INDEX POLYNOMIAL INVARIANTS OF TWISTED LINKS

2013 ◽  
Vol 22 (04) ◽  
pp. 1340005 ◽  
Author(s):  
NAOKO KAMADA
Keyword(s):  
Virtual Link ◽  
Alternative Definition ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Intersection Index ◽  
Definition Of

Bourgoin defined the notion of a twisted link. In a sense, it is a non-orientable version of a virtual link. Im, Lee and Lee defined a polynomial invariant of a virtual link by using the virtual intersection index. In this paper, we give an alternative definition of index polynomial by using indices of real crossings and extend it to a twisted links.

scholarly journals A POLYNOMIAL INVARIANT OF VIRTUAL LINKS

2013 ◽  
Vol 22 (12) ◽  
pp. 1341002 ◽  
Author(s):  
ZHIYUN CHENG ◽  
HONGZHU GAO
Keyword(s):  
Knot Theory ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Virtual Knots ◽  
The Third ◽  
Linking Number ◽  
Virtual Links ◽  
Definition Of ◽  
Knots And Links

In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms [Parity in knot theory, Sb. Math.201 (2010) 693–733] to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of the odd writhe polynomial defined by the first author in [A polynomial invariant of virtual knots, preprint (2012), arXiv:math.GT/1202.3850v1]. The relation between this new polynomial invariant and the affine index polynomial [An affine index polynomial invariant of virtual knots, J. Knot Theory Ramification22 (2013) 1340007; A linking number definition of the affine index polynomial and applications, preprint (2012), arXiv:1211.1747v1] is discussed. In the second part we introduce a polynomial invariant for long flat virtual knots. In the third part we define a polynomial invariant for 2-component virtual links. This polynomial invariant can be regarded as a generalization of the linking number.

A PARITY AND A MULTI-VARIABLE POLYNOMIAL INVARIANT FOR VIRTUAL LINKS

2013 ◽  
Vol 22 (13) ◽  
pp. 1350073 ◽  
Author(s):  
YOUNG HO IM ◽  
KYOUNG IL PARK
Keyword(s):  
Knot Theory ◽  
Virtual Link ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Virtual Knot ◽  
Virtual Knots ◽  
Link Diagrams ◽  
Virtual Links ◽  
Knot Diagrams

We introduce a parity of classical crossings of virtual link diagrams which extends the Gaussian parity of virtual knot diagrams and the odd writhe of virtual links that extends that of virtual knots introduced by Kauffman [A self-linking invariants of virtual knots, Fund. Math.184 (2004) 135–158]. Also, we introduce a multi-variable polynomial invariant for virtual links by using the parity of classical crossings, which refines the index polynomial introduced in [Index polynomial invariants of virtual links, J. Knot Theory Ramifications19(5) (2010) 709–725]. As consequences, we give some properties of our invariant, and raise some examples.

Parities and polynomial invariants for virtual links

2014 ◽  
Vol 23 (12) ◽  
pp. 1450066 ◽  
Author(s):  
Young Ho Im ◽  
Kyoung Il Park ◽  
Mi Hwa Shin
Keyword(s):  
Knot Theory ◽  
Virtual Link ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Virtual Knots ◽  
Link Diagrams ◽  
Virtual Links ◽  
Kauffman Polynomial

We introduce the odd Jones–Kauffman polynomial and odd Miyazawa polynomials of virtual link diagrams by using the parity of virtual link diagrams given in [Y. H. Im and K. I. Park, A parity and a multi-variable polynomial invariant for virtual links, J. Knot Theory Ramifications22(13) (2013), Article ID: 1350073, 18pp.], which are different from the original Jones–Kauffman and Miyazawa polynomials. Also, we give a family of parities and odd polynomials for virtual knots so that many virtual knots can be distinguished.

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 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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