The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free group. For the mapping class group, the kernel of the Birman exact sequence is a surface braid group. We prove that in the context of the automorphism group of a free group, ...

For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

A recurrent graph G has the infinite collision property if two independent random walks on G, started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton-Watson tree with finite variance conditioned to survive, the incipient infinite cluster in Z with d ≥ 19 and the ...

A new non-reflecting boundary scheme is proposed for time-dependent wave problems in unbounded domains. The linear time-dependent wave equation, with or without a dispersive term, is considered in a semi-infinite wave guide. The infinite domain is truncated via an artificial boundary B, and a high-order non-reflecting boundary condition (NRBC) is imposed onB. Then the problem is solved numerica...

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear i...

The object of this paper is to indicate the immediate usefulness of Caratheodory's theory of the conformal mapping of variable regions in the study of boundary behavior of a fixed but arbitrary conformal map. We study especially the mapping of an infinite strip and its behavior at infinity. Studies of an infinite strip by other methods have previously been made, especially by Ahlfors, Ferrand, ...

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Gene...

The Gelfand–Tsetlin graph is an infinite graded graph that encodes branching of irreducible characters of the unitary groups. The boundary of the Gelfand–Tsetlin graph has at least three incarnations — as a discrete potential theory boundary, as the set of finite indecomposable characters of the infinitedimensional unitary group, and as the set of doubly infinite totally positive sequences. An ...

The problem of boundary control in first order linear parameter varying (LPV) hyperbolic systems with dynamics associated with the boundary conditions is considered in this article. By means of Lyapunov based techniques, some sufficient conditions are derived for the exponential stability of these infinite dimensional systems. A polytopic approach is developed in order to synthesize a robust bo...