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Cylinders' percolation: decoupling and applications [article]

Alves, Caio and Teixeira, Augusto
2021 arXiv   pre-print
More precisely, we prove that 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.  ... 
arXiv:2112.10055v1 fatcat:5o4v2mdupbdgzetxuxmr2h6lhq

Analysis of boundary effects on PDE-based sampling of Whittle-Matérn random fields [article]

Ustim Khristenko, Laura Scarabosio, Piotr Swierczynski, Elisabeth Ullmann, Barbara Wohlmuth
2018 arXiv   pre-print
We provide 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).  ... 
arXiv:1809.07570v1 fatcat:pt5xacmzlrgjxkialzzw6zctge

Aspects of the BTZ black hole interacting with fields [article]

Leonardo Ortíz, Nora Bretón
2018 arXiv   pre-print
Then we outline the calculation of the expression 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  ... 
arXiv:1808.07521v2 fatcat:knzivopwtvgkdhbylsxpqo3bee

Bernoulli-Euler numbers and multiboundary singularities of type B_n^l [article]

Oleg Karpenkov
2009 arXiv   pre-print
In this paper we study properties of numbers K_n^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  ... 
arXiv:0910.4046v1 fatcat:vhdn572h6na7ba4oq3lsi42qty

Parameterized mixed cluster editing via modular decomposition [article]

Maise Dantas da Silva, Fábio Protti, Jayme Luiz Szwarcfiter
2015 arXiv   pre-print
Using modular decomposition techniques previously applied to Cluster/Bicluster Editing, we present 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 -cliques can be omitted from consideration.  ... 
arXiv:1506.00944v1 fatcat:xq2zf5tonvgjvbdpzumipi4erq

A polynomial invariant for knots via von Neumann algebras

Vaughan F. R. Jones
1985 Bulletin of the American Mathematical Society  
Here the braid index of 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  ... 
doi:10.1090/s0273-0979-1985-15304-2 fatcat:d3osrxplzfdnzk74eh5vxrbaqi

A momentum space analysis of the triple pomeron vertex in pQCD

J. Bartels, K. Kutak
2008 European Physical Journal C: Particles and Fields  
We also comment on the 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  ... 
doi:10.1140/epjc/s10052-007-0501-6 fatcat:y4rtbzkouzhvfhdcnema24pkcy

Nonlocal and quasilocal field theories

E. T. Tomboulis
2015 Physical Review D  
We investigate nonlocal field theories, 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/.  ... 
doi:10.1103/physrevd.92.125037 fatcat:ze3cce45ijberb7fdbw4rgwuze

Topological Entropy and ε-Entropy for Damped Hyperbolic Equations

P. Collet, J.-P. Eckmann
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 for large momenta, and a novel submultiplicativity argument in W^1,∞.  ...  For each component, we get a set of 2(2Lk * ) + 1 numbers q , with || ≤ 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 ).  ... 
doi:10.1007/pl00001013 fatcat:dv4s24k7cbgk7ezg2wkbi2qlxq

Selberg supertrace formula for super Riemann surfaces

Christian Grosche
1994 Communications in Mathematical Physics  
This paper is the third in 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] .  ... 
doi:10.1007/bf02101748 fatcat:cutefbsm4be3ngd6kjx7r3pin4

Khovanov homology of alternating links and SU(2) representations of the link group [article]

Sam Lewallen
2010 arXiv   pre-print
In addition, we prove 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 ).  ... 
arXiv:0910.5047v2 fatcat:kozakipjhvdnri34mxv2d3x42i

Homotopy and q-homotopy skein modules of 3-manifolds: an example in Algebra Situs [article]

Jozef H. Przytycki
2004 arXiv   pre-print
Algebraic topology based on knots may be characterized as 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  ... 
arXiv:math/0402304v1 fatcat:gnnblqjfe5djjghgcrmvlgutv4

Skein modules at the 4th roots of unity [article]

Adam S. Sikora
2001 arXiv   pre-print
The Kauffman bracket skein modules, S(M,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.  ... 
arXiv:math/0011148v2 fatcat:7jczvijuxfemhaawflt5jdadja

Knots, Links, and 4-Manifolds [article]

Ronald Fintushel, Ronald J. Stern
1997 arXiv   pre-print
As 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  ... 
arXiv:dg-ga/9612014v2 fatcat:3k7lcghdsbhnvgtnvupu5r2ro4

First order local invariants of apparent contours

Toru Ohmoto, Francesca Aicardi
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.  ... 
doi:10.1016/j.top.2005.04.005 fatcat:qu3fp6d37rb6pc3zufjgia2pea
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