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Cylinders' percolation: decoupling and applications
[article]

2021
*
arXiv
*
pre-print

More precisely, we prove that

arXiv:2112.10055v1
fatcat:5o4v2mdupbdgzetxuxmr2h6lhq
*for**a*small enough density of cylinders,*a*random walk on*a**connected**component*of the vacant set is transient*for*all dimensions d ≥ 3. ... Our work introduces*a*new notion of fast decoupling, proves that it holds*for*the model in question and finishes with an application. ... unbounded*connected**component*. ...##
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Analysis of boundary effects on PDE-based sampling of Whittle-Matérn random fields
[article]

2018
*
arXiv
*
pre-print

We provide

arXiv:1809.07570v1
fatcat:pt5xacmzlrgjxkialzzw6zctge
*a*rigorous analysis*for*the error in the covariance introduced by the window technique,*for*homogeneous Dirichlet, homogeneous Neumann, and periodic boundary conditions. ... Every sample requires the solution of*a*differential equation with Gaussian white noise forcing, formulated on*a*bounded computational domain. ... Let D ⊂ R d be an open, simply*connected*, bounded domain,*for*d = 1, 2, 3, and let (Ω,*A*, P) be*a*probability space (with Ω the set of events,*A**a*σ-algebra and P*a*probability measure). ...##
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Aspects of the BTZ black hole interacting with fields
[article]

2018
*
arXiv
*
pre-print

Then we outline the calculation of the expression

arXiv:1808.07521v2
fatcat:knzivopwtvgkdhbylsxpqo3bee
*for*the renormalized energy-momentum tensor, the effective action as well as the heat*kernel**for*the Dirac field*for*the BTZ black hole. ... We show that there is no superradiance*for*the Dirac field in the rotating BTZ black hole if the field vanishes at infinity. ... ), (26) where*a*= −(*2lk*+ −*2lk*− − 2iml + i)/4i, b = −(*2lk*+ +*2lk*− − i(2ml + 1))/4i, c = 1/2 − ilk + , d = (2ilk + − 2ilk − − 2ml + 1)/4, e = (2ilk + + 2ilk − − 2lm+ 3)/4, f = ilk + + 3/2 and k 1 and ...##
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Bernoulli-Euler numbers and multiboundary singularities of type B_n^l
[article]

2009
*
arXiv
*
pre-print

In this paper we study properties of numbers K_n^

arXiv:0910.4046v1
fatcat:vhdn572h6na7ba4oq3lsi42qty
*l*of*connected**components*of bifurcation diagrams*for*multiboundary singularities B_n^*l*. These numbers generalize classic Bernoulli-Euler numbers. ... We also find the generating functions*for*K_n^*l*with small fixed*l*and write partial differential equations*for*the general case. ...*For*any*connected**component*of the set of very nice M-morsifications with*l*+1 boundary and n−3 critical points by the above procedure we bijectively associate*a*couple of*connected**components*of very nice ...##
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Parameterized mixed cluster editing via modular decomposition
[article]

2015
*
arXiv
*
pre-print

Using modular decomposition techniques previously applied to Cluster/Bicluster Editing, we present

arXiv:1506.00944v1
fatcat:xq2zf5tonvgjvbdpzumipi4erq
*a*linear-time algorithm to construct*a*problem*kernel**for*the parameterized version of*L*-Cluster Editing ... The graph G' is called*a*mixed cluster graph or M-cluster graph. Let K denote the family of complete graphs, KL the family of complete*l*-partite graphs (*l*≥ 2), and*Ł*= K∪ KL. ... Building the Problem*Kernel*Clearly,*connected**components*of the input graph G that are already cliques or*ℓ*-cliques can be omitted from consideration. ...##
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A polynomial invariant for knots via von Neumann algebras

1985
*
Bulletin of the American Mathematical Society
*

Here the braid index of

doi:10.1090/s0273-0979-1985-15304-2
fatcat:d3osrxplzfdnzk74eh5vxrbaqi
*a*link*L*is the smallest n*for*which there is*a*pair (6, n) with b*A*=*L*. The*kernel*of r t is not hard to get into*for*these values oft. COROLLARY 9. ... If b is in B n and there is an integer k greater than 3*for*which b G kerr t , t = e*2lK*%*l*k , then b*A*has braid index n. ... 19 »20 21 II 3 1 lia^ia" 1 I li 5 1 \2 2*l*-1 21* | | 12 _1 13" 1 23 -1 2" 1 | u^ai-V i U'Vl"^ | I*l*7 1 |*l*" 1 3 3 21 2 3" 1 2 |2 5 12 2 1" 2 | |3 2 1" 1 23" 1 21 2 2 |2 3 12 4 1" 2 |3"" 1 1~12113 ...##
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A momentum space analysis of the triple pomeron vertex in pQCD

2008
*
European Physical Journal C: Particles and Fields
*

We also comment on the

doi:10.1140/epjc/s10052-007-0501-6
fatcat:y4rtbzkouzhvfhdcnema24pkcy
*kernels*in nonlinear evolution equations. ... Next, at the TPV we searched*for*terms of the*order*m 2*l*2 k 2 , and, finally,*for*the two BFKL*kernels*below the TPV, again the twist-2 approximation (27). ... The corresponding integrals are: I C 1 = 1 (2π) 2 2π 0 dαdβ k 4*l*2 (k 2 −*2lk*cos(α + β) +*l*2 )(k 2 + 2mk cos β + m 2 ) , (39) I C 2 = 1 (2π) 2 2π 0 dαdβ 2k 4 |*l*||m| cos α (k 2 −*2lk*cos(α + β) +*l*2 ...##
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Nonlocal and quasilocal field theories

2015
*
Physical Review D
*

We investigate nonlocal field theories,

doi:10.1103/physrevd.92.125037
fatcat:ze3cce45ijberb7fdbw4rgwuze
*a*subject that has attracted some renewed interest in*connection*with nonlocal gravity models. ... One finds that, remarkably,*for*quasi-local*kernels*all acausal effects are confined within the compact support regions. ... nonvanishing only*for*momenta of*order*1/*ℓ*. ...##
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Topological Entropy and ε-Entropy for Damped Hyperbolic Equations

2000
*
Annales de l'Institute Henri Poincare. Physique theorique
*

These results are shown using two main techniques: Bounds in bounded domains in position space and

doi:10.1007/pl00001013
fatcat:dv4s24k7cbgk7ezg2wkbi2qlxq
*for*large momenta, and*a*novel submultiplicativity argument in W^1,∞. ...*For*each*component*, we get*a*set of 2(*2Lk** ) + 1 numbers q*ℓ*, with |*ℓ*| ≤*2Lk** . ... We bound now in detail the sum in S*L*Q k * (ϕ − ψ) as defined in (8.15 ). We fix one of the (8nC 37 ) 4(*2Lk** )+1 grid points*for*the*components*of Q k * (ϕ − ψ) (x j ). ...##
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Selberg supertrace formula for super Riemann surfaces

1994
*
Communications in Mathematical Physics
*

This paper is the third in

doi:10.1007/bf02101748
fatcat:cutefbsm4be3ngd6kjx7r3pin4
*a*sequel to develop*a*super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. ... Giddings*for*helpful communications. I would also like to thank the members of the II.Institut für Theoretische Physik, Hamburg University,*for*their kind hospitality. ... resolvent*kernel**for*the operator 2 [3, 54] . ...##
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Khovanov homology of alternating links and SU(2) representations of the link group
[article]

2010
*
arXiv
*
pre-print

In addition, we prove

arXiv:0910.5047v2
fatcat:kozakipjhvdnri34mxv2d3x42i
*a*conjecture of Shumakovitch that the Khovanov homology of alternating knots and 2-*component*links contains no n-torsion*for*n > 2. ... We prove that the Khovanov homology of alternating knots and 2-*component*links is equal (as*a*singly graded group) to the singular homology of*a*certain space of trace- free, binary dihedral representations ...*For*any*a*∈ CKh*L*,Q , let [*a*] denote the image of*a*in Kh*L*,Q (implicitly,*a*is assumed to be in the*kernel*of d ). ...##
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Homotopy and q-homotopy skein modules of 3-manifolds: an example in Algebra Situs
[article]

2004
*
arXiv
*
pre-print

Algebraic topology based on knots may be characterized as

arXiv:math/0402304v1
fatcat:gnnblqjfe5djjghgcrmvlgutv4
*a*study of properties of manifolds by considering links (submanifolds) in*a*manifold and their algebraic structure. ... We concentrate, in this lecture, on one relatively simple example of*a*skein module of 3-manifolds -- the q-homotopy skein module. ... Theorem 7.1 Let F be*a*surface (not necessary compact) which contains*a*disc with 2 holes or*a*torus with*a*hole embedded π 1 -injectively; equivalently, π 1 (F 0 ) is not abelian*for**a**connected**component*...##
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Skein modules at the 4th roots of unity
[article]

2001
*
arXiv
*
pre-print

The Kauffman bracket skein modules, S(M,

arXiv:math/0011148v2
fatcat:7jczvijuxfemhaawflt5jdadja
*A*), have been calculated*for**A*=+1,-1,*for*all 3-manifolds M by relating them to the SL(2,C)-character varieties. ... We extend this description to the case when*A*is*a*4-th root of 1 and M is either*a*surface x [0,1] or*a*rational homology sphere (or its submanifold). ... In*order*to establish Lemma 4 it is enough to prove that d(∂ +*L*, ∂ −*L*) will not change if we change the splitting ∂*L*= ∂ −*L*∪ ∂ +*L*by one*connected**component*. ...##
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Knots, Links, and 4-Manifolds
[article]

1997
*
arXiv
*
pre-print

As

arXiv:dg-ga/9612014v2
fatcat:3k7lcghdsbhnvgtnvupu5r2ro4
*a*corollary of this initial investigation, we begin to uncover the surprisingly rich structure of diffeomorphism types of manifolds homeomorphic to the K3 surface. ... In*order*to state the internal fiber sum formula, let X be*a*simply*connected*4-manifold with b + X = 1. ... Let*L*= {K 1 , . . . , K n } be an (n ≥ 2)-*component**ordered*link in S 3 and suppose that X j , j = 1, . . . , n, are simply*connected*smooth 4-manifolds with b + ≥ 1 and each containing*a*smoothly embedded ...##
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First order local invariants of apparent contours

2006
*
Topology
*

*For*

*a*smooth map from

*a*closed surface to the two-dimensional plane, its critical value set is called the apparent contour. ... In this paper we study first

*order*local Vassiliev-type invariants of generic apparent contours. ...

*A*

*component*of is the image of

*a*

*connected*

*component*of the singular point set. ...

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