Strong cell decomposition property in o-minimal traces

2020 ◽  
Author(s):  
Somayyeh Tari
Keyword(s):  
Cell Decomposition ◽  
Decomposition Property

scholarly journals TOPOLOGICAL CELL DECOMPOSITION AND DIMENSION THEORY IN P-MINIMAL FIELDS

2017 ◽  
Vol 82 (1) ◽  
pp. 347-358 ◽  
Author(s):  
PABLO CUBIDES KOVACSICS ◽  
LUCK DARNIÈRE ◽  
EVA LEENKNEGT
Keyword(s):  
Algebraic Geometry ◽  
Open Subset ◽  
Cell Decomposition ◽  
Real Algebraic Geometry ◽  
Dimension Theory ◽  
Definable Set ◽  
Image Position ◽  
Definable Function

AbstractThis paper addresses some questions about dimension theory for P-minimal structures. We show that, for any definable set A, the dimension of $\bar A\backslash A$ is strictly smaller than the dimension of A itself, and that A has a decomposition into definable, pure-dimensional components. This is then used to show that the intersection of finitely many definable dense subsets of A is still dense in A. As an application, we obtain that any definable function $f:D \subseteq {K^m} \to {K^n}$ is continuous on a dense, relatively open subset of its domain D, thereby answering a question that was originally posed by Haskell and Macpherson.In order to obtain these results, we show that P-minimal structures admit a type of cell decomposition, using a topological notion of cells inspired by real algebraic geometry.

ON ∞-COMPLEX SYMMETRIC OPERATORS

2017 ◽  
Vol 60 (1) ◽  
pp. 35-50
Author(s):  
MUNEO CHŌ ◽  
EUNGIL KO ◽  
JI EUN LEE
Keyword(s):  
Spectral Properties ◽  
Symmetric Operator ◽  
Complex Symmetric Operator ◽  
Decomposition Property ◽  
Complex Symmetric ◽  
Symmetric Operators

AbstractIn this paper, we study spectral properties and local spectral properties of ∞-complex symmetric operators T. In particular, we prove that if T is an ∞-complex symmetric operator, then T has the decomposition property (δ) if and only if T is decomposable. Moreover, we show that if T and S are ∞-complex symmetric operators, then so is T ⊗ S.

scholarly journals Shellability of a Poset of Polygonal Subdivisions

10.37236/89 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Torsten Ekedahl
Keyword(s):  
Cell Decomposition ◽  
The Face

We introduce a sequence of posets closely related to the associahedra. In this we are motivated by reasons similar to those of Stasheff in the case of the associahedra. We make a study of this poset showing that it has an inductive structure with proper downwards intervals being products of smaller posets in the same series and associahedra. Using this we also show that they are thin dual CL-shellable and in particular that they are the face poset of a regular cell decomposition of the ball.

scholarly journals Path Planning Methods in an Environment with Obstacles (A Review)

2018 ◽  
pp. 15-58 ◽  
Author(s):  
W. Liu
Keyword(s):  
Path Planning ◽  
Incomplete Information ◽  
Cell Decomposition ◽  
Reference Points ◽  
Mobile Robot Navigation ◽  
Problem Solution ◽  
Local Path Planning ◽  
Starting Point ◽  
Planning Methods ◽  
Local Path

Planning the path is the most important task in the mobile robot navigation. This task involves basically three aspects. First, the planned path must run from a given starting point to a given endpoint. Secondly, it should ensure robot’s collision-free movement. Thirdly, among all the possible paths that meet the first two requirements it must be, in a certain sense, optimal.Methods of path planning can be classified according to different characteristics. In the context of using intelligent technologies, they can be divided into traditional methods and heuristic ones. By the nature of the environment, it is possible to divide planning methods into planning methods in a static environment and in a dynamic one (it should be noted, however, that a static environment is rare). Methods can also be divided according to the completeness of information about the environment, namely methods with complete information (in this case the issue is a global path planning) and methods with incomplete information (usually, this refers to the situational awareness in the immediate vicinity of the robot, in this case it is a local path planning). Note that incomplete information about the environment can be a consequence of the changing environment, i.e. in a dynamic environment, there is, usually, a local path planning.Literature offers a great deal of methods for path planning where various heuristic techniques are used, which, as a rule, result from the denotative meaning of the problem being solved. This review discusses the main approaches to the problem solution. Here we can distinguish five classes of basic methods: graph-based methods, methods based on cell decomposition, use of potential fields, optimization methods, фтв methods based on intelligent technologies.Many methods of path planning, as a result, give a chain of reference points (waypoints) connecting the beginning and end of the path. This should be seen as an intermediate result. The problem to route the reference points along the constructed chain arises. It is called the task of smoothing the path, and the review addresses this problem as well.

scholarly journals Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals

2010 ◽  
Vol 106 (1) ◽  
pp. 88 ◽  
Author(s):  
Luis A. Dupont ◽  
Rafael H. Villarreal
Keyword(s):  
Monomial Ideal ◽  
Lattice Points ◽  
Edge Ideal ◽  
Comparability Graph ◽  
Decomposition Property ◽  
Edge Ideals ◽  
Finite Poset ◽  
Integer Decomposition Property ◽  
Torsion Free ◽  
Min Cut

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let $G$ be the comparability graph of a finite poset. If $\mathrm{cl}(G)$ is the clutter of maximal cliques of $G$, we prove that $\mathrm{cl}(G)$ satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.

scholarly journals Characterizing rings by a direct decomposition property of their modules

2006 ◽  
Vol 80 (3) ◽  
pp. 359-366 ◽  
Author(s):  
Dinh Van Huynh ◽  
S. Tariq Rizvi
Keyword(s):  
Projective Module ◽  
Direct Decomposition ◽  
Decomposition Property ◽  
Direct Sum ◽  
Continuous Module

AbstractA module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module and a quasi-continuous module. In an earlier paper, we described the structure of rings over which every (countably generated) right module satisfies (℘*), and it was shown that such a ring is right artinian. In this note some additional properties of these rings are obtained. Among other results, we show that a ring over which all right modules satisfy (℘*) is also left artinian, but the property (℘*) is not left-right symmetric.

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