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o-minimal analytic separation of sets in dimension 2
2009
Annals of Pure and Applied Logic
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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]
2006
Lecture Notes in Computer Science
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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
2009
Annales Polonici Mathematici
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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]
2014
arXiv
pre-print
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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
1968
Pacific Journal of Mathematics
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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
2004
Pacific Journal of Mathematics
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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
1987
Journal of Mathematical Analysis and Applications
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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]
2022
arXiv
pre-print
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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
1997
Graphical Models and Image Processing
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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
2015
Journal of Chromatography & Separation Techniques
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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]
2020
arXiv
pre-print
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2022 accepted arXiv:2012.06998v2 fatcat:pup3tzggzjhcxp6oglmif7yw4i
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]
2020
arXiv
pre-print
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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
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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
2014
Journal of Chromatography A
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(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
2012
Discrete Applied Mathematics
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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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