scholarly journals Refined intersection homology on non-Witt spaces

2014 ◽  
Vol 07 (01) ◽  
pp. 105-133 ◽  
Author(s):  
Pierre Albin ◽  
Markus Banagl ◽  
Eric Leichtnam ◽  
Rafe Mazzeo ◽  
Paolo Piazza
Keyword(s):  
Homology Theory ◽  
Cohomology Theory ◽  
The Self ◽  
Intersection Cohomology ◽  
Intersection Homology ◽  
Stratified Spaces ◽  
Constructible Sheaves ◽  
De Rham Theory ◽  
De Rham ◽  
Definition Of

We investigate a generalization to non-Witt stratified spaces of the intersection homology theory of Goresky–MacPherson. The second-named author has described the self-dual sheaves compatible with intersection homology, and the other authors have described a generalization of Cheeger's L2 de Rham cohomology. In this paper we first extend both of these cohomology theories by describing all sheaf complexes in the derived category of constructible sheaves that are compatible with middle perversity intersection cohomology, though not necessarily self-dual. Our main result is that this refined intersection cohomology theory coincides with the analytic de Rham theory on Thom–Mather stratified spaces. The word "refined" is motivated by the fact that the definition of this cohomology theory depends on the choice of an additional structure (mezzo-perversity) which is automatically zero in the case of a Witt space.

scholarly journals Intersection space cohomology of three-strata pseudomanifolds

2019 ◽  
pp. 1-50
Author(s):  
J. Timo Essig
Keyword(s):  
Mirror Symmetry ◽  
Differential Forms ◽  
Main Property ◽  
Homology Theory ◽  
Cohomology Theory ◽  
Intersection Homology ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Cell Complexes ◽  
Space Cohomology

The theory of intersection spaces assigns cell complexes to certain stratified topological pseudomanifolds depending on a perversity function in the sense of intersection homology. The main property of the intersection spaces is Poincaré duality over complementary perversities for the reduced singular (co)homology groups with rational coefficients. This (co)homology theory is not isomorphic to intersection homology, instead they are related by mirror symmetry. Using differential forms, Banagl extended the intersection space cohomology theory to 2-strata pseudomanifolds with a geometrically flat link bundle. In this paper, we use differential forms on manifolds with corners to generalize the intersection space cohomology theory to a class of 3-strata spaces with flatness assumptions for the link bundles. We prove Poincaré duality over complementary perversities for the cohomology groups. To do so, we investigate fiber bundles on manifolds with boundary. At the end, we give examples for the application of the theory.

scholarly journals An approach to intersection theory on singular varieties using motivic complexes

2016 ◽  
Vol 152 (11) ◽  
pp. 2371-2404 ◽  
Author(s):  
Eric M. Friedlander ◽  
J. Ross
Keyword(s):  
Equivalence Relation ◽  
Homology Theory ◽  
Intersection Theory ◽  
Equivalence Classes ◽  
Cohomology Theory ◽  
Intersection Homology ◽  
Localization Property ◽  
Singular Varieties

We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky–MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversity homology theory and a companion perversity cohomology theory based on generalized cocycle spaces. These theories lead to conditions on pairs of cycles which can be intersected and a suitable equivalence relation on cocycles/cycles enabling pairings on equivalence classes. We establish suspension and splitting theorems, as well as a localization property. Some examples of intersections on singular varieties are computed.

Delving into Horror

2019 ◽  
Vol 29 (5) ◽  
pp. 135-150
Keyword(s):  
The Self ◽  
Time And Space ◽  
The Third ◽  
The World ◽  
The Subject ◽  
Perception Of Time ◽  
Definition Of

The springboard for this essay is the author’s encounter with the feeling of horror and her attempts to understand what place horror has in philosophy. The inquiry relies upon Leonid Lipavsky’s “Investigation of Horror” and on various textual plunges into the fanged and clawed (and possibly noumenal) abyss of Nick Land’s work. Various experiences of horror are examined in order to build something of a typology, while also distilling the elements characteristic of the experience of horror in general. The essay’s overall hypothesis is that horror arises from a disruption of the usual ways of determining the boundaries between external things and the self, and this leads to a distinction between three subtypes of horror. In the first subtype, horror begins with the indeterminacy at the boundaries of things, a confrontation with something that defeats attempts to define it and thereby calls into question the definition of the self. In the second subtype, horror springs from the inability to determine one’s own boundaries, a process opposed by the crushing determinacy of the world. In the third subtype, horror unfolds by means of a substitution of one determinacy by another which is unexpected and ungrounded. In all three subtypes of horror, the disturbance of determinacy deprives the subject, the thinking entity, of its customary foundation for thought, and even of an explanation of how that foundation was lost; at times this can lead to impairment of the perception of time and space. Understood this way, horror comes within a hair’s breadth of madness - and may well cross over into it.

scholarly journals Path homology theory of edge-colored graphs

2021 ◽  
Vol 19 (1) ◽  
pp. 706-723
Author(s):  
Yuri V. Muranov ◽  
Anna Szczepkowska
Keyword(s):  
Spectral Sequence ◽  
Edge Coloring ◽  
Homology Theory ◽  
Homotopy Category ◽  
Homology Groups ◽  
Colored Graphs ◽  
Natural Filtration ◽  
Definition Of ◽  
Exact Sequences

Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresponding spectral sequence, and obtain commutative diagrams and braids of exact sequences.

Evaluation of invulnerability of scale-free networks using total information of local sub-graph

2018 ◽  
Vol 29 (08) ◽  
pp. 1850075
Author(s):  
Tingyuan Nie ◽  
Xinling Guo ◽  
Mengda Lin ◽  
Kun Zhao
Keyword(s):  
Mutual Information ◽  
Complex Network ◽  
Fundamental Problem ◽  
The Self ◽  
Practical Significance ◽  
Scale Free ◽  
Total Information ◽  
Scale Free Networks ◽  
Influential Nodes ◽  
Definition Of

The quantification for the invulnerability of complex network is a fundamental problem in which identifying influential nodes is of theoretical and practical significance. In this paper, we propose a novel definition of centrality named total information (TC) which derives from a local sub-graph being constructed by a node and its neighbors. The centrality is then defined as the sum of the self-information of the node and the mutual information of its neighbor nodes. We use the proposed centrality to identify the importance of nodes through the evaluation of the invulnerability of scale-free networks. It shows both the efficiency and the effectiveness of the proposed centrality are improved, compared with traditional centralities.

Counter-Hegemonic Visions of Self-Respect in a Novel: Ramamirthammal’s Challenge to Indian Nationalism

2020 ◽  
Vol 5 (2) ◽  
pp. 119-131
Author(s):  
Sitharthan Sriharan
Keyword(s):  
The Self ◽  
National Liberation ◽  
Equal Footing ◽  
Indian Nationalism ◽  
Definition Of

Periyar’s Self-Respect Movement challenged the ideological hegemony of the Indian Independence struggle by demanding that equality between sexes and eradicating caste be put on an equal footing with national liberation. The author analyses a chapter in a novel written by Muvalur Ramamirthammal, a reformer from a devadasi community, who joined the Self-Respect Movement and became an ardent abolitionist of the devadasi system. In a dialogue between an ex-devadasi, who is represented as a Self-Respect activist, and a Brahmin man with Indian nationalist views, the former devadasi highlights the Self-Respect Movement’s definition of modern citizenship based on the principles of self-respect and dignity of all beginning with women. The article concludes by discussing the novel's wider connection to the Self-Respect Movement and why further research on both respectively is crucial.

Fine-tuning the Relationship between Religion and Intellectual Humility

2018 ◽  
Vol 46 (4) ◽  
pp. 305-314 ◽  
Author(s):  
Everett L. Worthington
Keyword(s):  
Religious Belief ◽  
The Self ◽  
Content Area ◽  
Fine Tuning ◽  
Epistemic Status ◽  
Intellectual Humility ◽  
The Core ◽  
Definition Of ◽  
Meaning System ◽  
The Relationship

I examine religious humility, which is one content area of intellectual humility. Intellectual humility is the subtype of humility that involves taking a humble stance in sharing ideas, especially when one is challenged or when an idea is threatening. I position religious humility within the context of general humility, spiritual humility, and relational humility, and thus arrive at several propositions. People who are intensely spiritually humble can hold dogmatic beliefs and believe themselves to be religiously humble, yet be perceived by others of different persuasions as religiously dogmatic and even arrogant. For such people to be truly religiously humble, they must feel that the religious belief is core to their meaning system. This requires discernment of which of the person’s beliefs are truly at the core. But also the religiously humble person must fulfill the definition of general humility, accurately perceiving the strengths and limitations of the self, being teachable to correct weaknesses, presenting oneself modestly, and being positively other-oriented. Humility thus involves (1) beliefs, values, and attitudes and (2) an interpersonal presentational style. Therefore, intellectually humble people must track the positive epistemic status of their beliefs and also must present with convicted civility.

Efficiency limits of fans

2019 ◽  
Vol 234 (5) ◽  
pp. 739-748
Author(s):  
Konrad Bamberger ◽  
Thomas Carolus
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Number ◽  
Geometrical Parameter ◽  
The Self ◽  
Complex Geometries ◽  
Relevant Parameter ◽  
Optimization Scheme ◽  
Loss Models ◽  
Definition Of

The purpose of this work is to identify upper efficiency limits of industrial fans such as axial rotor-only fans, axial with guide vanes, centrifugal rotor-only and centrifugal with volute. The efficiency limit is always a function of the class, the design point within the class and the definition of efficiency (total-to-static and total-to-total). The characteristic Reynolds number is another relevant parameter. First, based on analytical and empirical loss models, a theoretical efficiency limit is estimated. A set of idealizing assumptions in the loss models yields efficiencies which are assumed to be an insuperable limit but may be unrealistically high. Second, more realistic efficiency limits are estimated using a computational fluid dynamics-based optimization scheme, seeking for the best designs and hence the maximum achievable efficiencies in all classes. Given the self-imposed constraints in the geometrical parameter space considered, the thus-obtained practical efficiency limits can only be exceeded by admitting more complex geometries of the fans.

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