Results 11 to 20 of about 850,072 (303)
Fundamental class of real algebraic sets
Topology and its Applications, 2001 Consider a polynomial map \(F:\mathbb{R}^n \to\mathbb{R}^k\) (where \(n\geq k)\) and assume that the fiber \(X=F^{-1}(0)\) is compact. The author defines a fundamental class \([X]_F\in H_{n-k} (X;\mathbb{Z})\) and a topological degree for a map \(G:X\to \mathbb{R}^{n-k+1} \smallsetminus \{0\}\).
Z. Szafraniec
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Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets [PDF]
arXiv.org, 2016 Let $\mathrm{R}$ be a real closed field and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincar\'e characteristic of real algebraic as well as semi-algebraic subsets of ...
S. Basu, C. Riener
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Survey of the topology of real algebraic sets
Rocky Mountain Journal of Mathematics, 1984 The paper is a very lively presentation of the subject. First the author discusses the restriction on the topology of real algebraic sets: a real algebraic set is triangulable hence is a cone on a space X. Sullivan proved that X has even Euler characteristic.
H. King
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On homology of real algebraic sets
Inventiones Mathematicae, 1985 Given a compact, connected, smooth (i.e. \(C^{\infty})\) surface, not diffeomorphic to the two-sphere, real projective plane, or Klein bottle, we construct a nonsingular real algebraic surface diffeomorphic to it whose first homology group with coefficients in the integers modulo 2 is not generated by algebraic cycles.
W. Kucharz
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Topology of real algebraic sets of dimension 4: necessary conditions [PDF]
Topology, 1998 Operators on the ring of algebraically constructible functions are used to compute local obstructions for a four-dimensional semialgebraic set to be homeomorphic to a real algebraic set. The link operator and arithmetic operators yield $2^{43}-43$ independent characteristic numbers mod 2, which generalize the Akbulut-King numbers in dimension three.
C. McCrory, A. Parusiński
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Complex monodromy and the topology of real algebraic sets [PDF]
Compositio Mathematica, 1994 A relation between the Euler characteristics of the Milnorfibres of a real analytic function is derived from a simple identity involvingcomplex monodromy and complex conjugation. A corollary is the result of Costeand Kurdyka that the Euler characteristic
C. McCrory, A. Parusiński
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All compact manifolds are homeomorphic to totally algebraic real algebraic sets
Commentarii Mathematici Helvetici, 1991 The real algebraic set we obtain will in general be singular. The homeomorphism will be piecewise differentiable. Total algebraicity is a very useful concept since it eiliminates many obstructions to making a topological situation algebraic, c.f. [AK1], [AK2], [AK5].
S. Akbulut, H. King
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Some new operations on fuzzy soft sets and their applications in decision-making [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 This paper aims to introduce various types of useful operations on fuzzy soft sets (FSSs), such as Einstein sum, Einstein product, algebraic sum, algebraic product, bounded product, bounded sum, and the basic properties of these new operations have ...
Ajoy Kanti Das +2 more
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Neutrosophic Cubic Fuzzy Dombi Hamy Mean Operators with Application to Multi-Criteria Decision Making [PDF]
Neutrosophic Sets and Systems, 2020 The aim of the paper is to find most optimistic results from among uncertain information or vague data. We theoretically use the notion of neutrosophic cubic sets to create enhanced decision-making models for multi-criteria. The advantage of neutrosophic
D. Ajay, J. Aldring, S. Nivetha
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Complexity, 2022 The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem because it combines the advantages of the neutrosophic cubic set and the hesitant fuzzy set.
Ateeq Ur Rehman +5 more
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