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o-minimal analytic separation of sets in dimension 2

Andreas Fischer
2009 Annals of Pure and Applied Logic  
If the set of analytic germs is dense in the Hardy field, then we can definably analytic separate sets in R 2 , and we can definably analytic approximate definable continuous unary functions.  ...  We study the Hardy field associated with an o-minimal expansion of the real numbers.  ...  Acknowledgements I would like to thank Patrick Speissegger for fruitful discussions about the o-minimal structures described in [16] .  ... 
doi:10.1016/j.apal.2008.09.005 fatcat:sy4xlrww5rfrdjrtok45xfed7a

Arithmetic Discrete Hyperspheres and Separatingness [chapter]

Christophe Fiorio, Jean-Luc Toutant
2006 Lecture Notes in Computer Science  
In the framework of arithmetic discrete geometry, a discrete object is provided with its own analytical definition corresponding to a discretization scheme.  ...  It can thus be considered as the equivalent, in a discrete space, of an euclidean object.  ...  Definition 3 (k-Simple Points, k-Minimality). Let d be the dimension of the space and k ∈ N such that k < d. Let also F and E be two discrete sets such that E is k-separating in F .  ... 
doi:10.1007/11907350_36 fatcat:qpwpuxusvvfptp76aoe2ukzsg4

Separation of global semianalytic sets

Hamedou Diakite
2009 Annales Polonici Mathematici  
Given global semianalytic sets A and B, we define a minimal analytic set N such that A \ N and B \ N can be separated by an analytic function.  ...  Our statement is very similar to the one proved by Bröcker for semialgebraic sets. 2000 Mathematics Subject Classification: 03C64, 12D15.  ...  We will define the nullspace N of A and B, which is roughly speaking a minimal global analytic set such that A and B can be generically separated in irreducible sets outside N (see Section 3 for a precise  ... 
doi:10.4064/ap95-2-8 fatcat:hkwrmjh7mbarrfqfg4i6ioqpji

On the dynamics of foliations in P^n tangent to Levi-flat hypersurfaces [article]

Arturo Fernández-Pérez, Rogério Mol, Rudy Rosas
2014 arXiv   pre-print
Let F be a codimension one holomorphic foliation in P^n, n≥ 2, leaving invariant a real-analytic Levi-flat hypersurface M with regular part M^*. Then every leaf of F outside M^* accumulates in M^*.  ...  In dimension two, however, the existence of both real-analytic Levi-flats and minimal sets are so far open problems.  ...  If F is a singular foliation of dimension r in a complex manifold X of dimension n > r, then a compact non-empty subset M ⊂ X is said to be a minimal set for F if the following properties are satisfied  ... 
arXiv:1403.4802v1 fatcat:exdgqg62lfgwvmfzs2cehoawhe

Further remarks on ideals of the principal class

Edward Davis
1968 Pacific Journal of Mathematics  
Hence: An ideal of a Noetherian ring is of the principal class if, and only if, it is generated by an analytically independent set.  ...  In a previous paper on this subject, the author gave a new proof of the theorem of "analytic independence of systems of parameters". The methods used can be applied to prove a converse result.  ...  Lemma 2 is well known in the case of R an integral domain (see, for example, generalize to the case at hand as follows.Let M o be a minimal prime ideal of S contained in M such that height (MlM Q ) = height  ... 
doi:10.2140/pjm.1968.27.49 fatcat:nxoogqvfp5gz7gcj3fqzcyo3hq

Separation of global semianalytic subsets of 2 - dimensional analytic manifolds

F. Broglia, F. Pieroni
2004 Pacific Journal of Mathematics  
In this paper we prove that two global semianalytic subsets of a real analytic manifold of dimension two are separable if and only if there is no analytic component of the Zariski closure of the boundary  ...  which intersects the interior of one of the two sets and they are separable in a neighbourhood of each singular point of the boundary.  ...  Acquistapace for her constant help in this work.  ... 
doi:10.2140/pjm.2004.214.1 fatcat:vmsyoapfcfdwtbrncpqvwy4pxi

Minimal representations of semiseparable kernels and systems with separable boundary conditions

I Gohberg, M.A Kaashoek
1987 Journal of Mathematical Analysis and Applications  
The results are applied to the problem of minimal realization of systems with separable boundary conditions. V 1987 Academx Press.  ...  Inc (0.2) Here for v = 1, 2 the functions F"( . ) and G,( .) are matrix functions of sizes m x n, and n, x m, respectively, and their entries are square integrable on [a, b].  ...  Thus SB-minimality is not the same as minimality in the class of systems with arbitrary well-posed boundary conditions. 1. 2 . 2 THEOREM.  ... 
doi:10.1016/0022-247x(87)90007-2 fatcat:sybio4s7zraw3hppsrbbk6y4ia

Tame topology and desingularization in Hensel minimal structures [article]

Krzysztof Jan Nowak
2022 arXiv   pre-print
This condition is satisfied by many of the classical tame structures on Henselian fields (including Henselian fields with analytic structure, V-minimal fields and polynomially bounded o-minimal structures  ...  Further, we establish definable versions of resolution of singularities (hypersurface case) and transformation to normal crossings by blowing up, on arbitrary strong analytic manifolds in Hensel minimal  ...  Yet already 1-h-minimality provides, likewise o-minimality does, powerful geometric tools as, for instance, cell decomposition, a good dimension theory or the Jacobian property (an analogue of the o-minimal  ... 
arXiv:2103.01836v7 fatcat:hipjj7asnzbzrfbnuks2mvtfsi

Discrete Analytical Hyperplanes

Eric Andres, Raj Acharya, Claudio Sibata
1997 Graphical Models and Image Processing  
They are defined analytically in the discrete dophysical device like a camera for a 2D DR, a CT or MR main by Diophantine equations.  ...  There are two main ways of obtaining a DR of a real world object. One is by acquisition with a This paper presents the properties of the discrete analytical hyperplanes.  ...  In Section 2, after a short preliminary presention of the The definition of a discrete analytical hyperplane P ϭ notations used in this paper, the analytical definition of P n (Ͱ 0 , . . . , Ͱ n , Ͷ) in  ... 
doi:10.1006/gmip.1997.0427 fatcat:6yw7e2g7rrdcvm7bcjvn56aqza

Comprehensive Two-Dimensional Liquid Chromatography in Metabolome Analysis

Lucas Willmann Manuel Schlimpert, Daqiang Pan Christoph Bauer, Jens Trafkowski Sonja Krieger
2015 Journal of Chromatography & Separation Techniques  
Due to similarity of many analytes, it is a challenging task to realise powerful LC separation as one dimensional LC often compromises separation of similar compounds.  ...  In order to increase the separation in the second dimension we aimed towards minimization of the injection volume from the first chromatographic dimension onto the second dimension in relation to the second  ... 
doi:10.4172/2157-7064.1000288 fatcat:jsly4k3xanacbhsvndi5apmw5u

Solutions of definable ODEs with regular separation and dichotomy interlacement versus Hardy [article]

Olivier Le Gal, Mickaël Matusinski, Fernando Sanz Sánchez
2020 arXiv   pre-print
We introduce a notion of regular separation for solutions of systems of ODEs y'=F(x, y), where F is definable in a polynomially bounded o-minimal structure and y= (y_1, y_2).  ...  In this context, we show that the set of trajectories with the regular separation property and asymptotic to a formal invariant curve is never empty and it is represented by a subanalytic set of minimal  ...  If F is a linear map in (y 1 , y 2 ) whose coefficients are functions of x definable in an o-minimal structure, O. Le Gal, F. Sanz and P.  ... 
arXiv:2012.06998v1 fatcat:4smpkesxungfplle5sfrogandy

A non-archimedean definable Chow theorem [article]

Abhishek Oswal
2020 arXiv   pre-print
Peterzil and Starchenko have proved the following surprising generalization of Chow's theorem: A closed analytic subset of a complex algebraic variety that is definable in an o-minimal structure, is in  ...  In this paper, we prove a non-archimedean analogue of this result.  ...  The dimension of i(Y ) as a subset of R n (in the sense of Definition 3.10) is the same as the dimension of Y as a rigid analytic space. 2.  ... 
arXiv:2009.06134v1 fatcat:hasct7vogvdgbcayatwe5qc3mu

Page 1536 of Mathematical Reviews Vol. 50, Issue 5 [page]

1975 Mathematical Reviews  
In 1967, in a survey of dimension theory, J.  ...  Nagata proposed the problem of finding a general imbedding theorem analogous to the classical theorem which states that a separable metric space is of dimension <n if and only if it can be imbedded in  ... 

Parallel dual secondary column-dual detection: A further way of enhancing the informative potential of two-dimensional comprehensive gas chromatography

Luca Nicolotti, Chiara Cordero, Davide Bressanello, Cecilia Cagliero, Erica Liberto, Federico Magagna, Patrizia Rubiolo, Barbara Sgorbini, Carlo Bicchi
2014 Journal of Chromatography A  
(typically 0.5-2 m, 0.1 mm d c ) where separation is run in a few seconds.  ...  The column set usually consists of a long, conventional-inner-diameter first dimension ( 1 D) 27 (typically 15-30 m long, 0.32-0.25 mm d c ), and a short, narrow-bore second dimension ( 2 D) column 28  ...  The configuration and optimization of a GC×GC 64 set-up is thus a crucial, but also a complex step, since separation in the two dimensions is differently 65 influenced in the two separation dimensions  ... 
doi:10.1016/j.chroma.2014.07.081 pmid:25130094 fatcat:7of7eaojwbg5lefr5tvc26b5ym

Minimizing the error of linear separators on linearly inseparable data

Boris Aronov, Delia Garijo, Yurai Núñez-Rodríguez, David Rappaport, Carlos Seara, Jorge Urrutia
2012 Discrete Applied Mathematics  
Given linearly inseparable sets R of red points and B of blue points, we consider several measures of how far they are from being separable.  ...  sets.  ...  The sixth author's research was supported in part by MTM2006-03909 (Spain) and SEP-CONACYT of México, Proyecto 80268.  ... 
doi:10.1016/j.dam.2012.03.009 fatcat:2bl4zouehvdufbwunw6xqvztu4
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