scholarly journals An Alternative Definition of the Notion Valuation in the Theory of Near Polygons

10.37236/105 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Polar Spaces ◽  
Alternative Definition ◽  
Near Polygon ◽  
Point Set ◽  
Definition Of ◽  
Dual Polar Spaces

Valuations of dense near polygons were introduced in [9]. A valuation of a dense near polygon ${\cal S}=({\cal P},{\cal L},{\rm I})$ is a map $f$ from the point-set ${\cal P}$ of ${\cal S}$ to the set $\Bbb N$ of nonnegative integers satisfying very nice properties with respect to the set of convex subspaces of ${\cal S}$. In the present paper, we give an alternative definition of the notion valuation and prove that both definitions are equivalent. In the case of dual polar spaces and many other known dense near polygons, this alternative definition can be significantly simplified.

scholarly journals The Valuations of the Near Octagon ${\Bbb I}_4$

10.37236/1102 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Bart De Bruyn ◽  
Pieter Vandecasteele
Keyword(s):  
Polar Space ◽  
Polar Spaces ◽  
Near Polygon ◽  
Hyperbolic Quadric ◽  
Dual Polar Space ◽  
Full Embedding ◽  
Parabolic Quadric ◽  
Dual Polar Spaces

The maximal and next-to-maximal subspaces of a nonsingular parabolic quadric $Q(2n,2)$, $n \geq 2$, which are not contained in a given hyperbolic quadric $Q^+(2n-1,2) \subset Q(2n,2)$ define a sub near polygon ${\Bbb I}_n$ of the dual polar space $DQ(2n,2)$. It is known that every valuation of $DQ(2n,2)$ induces a valuation of ${\Bbb I}_n$. In this paper, we classify all valuations of the near octagon ${\Bbb I}_4$ and show that they are all induced by a valuation of $DQ(8,2)$. We use this classification to show that there exists up to isomorphism a unique isometric full embedding of ${\Bbb I}_n$ into each of the dual polar spaces $DQ(2n,2)$ and $DH(2n-1,4)$.

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

scholarly journals Minimal scattered sets and polarized embeddings of dual polar spaces

2007 ◽  
Vol 28 (7) ◽  
pp. 1890-1909 ◽  
Author(s):  
Bart De Bruyn ◽  
Antonio Pasini
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

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.

An alternative definition of Gabor focus

1992 ◽  
Vol 41 (4) ◽  
pp. 441 ◽  
Author(s):  
P.W. Hawkes
Keyword(s):  
Alternative Definition ◽  
Definition Of

scholarly journals Opposite Relation on Dual Polar Spaces and Half-Spin Grassmann Spaces

2009 ◽  
Vol 54 (3-4) ◽  
pp. 301-308 ◽  
Author(s):  
Mariusz Kwiatkowski ◽  
Mark Pankov
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

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.

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