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Deformations of real analytic functions and the natural stratification of the space of real analytic functions [PDF]
Nagoya Mathematical Journal, 1976 Let A be a real analytic set, M be a compact real analytic manifold and f : A × M → R be a real analytic function. Then we have a family of real analytic functions fa, a ∈ A, on M defined by fa(X) = f(a, x).
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A note on neighborhoods of analytic functions having positive real part
International Journal of Mathematics and Mathematical Sciences, 1990 Let P denote the set of all functions analytic in the unit disk D={z||z|0. For δ≥0, let Nδ(p) be those functions q(z)=1+∑k=1∞qkzk analytic in D with ∑k=1∞|pk−qk|≤δ.
Janice B. Walker
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Forum of Mathematics, Sigma, 2023 Erdős [7] proved that the Continuum Hypothesis (CH) is equivalent to the existence of an uncountable family $\mathcal {F}$ of (real or complex) analytic functions, such that $\big \{ f(x) \ : \ f \in \mathcal {F} \big \}$ is countable for ...
Brent Cody, Sean Cox, Kayla Lee
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A screw dislocation located outside, inside or on the interface of a parabolic elastic inhomogeneity
Archives of Mechanics, 2021 Using conformal mapping techniques, superposition and analytic continuation, we derive analytic solutions to the problem of a screw dislocation interacting with a parabolic elastic inhomogeneity.
X. Wang, P. Schiavone
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On real analytic functions of unbounded type [PDF]
Revista Matemática Complutense, 2012 In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on ...
López-Salazar Codes, Jerónimo +2 more
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Generating series of all modular graph forms from iterated Eisenstein integrals
Journal of High Energy Physics, 2020 We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution for their low ...
Jan E. Gerken +2 more
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The Zero Set of a Real Analytic Function [PDF]
Mathematical Notes, 2020 A brief proof of the statement that the zero-set of a nontrivial real-analytic function in $d$-dimensional space has zero measure is provided.
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Piecewise Linearization of Real Analytic Functions
Publications of the Research Institute for Mathematical Sciences, 1984 Une fonction définie sur un polyèdre est appelée P. L. s'il existe une triangulation du polyèdre telle que la restriction de la fonction à tout simplexe soit linéaire. Une triangulation \(C^{\infty}\) d'une variété réelle analytique M est un couple formé par un complexe simplicial K et d'un homéomorphisme \(g: | K| \to M\), où \(| K|\) est le polyèdre ...
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Exact spin correlators of integrable quantum circuits from algebraic geometry
SciPost PhysicsWe calculate the correlation functions of strings of spin operators for integrable quantum circuits exactly. These observables can be used for the calibration of quantum simulation platforms.
Arthur Hutsalyuk, Yunfeng Jiang, Balazs Pozsgay, Hefeng Xu, Yang Zhang
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A remark on the intersections of subanalytic leaves [PDF]
Opuscula Mathematica, 2016 We discuss a new sufficient condition - weaker than the usual transversality condition - for the intersection of two subanalytic leaves to be smooth. It involves the tangent cone of the intersection and, as typically non-transversal, it is of interest in
Maciej P. Denkowski
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