scholarly journals The Singular Temperley-Lieb Category

ISRN Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Carmen Caprau ◽  
Joel Smith
Keyword(s):  
Category Theory ◽  
Point Of View ◽  
State Model ◽  
Link Invariant ◽  
Polynomial Invariants ◽  
Oriented Link ◽  
Theory Point

We introduce and study the singular Temperley-Lieb category over ℤ[q,q-1], which is a free pivotal category over two self-dual generators and is an extension of the (classical) Temperley-Lieb category. Our construction is motivated by a state model for the sl(2)  polynomial of an oriented link and provides a categorical perspective to this link invariant. We also construct a couple of polynomial invariants for oriented tangles from category theory point of view.

scholarly journals Identifying the Invariants for Classical Knots and Links from the Yokonuma–Hecke Algebras

2018 ◽  
Vol 2020 (1) ◽  
pp. 214-286 ◽  
Author(s):  
Maria Chlouveraki ◽  
Jesús Juyumaya ◽  
Konstantinos Karvounis ◽  
Sofia Lambropoulou
Keyword(s):  
Hecke Algebras ◽  
Hecke Algebra ◽  
Type A ◽  
Closed Formula ◽  
Link Invariant ◽  
Polynomial Invariants ◽  
Oriented Link ◽  
Linking Numbers ◽  
Markov Trace ◽  
Knots And Links

Abstract We announce the existence of a family of new 2-variable polynomial invariants for oriented classical links defined via a Markov trace on the Yokonuma–Hecke algebra of type A. Yokonuma–Hecke algebras are generalizations of Iwahori–Hecke algebras, and this family contains the HOMFLYPT polynomial, the famous 2-variable invariant for classical links arising from the Iwahori–Hecke algebra of type A. We show that these invariants are topologically equivalent to the HOMFLYPT polynomial on knots, but not on links, by providing pairs of HOMFLYPT-equivalent links that are distinguished by our invariants. In order to do this, we prove that our invariants can be defined diagrammatically via a special skein relation involving only crossings between different components. We further generalize this family of invariants to a new 3-variable skein link invariant that is stronger than the HOMFLYPT polynomial. Finally, we present a closed formula for this invariant, by W. B. R. Lickorish, that uses HOMFLYPT polynomials of sublinks and linking numbers of a given oriented link.

Chemical analysis: Information contribution of results

1991 ◽  
Vol 56 (3) ◽  
pp. 505-559 ◽  
Author(s):  
Karel Eckschlager
Keyword(s):  
Analytical Chemistry ◽  
Information Theory ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Information Gain ◽  
Analytical Signal ◽  
Point Of View ◽  
System A ◽  
Review Analysis ◽  
Theory Point

In this review, analysis is treated as a process of gaining information on chemical composition, taking place in a stochastic system. A model of this system is outlined, and a survey of measures and methods of information theory is presented to an extent as useful for qualitative or identification, quantitative and trace analysis and multicomponent analysis. It is differentiated between information content of an analytical signal and information gain, or amount of information, obtained by the analysis, and their interrelation is demonstrated. Some notions of analytical chemistry are quantified from the information theory and system theory point of view; it is also demonstrated that the use of fuzzy set theory can be suitable. The review sums up the principal results of the series of 25 papers which have been published in this journal since 1971.

scholarly journals A TORSIONAL TOPOLOGICAL INVARIANT

2007 ◽  
Vol 22 (29) ◽  
pp. 5237-5244 ◽  
Author(s):  
H. T. NIEH
Keyword(s):  
Affine Connection ◽  
Euler Class ◽  
Christoffel Symbol ◽  
Space Time ◽  
Topological Invariant ◽  
Point Of View ◽  
Underlying Space ◽  
Recent Developments ◽  
Theory Point ◽  
Curvature And Torsion

Curvature and torsion are the two tensors characterizing a general Riemannian space–time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space–time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space–time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.

scholarly journals Electron-capture modes with realistic nuclear structure calculations

2019 ◽  
Vol 21 ◽  
pp. 4
Author(s):  
P. G. Giannaka ◽  
T. S. Kosmas
Keyword(s):  
Electron Capture ◽  
Cross Sections ◽  
Nuclear Reactions ◽  
Random Phase ◽  
Point Of View ◽  
Electron Neutrino ◽  
Β Decay ◽  
Decay Modes ◽  
Theory Point ◽  
Nuclear Structure Calculations

Nuclear electron capture posses prominent position among other weak interaction processes occuring in explosive nucleosynthesis. In particular, this process plays important role in the core-colapse of massive stars by modifying the electron to baryon ratio Ye. From a nuclear theory point of view, such processes may be studied by using the same nuclear methods (e.g. the quasi-particle random phase approximation, QRPA), employed in the present work with these used for the one-body charge changing nuclear reactions (β-decay modes, charged-current electron-neutrino absorption by nuclei, etc). In this work we calculate e−-capture cross sections on 56Fe using two different approaches. At first, original cross section calculations are perfored by using the pn-QRPA method considering all the accessible transitions of the final nucleus 56Mn. Secondly, we evaluate the Gamow-Teller strength distributions and obtain the cross sections at the limit of zero-momentum transfer. The agreement between the two methods is very good.

scholarly journals ALL LINK INVARIANTS FOR TWO DIMENSIONAL SOLUTIONS OF YANG–BAXTER EQUATION AND DRESSINGS

2006 ◽  
Vol 15 (10) ◽  
pp. 1279-1301
Author(s):  
N. AIZAWA ◽  
M. HARADA ◽  
M. KAWAGUCHI ◽  
E. OTSUKI
Keyword(s):  
Jones Polynomial ◽  
Alexander Polynomial ◽  
Baxter Equation ◽  
Two Dimensional ◽  
Link Invariant ◽  
Three Solutions ◽  
Polynomial Invariants ◽  
Link Invariants ◽  
Higher Dimensional

All polynomial invariants of links for two dimensional solutions of Yang–Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there exist three solutions connecting to the Alexander polynomial. Invariants for higher dimensional solutions, obtained by the so-called dressings, are also investigated. It is observed that the dressings do not improve link invariant unless some restrictions are put on dressed solutions.

Aliansi Strategis dan Kinerja Perusahaan: Perspektif Teori Institusional

2020 ◽  
Vol 1 (2) ◽  
pp. 83-90
Author(s):  
Rebi Fara Handika
Keyword(s):  
Firm Performance ◽  
Institutional Theory ◽  
Empirical Research ◽  
Strategic Alliances ◽  
Strategic Alliance ◽  
Point Of View ◽  
Theory Point ◽  
And Performance ◽  
The Relationship

Abstract   This paper discussed the company's motive to join a strategic alliance from the institutional theory point of view. The theory views that strategic alliances are considered as the medium to acquire legitimation from the environment. Such legitimation then improves the company’s competitive positions and performance. Further, we propose the framework to discuss the relationship between strategic alliances and a company’s performance. The paper proceeds as follows: in the next section, we discuss the institutional theory, the strategic alliance, and firm performance. Afterward, we develop the propositions and discuss the implications for future empirical research.   Abstrak   Artikel ini membahas motif perusahaan untuk bergabung dengan aliansi strategis dari sudut pandang teori institusional. Teori ini memandang bahwa aliansi strategis dianggap sebagai media untuk memperoleh legitimasi dari lingkungan. Legitimasi tersebut kemudian dipercayai akan meningkatkan posisi kompetitif dan kinerja perusahaan. Selanjutnya, kami mengusulkan framework untuk membahas hubungan antara aliansi strategis dan kinerja perusahaan. Artikel ini akan dilanjutkan sebagai berikut: pada bagian berikutnya, kita membahas teori institusional, aliansi strategis, dan kinerja perusahaan. Setelah itu, kami mengembangkan proposisi dan membahas implikasi untuk penelitian empiris di masa depan.

scholarly journals Multiverse—Too Much or Not Enough?

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 113 ◽  
Author(s):  
Michael Heller
Keyword(s):  
Philosophy Of Science ◽  
Infinite Number ◽  
Category Theory ◽  
Explanatory Power ◽  
Point Of View ◽  
Anthropic Principle ◽  
Philosophical Perspective ◽  
Einstein's Equations ◽  
If Logic ◽  
The Way

The aim of this essay is to look at the idea of the multiverse—not so much from the standpoint of physics or cosmology, but rather from a philosophical perspective. The modern story of the multiverse began with Leibniz. Although he treated “other worlds” as mere possibilities, they played an important role in his logic. In a somewhat similar manner, the practice of cosmology presupposes a consideration of an infinite number of universes, each being represented by a solution to Einstein’s equations. This approach prepared the way to the consideration of “other universes” which actually exist, first as an auxiliary concept in discussing the so-called anthropic principle, and then as real universes, the existence of which were supposed to solve some cosmological conundrums. From the point of view of the philosophy of science, the question is: Could the explanatory power of a multiverse ideology compensate for the relaxation of empirical control over so many directly unobservable entities? It is no surprise that appealing to a possibly infinite number of “other universes” in order to explain some regularities in our world would seem “too much” for a self-disciplined philosopher. With no strict empirical control at our disposal, it is logic that must be our guide. Also, what if logic changes from one world to another in the multiverse? Such a possibility is suggested by the category theory. From this point of view, our present concepts of the multiverse are certainly “not enough”. Should this be read as a warning that the learned imagination can lead us too far into the realms of mere possibilities?

A Calculus for (Meta)Models and Transformations

2014 ◽  
Vol 24 (05) ◽  
pp. 715-730 ◽  
Author(s):  
Laurent Thiry ◽  
Michel Hassenforder
Keyword(s):  
Category Theory ◽  
Point Of View ◽  
Modeling Languages ◽  
Formal Representation ◽  
Equational Reasoning ◽  
Natural Transformations ◽  
Formal Point

This paper proposes a formal representation of modeling languages based on category theory. These languages are generally described by "metamodels", i.e. structures composed by classes and relations, and related by "transformations". Thus, this paper studies how the key categorical concepts such as functors and relations between functors (called natural transformations) can be used for equational reasoning about modeling artifacts (models, metamodels, transformations). As a result, this paper proposes a formal point of view of models usable to specify/prove equivalence between models or transformations (with an application to refactoring).

THE RESPONSE CURVE OF GAFCHROMIC EBT FILMS FROM THE PERCOLATION THEORY POINT OF VIEW

2009 ◽  
Vol 92 ◽  
pp. S217-S218
Author(s):  
F. Del Moral ◽  
A. Lopez Medina ◽  
J.A. Vazquez ◽  
J.J. Ferrero ◽  
A. Teijeiro ◽  
...  
Keyword(s):  
Percolation Theory ◽  
Response Curve ◽  
Point Of View ◽  
Theory Point
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