Search results for "knot"
showing 10 items of 156 documents
The Link Between Standardization and Economic Growth: A Bibliometric Analysis
2021
We analyze the link between standardization and economic growth by systematically reviewing leading economics journals, leading economic growth researchers’ articles, and economic growth-related books. We make the following observations: 1) No article has analyzed the link between standardization and economic growth in top5 economics journals between 1996 and 2018. 2) A representative sample of the leading researchers of economic growth has allocated little attention to the link between standardization and economic growth. 3) Typically, economic growth textbooks do not contain “standards” or “standardization” in their word indexes. These findings suggest that the economic growth theory has …
BEM application on an external problem comparison with both theoretical and finite elements results and observations on divergence strip
1992
Abstract By means of a computer program the Boundary Element Method is applied to a central hole in an undefined plate with uniform load along the boundary. Results are compared with those obtained by Kirsch's theoretical solution and a previous analysis by the Finite Element Method. The calculus of percentage error shows the advantage of the Boundary Element Method on the external problem with regard to the Finite Element Method. The error causes near the boundary internal points are analysed with the existence of a strip, where the result is not reliable in evidence.
The Links-Gould invariants as generalizations of the Alexander polynomial
2016
In this thesis we focus on the connections that exist between two link invariants: first the Alexander-Conway invariant ∆ that was the first polynomial link invariant to be discovered, and one of the most thoroughly studied since alongside with the Jones polynomial, and on the other hand the family of Links-Gould invariants LGn,m that are quantum link invariants derived from super Hopf algebras Uqgl(n|m). We prove a case of the De Wit-Ishii-Links conjecture: in some cases we can recover powers of the Alexander polynomial as evaluations of the Links-Gould invariants. So the LG polynomials are generalizations of the Alexander invariant. Moreover we give evidence that these invariants should s…
A link between the residual-based gradient plasticity theory and the analogous theories based on the virtual work principle
2009
A link is shown to exist between the so-called residual-based strain gradient plasticity theory and the analogous theories based on the (extended) virtual work principle (VWP). To this aim, the former theory is reformulated and cast in a residual-free form, whereby the insulation condition and the (nonlocal) Clausius–Duhem inequality, on which the theory is grounded, are substituted with equivalent residual-free ingredients, namely the energy balance condition and the residual-free form of the Clausius–Duhem inequality. The equivalence of the residual-free formulation to the original one is shown, also in their ability to cope with energetic size effects and interfacial energy ones. It emer…
Weight Systems from Feynman Diagrams
1996
We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.
Caustics for spherical waves
2016
We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an $SO(p)$-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple $SO(p)$-waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.
Swampland Bounds on the Abelian Gauge Sector
2019
We derive bounds on the number of abelian gauge group factors in six-dimensional gravitational theories with minimal supersymmetry and in their F-theoretic realisations. These bounds follow by requiring consistency of certain BPS strings in the spectrum of the theory, as recently proposed in the literature. Under certain assumptions this approach constrains the number of abelian gauge group factors in six-dimensional supergravity theories with at least one tensor multiplet to be $N \leq 20$ (or $N \leq 22$ in absence of charged matter). For any geometric F-theory realisation with at least one tensor multiplet we establish the bound $N \leq 16$ by demanding unitarity of a heterotic solitonic…
Numerical evaluation of iterated integrals related to elliptic Feynman integrals
2021
We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The implementation includes iterated integrals of modular forms as well as iterated integrals involving the Kronecker coefficient functions $g^{(k)}(z,\tau)$. For the Kronecker coefficient functions iterated integrals in $d\tau$ and $dz$ are implemented. This includes elliptic multiple polylogarithms.
A construction of Frobenius manifolds from stability conditions
2018
A finite quiver $Q$ without loops or 2-cycles defines a 3CY triangulated category $D(Q)$ and a finite heart $A(Q)$. We show that if $Q$ satisfies some (strong) conditions then the space of stability conditions $Stab(A(Q))$ supported on this heart admits a natural family of semisimple Frobenius manifold structures, constructed using the invariants counting semistable objects in $D(Q)$. In the case of $A_n$ evaluating the family at a special point we recover a branch of the Saito Frobenius structure of the $A_n$ singularity $y^2 = x^{n+1}$. We give examples where applying the construction to each mutation of $Q$ and evaluating the families at a special point yields a different branch of the m…
Remarks on the Historiography of Mathematics
2021
In this paper, I examine aspects of the methodological debate that originated in 2010, when the distinguished historian of mathematics Sabetai Unguru reviewed Roshdi Rashed’s edition of the Arabic translation of Apollonius’ Conics. In his review, Unguru criticized what Rashed calls “l’usage instrumental d’une autre mathématique pour commenter une oeuvre ancienne”. I consider this debate very important and will try to place it within in the discussion of the so-called “geometric algebra” that goes back to the seventies, by tracing the contributions of the main figures who took part in it. Published Online (2021-04-30)Copyright © 2021 by Aldo Brigaglia Article PDF Link: https://jps.library.ut…