Results 291 to 300 of about 87,568 (329)
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Forum Mathematicum, 2003
The authors define phantom orders, which are ordinal numbers, for homotopy classes of maps between CW complexes \(X\) and \(Y\). Every map from \(X\) to \(Y\) has phantom order at least \(0\). For \(\alpha>0\), a map from \(X\) to \(Y\) has phantom order at least \(\alpha\) if for every \(n\)-skeleton \(X_n\) and for every ordinal ...
Lê Minh Hà, Strom, Jeffrey
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The authors define phantom orders, which are ordinal numbers, for homotopy classes of maps between CW complexes \(X\) and \(Y\). Every map from \(X\) to \(Y\) has phantom order at least \(0\). For \(\alpha>0\), a map from \(X\) to \(Y\) has phantom order at least \(\alpha\) if for every \(n\)-skeleton \(X_n\) and for every ordinal ...
Lê Minh Hà, Strom, Jeffrey
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$$\xi $$-Phantom Maps in $$(n+2)$$-Angulated Categories
Bulletin of the Iranian Mathematical Society, 2021The authors generalize the notion of $n$-proper classes in $n$-exangulated categories to $n$-proper classes in $(n+2)$-angulated categories (constructing a complete lattice), and also they introduce the notion of phantom maps over this object (related with ideals); this allows them to study a relative version of homological algebra.
Yuxia Mei, Jiaqun Wei, Qilian Zheng
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Numerical invariants of phantom maps
American Journal of Mathematics, 2001In this paper two numerical invariants of phantom maps are studied; the Gray index G ( f ) and the essential category weight E ( f ) of a phantom map f . The possible values of these invariants are determined along with bounds on their values given in terms of the domain and range of the phantom map.
McGibbon, C. A., Strom, Jeffrey
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Phantom Development for Comparison of Thermal Mapping
ISMRM Annual Meeting, 2023Thermal Mapping using MRI is a non-invasive method for probing the body and has both diagnostic and interventional applications. If conducted on more accessible low field strength systems, these can improve the accessibility of the method for wider use.
Diego Martinez +5 more
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Automatic hand phantom map detection methods
2015 IEEE Biomedical Circuits and Systems Conference (BioCAS), 2015Many amputees have maps of referred sensation from their missing hand on their residual limb (phantom maps). This skin area can serve as a target for providing amputees with tactile sensory feedback. Providing tactile feedback on the phantom map can improve the object manipulation ability, enhance embodiment of myoelectric prostheses users and help ...
Huaiqi Huang +6 more
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Weak identities, phantom maps andH-spaces
Israel Journal of Mathematics, 1989zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Phantom Maps and the Towers which Determine them
Journal of the London Mathematical Society, 1997Let \(X\) and \(Y\) be spaces of finite type, and let \(\text{Ph} (X, Y)\) be the set of homotopy classes of phantom maps from \(X\) to \(Y\). We study the closely associated countable torsion-free abelian group \[ AP (X, Y)= \text{colim}_n \Hom ([X, \Omega Y^{(n)} ], \mathbb{Z}), \] where \(\{\Omega Y^{(n)}\}\) is the Postnikov tower of the loop space
McGibbon, C. A., Steiner, Richard
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Phantom Maps from a Strong Homology Viewpoint
Acta Mathematica Sinica, English Series, 2005Let \(X\) be a based CW complex, \(X_n\) its \(n\)-skeleton, \(Y\) any topological space and \(f: X \to Y\) a based continuous mapping. The author calls \(f\) a \textit{phantom map} whenever \(f \mid X_n\), for all \(n\), is null homotopic. Like other authors he has as his main objective a more algebraic description of \(Ph(X,Y)\), the set of all ...
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Connective coverings, phantom maps and genus sets
Indiana University Mathematics Journal, 1998Let \(X\langle n\rangle\) denote the \(n\)-connective covering of a space \(X\). For a number of familiar finite type CW-complexes \(X,Y\) the authors study: (i) the set \(\text{Ph} (X\langle n\rangle,Y)\), consisting of homotopy classes of phantom maps from \(X\langle n\rangle\) to \(Y\), together with the group structure on this set when \(Y\) is a ...
McGibbon, C. A., Roitberg, Joseph
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Phantom Maps and Representability
2016Let \(\mathcal {T}\) be a well generated triangulated category and let \(\mathcal {F}\) be the ideal of phantom maps with respect to the \(\alpha \)-compact objects. In [5] we have proved that the ideal \(\bigcap _{n\ge 1}\mathcal {F}^n\) has always square zero.
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