32,215 research outputs found
On Artin's braid group and polyconvexity in the calculus of variations
No full textLet Ω ⊂ 2 be a bounded Lipschitz domain and let
F : Ω × 2×2
+
−→
be a Carathèodory integrand such that F (x, ·) is polyconvex for L2-a.e. x ∈ Ω. Moreover assume that
F is bounded from below and satisfies the condition F (x, ξ) ∞ as det ξ 0 for L2-a.e. x ∈ Ω. The paper describes the effect of domain topology on the existence and multiplicity of strong local minimizers of the functional
[u] :=
Ω
F (x,∇u (x)) dx,
where the map u lies in the Sobolev space W1,p
id (Ω,2) with p 2 and satisfies the pointwise condition
det ∇u (x) > 0 for L2-a.e. x ∈ Ω. The question is settled by establishing that [·] admits a set of strong
local minimizers on W1,p id (Ω,2) that can be indexed by the group n ⊕ n, the direct sum of Artin’s pure braid group on n strings and n copies of the infinite cyclic group. The dependence on the domain topology is through the number of holes n in Ω and the different mechanisms that give rise to such local minimizers are fully exploited by this particular representation
Letter from Carl T. Hayden to C. H. Gensler, Havasupai Reservation
No full textLetter from Carl T. Hayden to C. H. Gensler, Havasupai Indian Reservation, regarding Hualapai and Cataract Canyons geography
Collision-free motions of round robots on metric graphs
No full textIn this thesis, we study the path-connectivity problem of configuration spaces of two robots that move without collisions on a connected metric graph. The robots are modelled as metric balls of positive radii. In other words, we wish to find the number of path-connected components of such a configuration space. Finding a solution to this problem will help us to understand which configurations can be reached from any chosen configuration.
In order to solve the above problem, we show that any collision-free motion of two robots can be replaced by a finite sequence of elementary motions. As a corollary, we reduce the path-connectivity problem for a 2-dimensional configuration space to the same problem for a simple 1-dimensional subgraph (the configuration skeleton) of the space
On the cohomology rings of tree braid groups
No full textAbstractLet Γ be a finite connected graph. The (unlabelled) configuration space UCnΓ of n points on Γ is the space of n-element subsets of Γ. The n-strand braid group of Γ, denoted BnΓ, is the fundamental group of UCnΓ.We use the methods and results of [Daniel Farley, Lucas Sabalka, Discrete Morse theory and graph braid groups, Algebr. Geom. Topol. 5 (2005) 1075–1109. Electronic] to get a partial description of the cohomology rings H∗(BnT), where T is a tree. Our results are then used to prove that BnT is a right-angled Artin group if and only if T is linear or n<4. This gives a large number of counterexamples to Ghrist’s conjecture that braid groups of planar graphs are right-angled Artin groups
Hilden braid groups
No full textLet H g be a genus g handlebody and MCG 2n(T g) be the group of the isotopy classes of orientation preserving homeomorphisms of T g = ∂H g, fixing a given set of 2n points. In this paper we study two particular subgroups of MCG 2n(T g) which generalize Hilden groups defined by Hilden in [Generators for two groups related to the braid groups, Pacific J. Math. 59 (1975) 475486]. As well as Hilden groups are related to plat closures of braids, these generalizations are related to Heegaard splittings of manifolds and to bridge decompositions of links. Connections between these subgroups and motion groups of links in closed 3-manifolds are also provided. © 2012 World Scientific Publishing Company
Letter from Charles H. Burke to Carl Hayden
No full textLetter from Charles H. Burke to Carl T. Hayden about mining on Diné (formerly Navajo) national land
Braid group actions, Baxter polynomials, and affine quantum groups
No full textIt is a classical result in representation theory that the braid group
of a simple Lie algebra acts on any
integrable representation of via triple products of exponentials
in its Chevalley generators. In this article, we show that a modification of
this construction induces an action of on the
commutative subalgebra
of the Yangian by Hopf algebra automorphisms, which gives rise to a
representation of the Hecke algebra of type on a flat
deformation of the Cartan subalgebra .
By dualizing, we recover a representation of
constructed in the works of Y. Tan and V. Chari, which was used to obtain
sufficient conditions for the cyclicity of any tensor product of irreducible
representations of and the quantum loop algebra
. We apply this dual action to prove that the cyclicity
conditions from the work of Tan are identical to those obtained in the recent
work of the third author and S. Gautam. Finally, we study the
-counterpart of the braid group action on
, which arises from Lusztig's braid group operators
and recovers the aforementioned -action defined by
Chari.Comment: 44 pages. Updates: Theorem 3.5, Corollary 3.11 and Theorem 6.5 now
include descriptions of the inverse modified braid group operators. In
addition, Corollary 4.5 has been added and Remarks 4.2, 4.6 and 4.7 have been
adjusted. The numbering of some statements has changed accordingly. To appear
in Transactions of the American Mathematical Societ
Letter from John H. Page to Carl Hayden
No full textLetter from John H. Page to Carl T. Hayden regarding his company's rights to build a railway if they choose to
Training & Testing EL Image Dataset for Machine Learning
No full textAs discussed in A. M. Karimi, J. S. Fada, M. A. Hossain, S. Yang, T. J. Peshek, J. L. Braid, R. H. French, Automated Pipeline for Photovoltaic Module Electroluminescence Image Processing and Degradation Feature Classification, IEEE Journal of Photovoltaics. (2019) 1–12. https://doi.org/10.1109/JPHOTOV.2019.2920732
RTT relations, a modified braid equation and noncommutative planes
No full textLatex, 17 pages, minor changesWith the known group relations for the elements of a quantum matrix as input a general solution of the relations is sought without imposing the Yang - Baxter constraint for or the braid equation for . For three biparametric deformatios, and , the standard,the nonstandard and the hybrid one respectively, or is found to depend, apart from the two parameters defining the deformation in question, on an extra free parameter ,such that only for two values of , given explicitly for each case, one has the braid equation. Arbitray corresponds to a class (conserving the group relations independent of ) of the MQYBE or modified quantum YB equations studied by Gerstenhaber, Giaquinto and Schak. Various properties of the triparametric , and are studied. In the larger space of the modified braid equation (MBE) even can satisfy outside braid equation (BE) subspace. A generalized, - dependent, Hecke condition is satisfied by each 3-parameter . The role of in noncommutative geometries of the , and deformed planes is studied. K is found to introduce a "soft symmetry breaking", preserving most interesting properties and leading to new interesting ones. Further aspects to be explored are indicated
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