Coding Knots by T-Graphs

2020 ◽  
Vol 66 (4) ◽  
pp. 531-543
Author(s):  
O. N. Biryukov
Keyword(s):  
New Method ◽  
The Third ◽  
Reidemeister Moves

In this paper, knots are considered as smooth embeddings of a circle into 3 defined by their flat diagrams. We propose a new method of coding knots by T-graphs describing the torsion structure on a flat diagram. For this method of coding, we introduce conceptions of a cycle and a block and describe transformations of T-graphs under the first and the third Reidemeister moves applied to the flat diagram of a knot.

Reidemeister moves and parity polynomials of virtual knot diagrams

2017 ◽  
Vol 26 (10) ◽  
pp. 1750051
Author(s):  
Myeong-Ju Jeong
Keyword(s):  
Lower Bounds ◽  
Virtual Knot ◽  
The Third ◽  
Reidemeister Moves ◽  
Polynomial Formula ◽  
Knot Diagrams

When two virtual knot diagrams are virtually isotopic, there is a sequence of Reidemeister moves and virtual moves relating them. I introduced a polynomial [Formula: see text] of a virtual knot diagram [Formula: see text] and gave lower bounds for the number of Reidemeister moves in deformation of virtually isotopic knot diagrams by using [Formula: see text]. In this paper, I introduce bridge diagrams and polynomials of virtual knot diagrams based on parity of crossings, and show that the polynomials give lower bounds for the number of the third Reidemeister moves. I give an example which shows that the result is distinguished from that obtained from [Formula: see text].

scholarly journals (1, 2) AND WEAK (1, 3) HOMOTOPIES ON KNOT PROJECTIONS

2013 ◽  
Vol 22 (14) ◽  
pp. 1350085 ◽  
Author(s):  
NOBORU ITO ◽  
YUSUKE TAKIMURA
Keyword(s):  
Equivalence Relation ◽  
Finite Sequence ◽  
Reidemeister Move ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Homotopy Classes ◽  
The Third ◽  
Reidemeister Moves ◽  
Necessary And Sufficient

In this paper, we obtain the necessary and sufficient condition that two knot projections are related by a finite sequence of the first and second flat Reidemeister moves (Theorem 2.2). We also consider an equivalence relation that is called weak (1, 3) homotopy. This equivalence relation occurs by the first flat Reidemeister move and one of the third flat Reidemeister moves. We introduce a map sending weak (1, 3) homotopy classes to knot isotopy classes (Sec. 3). Using the map, we determine which knot projections are trivialized under weak (1, 3) homotopy (Corollary 4.1).

scholarly journals ISLAM DAN POSFEMINISME : WAJAH POSFEMINISME DALAM KOMODIFIKASI AGAMA DI MEDIA

2019 ◽  
Vol 13 (1) ◽  
pp. 9
Author(s):  
M Ali Sofyan
Keyword(s):  
Social Media ◽  
Gender Equality ◽  
Soft Power ◽  
Muslim Women ◽  
New Method ◽  
Pivotal Role ◽  
Third Wave ◽  
The Third ◽  
The Relationship ◽  
Religious Understanding

The relationship between masculine and feminine is collectively constructed. Both narrative and discourse of feminism has long emerged up to the third-wave. As Foucault has been pointed out that feminism itself has constructed discourse on inequality since it departs from patriarchy. Meanwhile, patriarchy has produced a threat even though it is under the pretext of feminism. The term postfeminism is thus arises after feminism, where there are no sources of oppression that originate from patriarchy.In fact, however, the interpretation of religious arguments (Islam in particular) does not subordinate women. But on the contrary, the religious argument actually wants to make women equal to men in the society. This article offers an analysis of the relation between Islam and postfeminism based on the perspective of religious commodification. It was noted that social media played a pivotal role in raising religion to engage on a global scale.Women from the perspective of postfeminism are seen as independent subjects. Freedom, gender equality, and pluralistic representation are the starting points for postfeminist women. Soft Power owned by social media contextualizes religion (Islam) and disseminates ideas including femininity in a new method, where the religious consumption can be enjoyed every second.Indonesian (Muslim) women campaign for gender equality and postfeminism awareness that is free in all things through social media (Instagram and YouTube). This is usually done in various ways such as lectures and fashion. Religious commodification, in this case is seen when religious understanding is capitalized. This perspective finally bringing Muslim women to say that "I am beautiful for myself". Although some argue that capitalizing religion appear to be less precise, when the commodification of religion can support women's freedom.

scholarly journals XIII. On a new method of approximation applicable to elliptic and ultra-elliptic functions

1860 ◽  
Vol 150 ◽  
pp. 223-227
Keyword(s):  
Geometric Mean ◽  
Elliptic Functions ◽  
New Method ◽  
Geometric Means ◽  
The Third ◽  
Harmonic Means ◽  
General Method

The difficulty of finding approximate values of elliptic functions of the third kind has led me to consider a general method of approximation, which I believe to be new, at least in its application to the evaluation of integrals of irrational functions. It depends on the known principle that the geometric mean between two quantities is also a geometric mean between their arithmetic and harmonic means. If we take any two positive quantities, we may approximate to their geometric means as follows:— Take the arithmetic and harmonic means of the two quantities, then again take the arithmetic and harmonic means of those means, and so on: the successive means will approximate with great rapidity to the geometric mean.

scholarly journals XXV. A new method of investigating the sums of infinite series. By the Rev. S. Vince, A.M. of Cambridge, in a letter to Henry Maty, A.M. Secretary

1782 ◽  
Vol 72 ◽  
pp. 389-416
Keyword(s):  
Infinite Series ◽  
Royal Society ◽  
New Method ◽  
General Will ◽  
The Third ◽  
The Subject ◽  
General Method

Sir, Having lately discovered some very easy methods of investigating the sums of certain infinite series, I have taken the liberty of requesting the favour of you to present them to the Royal Society. I have divided the subject into three parts: the first contains a new and general method of finding the sum of those series which De Moivre has found in one or two particular cases; but whose method, although it be in appearance general, will, upon trial, be found to be absolutely impracticable. The second contains the summation of certain series, the last differences of whose numerators become equal to nothing. The third contains observations on a correction which is necessary in investigating the sums of certain series by collecting two terms into one, with its application to a variety of cases.

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