scholarly journals Exact functors on perverse coherent sheaves

2015 ◽  
Vol 151 (9) ◽  
pp. 1688-1696
Author(s):  
Clemens Koppensteiner
Keyword(s):  
Symplectic Geometry ◽  
Coherent Sheaf ◽  
Alternative Definition ◽  
Coherent Sheaves ◽  
Constructible Sheaves ◽  
Definition Of ◽  
Symplectic Case

Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R{\rm\Gamma}_{Z}{\mathcal{F}}$ is concentrated in degree $0$ for special subvarieties $Z$ of $X$. These subvarieties $Z$ are analogs of Lagrangians in the symplectic case.

scholarly journals m-Blocks Collections and Castelnuovo-mumford Regularity in multiprojective spaces

2007 ◽  
Vol 186 ◽  
pp. 119-155 ◽  
Author(s):  
L. Costa ◽  
R. M. Miró-Roig
Keyword(s):  
Spectral Sequence ◽  
Projective Spaces ◽  
Coherent Sheaf ◽  
Derived Category ◽  
Projective Varieties ◽  
Coherent Sheaves ◽  
Definition Of ◽  
Formal Properties ◽  
Multiprojective Spaces ◽  
Smooth Projective Varieties

AbstractThe main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on n-dimensional smooth projective varieties X with an n-block collection B which generates the bounded derived category To this end, we use the theory of n-blocks and Beilinson type spectral sequence to define the notion of regularity of a coherent sheaf F on X with respect to the n-block collection B. We show that the basic formal properties of the Castelnuovo-Mumford regularity of coherent sheaves over projective spaces continue to hold in this new setting and we compare our definition of regularity with previous ones. In particular, we show that in case of coherent sheaves on ℙn and for the n-block collection Castelnuovo-Mumford regularity and our new definition of regularity coincide. Finally, we carefully study the regularity of coherent sheaves on a multiprojective space ℙn1x…x ℙnr with respect to a suitable n1 +…+ nr-block collection and we compare it with the multigraded variant of the Castelnuovo-Mumford regularity given by Hoffman and Wang in [14].

scholarly journals The Effect of an Alternative Definition of “Percent Highly Annoyed” on the Exposure–Response Relationship: Comparison of Noise Annoyance Responses Measured by ICBEN 5-Point Verbal and 11-Point Numerical Scales

2021 ◽  
Vol 18 (12) ◽  
pp. 6258
Author(s):  
Makoto Morinaga ◽  
Thu Lan Nguyen ◽  
Shigenori Yokoshima ◽  
Koji Shimoyama ◽  
Takashi Morihara ◽  
...  
Keyword(s):  
Sound Pressure ◽  
Response Relationship ◽  
Alternative Definition ◽  
Exposure Response ◽  
Noise Annoyance ◽  
Numerical Scale ◽  
Verbal Scale ◽  
Sound Pressure Levels ◽  
Acoustic Surveys ◽  
Definition Of

Since the development of the 5-point verbal and 11-point numerical scales for measuring noise annoyance by the ICBEN Team 6, these scales have been widely used in socio-acoustic surveys worldwide, and annoyance responses have been easily compared internationally. However, both the top two categories of the 5–point verbal scale and the top three ones of the 11-point numerical scale are correspond to high annoyance, so it is difficult to precisely compare annoyance responses. Therefore, we calculated differences in day–evening–night-weighted sound pressure levels (Lden) by comparing values corresponding to 10% highly annoyed (HA) on Lden_%HA curves obtained from measurements in 40 datasets regarding surveys conducted in Japan and Vietnam. The results showed that the Lden value corresponding to 10% HA using the 5-point verbal scale was approximately 5 dB lower than that of the 11-point numerical scale. Thus, some correction is required to compare annoyance responses measured by the 5-point verbal and the 11-point numerical scales. The results of this study were also compared with those of a survey in Switzerland.

An alternative definition of sustainable development using stability and chaos theories

2006 ◽  
Vol 14 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Amir Abbas Rassafi ◽  
Hossain Poorzahedy ◽  
Manouchehr Vaziri
Keyword(s):  
Sustainable Development ◽  
Alternative Definition ◽  
Definition Of

Categorical concepts for parameterized partial specifications

1995 ◽  
Vol 5 (2) ◽  
pp. 153-188 ◽  
Author(s):  
Ingo Claßen ◽  
Martin GroßE-Rhode ◽  
Uwe Wolter
Keyword(s):  
Structural Theory ◽  
Specification Languages ◽  
Alternative Definition ◽  
Categorical Approach ◽  
Categorical Constructions ◽  
Definition Of ◽  
Act One

Categorical constructions inherent to a theory of algebras with strict partial operations are presented and exploited to provide a categorical deduction calculus for conditional existence equations and an alternative definition of such algebras based on the notion of syntactic categories. A compact presentation of the structural theory of parameterized (partial) specifications is given using the categorical approach. This theory is shown to be suitable for providing initial semantics as well as the compositionality results necessary for the definition of specification languages like ACT ONE and ACT TWO

On the Very Idea of Civilisation

2021 ◽  
Vol 31 (2) ◽  
pp. 307-321
Author(s):  
Luke O’Sullivan ◽  
Keyword(s):  
Technological Development ◽  
Thomas Hobbes ◽  
Alternative Definition ◽  
Starting Point ◽  
Western Imperialism ◽  
Clash Of Civilisations ◽  
Definition Of ◽  
Contemporary Liberalism ◽  
Relationship Of ◽  
The Relationship

The concept of civilisation is a controversial one because it is unavoidably normative in its implications. Its historical associations with the effort of Western imperialism to impose substantive conditions of life have made it difficult for contemporary liberalism to find a definition of “civilization” that can be reconciled with progressive discourse that seeks to avoid exclusions of various kinds. But because we lack a way of identifying what is peculiar to the relationship of civilisation that avoids the problem of domination, it has tended to be conflated with other ideas. Taking Samuel Huntington's idea of a “Clash of Civilisations” as a starting point, this article argues that we suffer from a widespread confusion of civilisation with “culture,” and that we also confuse it with other ideas including modernity and technological development. Drawing on Thomas Hobbes, the essay proposes an alternative definition of civilisation as the existence of limits on how we may treat others.

Learning Patterns in the Disadvantaged

1967 ◽  
Vol 37 (4) ◽  
pp. 546-593 ◽  
Author(s):  
Susan Stodolsky ◽  
Gerald Lesser
Keyword(s):  
Educational Policy ◽  
Educational Opportunity ◽  
Equal Educational Opportunity ◽  
Alternative Definition ◽  
Future Directions ◽  
Disadvantaged Children ◽  
Learning Patterns ◽  
Definition Of

The authors review evidence and suggest future directions for research on the learning patterns of disadvantaged children. After a detailed description of a specific case of research, some implications for educational policy are discussed. The authors take issue with James S. Coleman's definition of the concept of "equal educational opportunity"and advance an alternative definition. The problem of achieving a useful definition of the term "disadvantaged"is addressed throughout the paper.

scholarly journals A Krull-Schmdit type theorem for coherent sheaves

2014 ◽  
Vol 22 (2) ◽  
pp. 51-56
Author(s):  
A. S. Argáez
Keyword(s):  
Finite Group ◽  
Projective Variety ◽  
Type Theorem ◽  
Coherent Sheaf ◽  
Irreducible Representations ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Coherent Sheaves ◽  
A Finite Group ◽  
Natural Decomposition

AbstractLet X be projective variety over an algebraically closed field k and G be a finite group with g.c.d.(char(k), |G|) = 1. We prove that any representations of G on a coherent sheaf, ρ : G → End(ℰ), has a natural decomposition ℰ ≃ ⊕ V ⊗k ℱV, where G acts trivially on ℱV and the sum run over all irreducible representations of G over k.

scholarly journals Mathematical and Physical Continuity

2008 ◽  
Vol 6 ◽  
Author(s):  
Mark Colyvan ◽  
Kenny Easwaran
Keyword(s):  
Common Sense ◽  
Natural Question ◽  
Alternative Definition ◽  
Continuous Motion ◽  
Mathematical Definition ◽  
Definition Of ◽  
Point Of Departure

There is general agreement in mathematics about what continuity is. In this paper we examine how well the mathematical definition lines up with common sense notions. We use a recent paper by Hud Hudson as a point of departure. Hudson argues that two objects moving continuously can coincide for all but the last moment of their histories and yet be separated in space at the end of this last moment. It turns out that Hudson’s construction does not deliver mathematically continuous motion, but the natural question then is whether there is any merit in the alternative definition of continuity that he implicitly invokes.

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.

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