ ≪ r ≪ 1, . In [2] Szafraniec introduced the notion of an -germ as a generalization of a germ defined by a weighted homogeneous polynomial satisfying some condition concerning the relation between its degree and weights (definition 1). He also proved that if f is an -germ (presumably with nonisolated singularity) then the number χ(F(f)/d mod 2 is a topological invariant of f, where χ(F(f)) is the Euler character
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Berraho, M. "Плюригармонические определимые функции в некоторых $o$-минимальных расширениях вещественного поля". Владикавказский математический журнал, № 4 (23 грудня 2021): 35–40. http://dx.doi.org/10.46698/w9805-4567-8091-g.

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In this paper, we first try to solve the following problem: If a pluriharmonic function $f$ is definable in an arbitrary o-minimal expansion of the structure of the real field $\overline{\mathbb{R}}:=(\mathbb{R},+,-,.,0,1,<)$, does this function be locally the real part of a holomorphic function which is definable in the same expansion? In Proposition 2.1 below, we prove that this problem has a positive answer if the Weierstrass division theorem holds true for the system of the rings of real analytic definable germs at the origin of $\mathbb{R}^n$. We obtain the same answer for an o-minimal
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Speissegger, Patrick. "Quasianalytic Ilyashenko Algebras." Canadian Journal of Mathematics 70, no. 1 (2018): 218–40. http://dx.doi.org/10.4153/cjm-2016-048-x.

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AbstractWe construct a quasianalytic field of germs at +∞ of real functions with logarithmic generalized power series as asymptotic expansions, such that is closed under differentiation and log-composition; in particular, is a Hardy field. Moreover, the field o (−log) of germs at 0+ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.
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Rainer, Armin, and Gerhard Schindl. "On the Borel mapping in the quasianalytic setting." MATHEMATICA SCANDINAVICA 121, no. 2 (2017): 293. http://dx.doi.org/10.7146/math.scand.a-97101.

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The Borel mapping takes germs at $0$ of smooth functions to the sequence of iterated partial derivatives at $0$. We prove that the Borel mapping restricted to the germs of any quasianalytic ultradifferentiable class strictly larger than the real analytic class is never onto the corresponding sequence space.
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SZAFRANIEC, ZBIGNIEW. "On topological invariants of real analytic singularities." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 1 (2001): 13–24. http://dx.doi.org/10.1017/s0305004100004795.

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Let F = (f1, …, fm): (Kn, 0) → (Km, 0), where K is either R or C, be an analytic mapping defined in a neighbourhood of the origin. Let Br ⊂ Kn be a closed ball of small radius r centred at the origin. For any regular value y ∈ Km close to the origin, the fibre Wy = F−1(y) ∩ Br is called the Milnor fibre of F. We assume that m [les ] n, because in the other case Wy is void.Several authors investigated the topology of the Milnor fibres. Let us recall the most important results in the complex case. Let [Oscr ]C,0 denote the ring of germs of analytic functions f: (Cn, 0) → C.
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Bartosiewicz, Zbigniew. "Local Observability of Systems on Time Scales." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/810625.

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Analytic systems on an arbitrary time-scale are studied. As particular cases they include continuous-time and discrete-time systems. Several local observability properties are considered. They are characterized in a unified way using the language of real analytic geometry, ideals of germs of analytic functions, and their real radicals. It is shown that some properties related to observability are preserved under various discretizations of continuous-time systems.
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Randriambololona, Serge. "Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation." Nagoya Mathematical Journal 215 (September 2014): 225–37. http://dx.doi.org/10.1017/s0027763000010965.

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AbstractThis article presents two constructions motivated by a conjecture of van den Dries and Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct maximal polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.
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Randriambololona, Serge. "Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation." Nagoya Mathematical Journal 215 (September 2014): 225–37. http://dx.doi.org/10.1215/00277630-2781221.

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AbstractThis article presents two constructions motivated by a conjecture of van den Dries and Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct maximal polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.
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Bonet, José, and Reinhold Meise. "On the Theorem of Borel for Quasianalytic Classes." MATHEMATICA SCANDINAVICA 112, no. 2 (2013): 302. http://dx.doi.org/10.7146/math.scand.a-15246.

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We investigate the surjectivity of the Borel map in the quasianalytic setting for classes of ultradifferentiable functions defined in terms of the growth of the Fourier-Laplace transform. We deal with both the Roumieu $\mathcal{E}_{\{\omega\}}$ and the Beurling $\mathcal{E}_{(\omega)}$ classes for a weight function $\omega$. In particular, we show that a classical result of Carleman for the quasianalytic classes $\mathcal{E}_{\{M_p\}}$ also holds for the classes defined using weights. We also characterize when the space of quasianalytic germs at the origin coincides with the space of real anal
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Kaneko, Akira. "On the analyticity of the locus of singularity of real analytic solutions with minimal dimension." Nagoya Mathematical Journal 104 (December 1986): 63–84. http://dx.doi.org/10.1017/s0027763000022686.

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Let P(x, D) be a linear partial differential operator with real analytic coefficients and let C ⊂ Rn be a germ of closed subset, say at the origin. We say that C is (the locus of) an irremovable singularity of a real analytic solution u of P(x, D)u = 0 if u is defined outside C on a neighborhood Ω of 0 but cannot be extended to the whole neighborhood Ω even as a hyperfunction solution of P(x, D)u = 0. This usage of the word “singularity” is the same as the one for the analytic functions in complex analysis, and is different of the usual usage of “singularities of solutions” in the theory of pa
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Dissertations / Theses on the topic "Germs of real analytic functions"

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Al-Bahadeli, Mohammed Salim Jbara. "Classification of real and complex analytic map-germs on the generalized cross cap." Thesis, University of Leeds, 2012. http://etheses.whiterose.ac.uk/2849/.

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This thesis consists of four parts. In the first part, we prove the following conjecture [HL091. Conjecture: Let (C2d-2, 0) - (C2d-1, 0) be the minimal cross cap of multiplicity d >2 and V be its image. In the second part, we develop computational method suitable for perform ing the classification theory. A computer package called CAST is developed. This is written in the Singular program and performs calculations such as complete transversals, finite determinacy and triviality. We discuss the pack- age in detail and give examples of calculations performed in this thesis. We consider the case
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Martín, Villaverde Rafael. "Local monomialization of generalized real analytic functions." Phd thesis, Université de Bourgogne, 2011. http://tel.archives-ouvertes.fr/tel-00695968.

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Les fonctions analytiques généralisées sont définies par des séries convergentes de monômes à coeficients réels et exposants réels positifs. Nous étudions l'extension de la géométrie analytique réelle associée à ces algèbres de fonctions. Nous introduisons pour cela la notion de variété analytique réelle généralisée. Il s'agit de variétés topologiques à bord munies de la structure du faisceau des fonctions analytiques réelles généralisées. Notre résultat principal est un théorème de monomialisation locale de ces fonctions.
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De, Castro Lisa. "Analytic Functions with Real Boundary Values in Smirnov Classes Ep." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4661.

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This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes Ep, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes Hp. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes. The preliminary and background information is g
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Campesato, Jean-Baptiste. "Une fonction zêta motivique pour l'étude des singularités réelles." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4104/document.

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Nous nous intéressons à l'étude des singularités réelles à l'aide d'arguments provenant de l'intégration motivique. Une telle démarche a été initiée par S. Koike et A. Parusiński puis poursuivie par G. Fichou. Afin de donner une classification des singularités réelles, T.-C. Kuo a défini la notion d'équivalence blow-analytique. Il s'agit d'une relation d'équivalence pour les germes analytiques réels n'admettant pas de module continu pour les singularités isolées. Cette notion est étroitement liée à la notion d'applications analytiques par arcs définie par K. Kurdyka. Il est donc naturel d'adap
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Avila, Leonardo. "Sobre singularidades analíticas de soluções de uma classe de campos vetoriais no Toro." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30032010-104911/.

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O objetivo principal deste trabalho é o estudo da regularidade anallítica global de certos operadores diferenciais definidos no toro. Uma ferramenta fundamental utilizada neste estudo são as séries parciais de Fourier, que nos permitem caracterizar tanto as distribuições periódicas quanto as funções anallíticas reais periódicas através do comportamento assintótico de seus coeficientes parciais de Fourier. Neste sentido, apresentamos também um estudo detalhado das relações destes objetos com seus coeficientes parciais de Fourier<br>The main goal of this work is to study global analytic regulari
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Kraus, Christiane. "On some maximal convergence theorems for real analytic functions in R^N." Doctoral thesis, 2004. https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-9795.

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Ausgangspunkt dieser Arbeit war eine Publikation von D. Braess [Bra01], in der die Approximationsgüte der Funktionen $$ \frac{1}{((x-x_0)^2 + (y-y_0)^2)^s}, \qquad x_0^2 + y_0^2 \ge 1, \quad s \in (0,\infty),$$ auf der Einheitskreisscheibe $x^2+y^2 \le 1$ durch reelle Polynome untersucht wurde. Braess's Ergebnisse und insbesondere die von ihm angesprochenen offenen Probleme waren von besonderem Interesse, da sie Anlaß zu der Vermutung gaben, dass die klassische Theorie der ``Maximalen Konvergenz'' in Sinne von Walsh auf (zunächst) die oben erwähnten reell analytischen Funktionen erweitert werd
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Tatarczak, Anna. "Properties of orthogonal polynomials and typically real functions related to generalized Koebe functions." Praca doktorska, 2015. http://ruj.uj.edu.pl/xmlui/handle/item/44197.

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Kraus, Christiane [Verfasser]. "On some maximal convergence theorems for real analytic functions in RN / vorgelegt von Christiane Kraus." 2004. http://d-nb.info/98076047X/34.

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Books on the topic "Germs of real analytic functions"

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Krantz, Steven G. A primer of real analytic functions. Birkhäuser Verlag, 1992.

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Krantz, Steven G., and Harold R. Parks. A Primer of Real Analytic Functions. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-0-8176-8134-0.

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Krantz, Steven G., and Harold R. Parks. A Primer of Real Analytic Functions. Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7644-5.

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1949-, Parks Harold R., ed. A primer of real analytic functions. 2nd ed. Birkhäuser, 2002.

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Pachpatte, B. G. Analytic Inequalities: Recent Advances. Atlantis Press, 2012.

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Patrizia, Macrì, and Tancredi Alessandro, eds. Topics on real analytic spaces. F. Vieweg, 1986.

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Precalculus: Real mathematics, real people. 6th ed. Brooks/Cole, Cengage Learning, 2012.

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Ecalle, Jean. Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Hermann, 1992.

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Murai, Takafumi. A real variable method for the Cauchy transform and analytic capacity. Springer-Verlag, 1988.

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1963-, Song Renming, and Vondraček Zoran 1959-, eds. Bernstein functions: Theory and applications. De Gruyter, 2010.

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Book chapters on the topic "Germs of real analytic functions"

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Łojasiewicz, Stanisław. "Rings of Germs of Holomorphic Functions." In Introduction to Complex Analytic Geometry. Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7617-9_4.

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Cialdea, A. "The Brothers Riesz Theorem: Complex and Real Versions." In Generalized Analytic Functions. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4613-3332-6_14.

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Nikol’skiĭ, Nikolaĭ K. "Generalized Spectrality and Interpolation of Germs of Analytic Functions." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-70151-1_10.

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Shiota, Masahiro. "Piecewise linearization of subanalytic functions II." In Real Analytic and Algebraic Geometry. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083925.

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Robson, Robert O. "Slices: Functions for abstract real analysis." In Real Analytic and Algebraic Geometry. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083922.

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Krantz, Steven G., and Harold R. Parks. "Multivariable Calculus of Real Analytic Functions." In A Primer of Real Analytic Functions. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-0-8176-8134-0_2.

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Nabutovsky, Alexander. "Isotopies and non-recursive functions in real algebraic geometry." In Real Analytic and Algebraic Geometry. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083921.

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Seade, José. "Remarks on the Topology of Real and Complex Analytic Map-Germs." In Singularities and Computer Algebra. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-28829-1_12.

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Krantz, Steven G., and Harold R. Parks. "Elementary Properties." In A Primer of Real Analytic Functions. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-0-8176-8134-0_1.

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Krantz, Steven G., and Harold R. Parks. "Classical Topics." In A Primer of Real Analytic Functions. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-0-8176-8134-0_3.

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Conference papers on the topic "Germs of real analytic functions"

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Marinov, S. M., George Venkov, Ralitza Kovacheva, and Vesela Pasheva. "On Analytic Functions of Four Cyclic Real Variables." In 35TH INTERNATIONAL CONFERENCE “APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS”: AMEE-2009. AIP, 2009. http://dx.doi.org/10.1063/1.3271618.

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Henry, Jean-Pierre, and Adam Parusiński. "Invariants of bi-Lipschitz equivalence of real analytic functions." In Geometric Singularity Theory. Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-5.

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Nguyen, Elitsa. "Best Chebyshev approximation and analytic continuation of functions (real case)." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766797.

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Slagel, J. Tanner, Lauren White, and Aaron Dutle. "Formal verification of semi-algebraic sets and real analytic functions." In CPP '21: 10th ACM SIGPLAN International Conference on Certified Programs and Proofs. ACM, 2021. http://dx.doi.org/10.1145/3437992.3439933.

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Domański, Paweł. "Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives." In Orlicz Centenary Volume. Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc64-0-5.

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Vogt, Dietmar. "Section spaces of real analytic vector bundles and a theorem of Grothendieck and Poly." In Linear and Non-Linear Theory of Generalized Functions and its Applications. Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc88-0-25.

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Akcay, Huseyin, and Semiha Turkay. "Subspace-based rational interpolation of analytic functions from real or imaginary parts of frequency-response data." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC 2009). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400020.

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Yao, Zijun, Yanjie Fu, Bin Liu, Wangsu Hu, and Hui Xiong. "Representing Urban Functions through Zone Embedding with Human Mobility Patterns." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/545.

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Urban functions refer to the purposes of land use in cities where each zone plays a distinct role and cooperates with each other to serve people’s various life needs. Understanding zone functions helps to solve a variety of urban related problems, such as increasing traffic capacity and enhancing location-based service. Therefore, it is beneficial to investigate how to learn the representations of city zones in terms of urban functions, for better supporting urban analytic applications. To this end, in this paper, we propose a framework to learn the vector representation (embedding) of city zo
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Lee, Yu-Tai. "Mysterious Behavior of Optimization Calculation With MOGA." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16505.

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Multi-Objective Generic Algorithm (MOGA) is a popular and viable optimization calculation scheme for many practical engineering problems. This is because MOGA provides reliable search results covering wide and multi-variable design spaces. Most importantly when an optimization problem involves using mixed design variables, i.e. continuous and discrete variables, MOGA is still applicable. However, in such a condition MOGA needs to be programmed in a binary mode, which requires a minimum number of bits to represent each real and integer design variable. The accuracy of the prediction of the opti
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Bai, Youdun, Xin Chen, and Zhijun Yang. "A Generic Method to Generate AS-Curve Profile in Commercial Motion Controller." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68053.

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It is well believed that S-curve motion profiles are able to reduce residual vibration, and are widely applied in the motion control fields. Recently, a new asymmetric S-curve (AS-curve) motion profile, which is able to effectively adjust the acceleration and deceleration periods, is proposed to enhance the performance of S-curve motion profile, and proved to be better than the traditional symmetric S-curve in many cases. However, most commercial motion controllers do not support the AS-curve motion profiles inherently. Special knowledge or expensive advanced controlling systems, such as dSPAC
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