Results 51 to 60 of about 358 (72)
On the limiting absorption principle and spectra of quantum graphs [PDF]
arXiv, 2005 The main result of the article is validity of the limiting absorption principle and thus absence of the singular continuous spectrum for compact quantum graphs with several infinite leads attached. The technique used involves Dirichlet-to-Neumann operators.
arxiv
Positive Eigenfunctions of a Schrödinger Operator [PDF]
, 2017 The paper considers the eigenvalue problem -Δu-αu+λg(x)u=0 withu∈H1(RN),u≠0 where ∞, λ ∈ and g(x)≡0 on Ω¯, g(x) ∈ (0,1] onRN \ Ω¯ and lim|x|→+∞g(x)=1 for some bounded open set Ω∈RN. Given α>0, does there exist a value of λ>0 for which the problem has
Stuart, C. A., Zhou, Huan-Song
core
A Class of Monotonic Quantities along the Ricci Flow [PDF]
arXiv, 2007 We construct a class of monotonic quantities along the normalized Ricci flow on closed n-dimensional manifolds.
arxiv
arXiv, 2008 We study the heat content asymptotics with either Dirichlet or Robin boundary conditions where the initial temperature exhibits radial blowup near the boundary. We show that there is a complete small-time asymptotic expansion and give explicit geometrical formulas for the first few terms in the expansion.
arxiv
Pleijel's nodal domain theorem for free membranes [PDF]
arXiv, 2008 We prove an analogue of Pleijel's nodal domain theorem for piecewise analytic planar domains with Neumann boundary conditions. This confirms a conjecture made by Pleijel in 1956. The proof is a combination of Pleijel's original approach and an estimate due to Toth and Zelditch for the number of boundary zeros of Neumann eigenfunctions.
arxiv
Heat trace asymptotics with singular weight functions [PDF]
arXiv, 2008 We study the weighted heat trace asymptotics of an operator of Laplace type with Dirichlet boundary conditions where the weight function exhibits radial blowup. We give formulas for the first few terms in the expansion in terms of geometrical data.
arxiv
Special value formula for the spectral zeta function of the non-commutative harmonic oscillator [PDF]
arXiv, 2009 We calculate the special values of the spectral zeta function of the non-commutative harmonic oscillator, and give a general formula for them as integrals of certain algebraic functions. This is a generalization of the result by Ichinose-Wakayama (2005), in which the first two special values are studied.
arxiv
Efficiency and localisation for the first Dirichlet eigenfunction
, 2019 Bounds are obtained for the efficiency or mean to peak ratio $E(\Omega)$ for the first Dirichlet eigenfunction (positive) for open, connected sets $\Omega$ with finite measure in Euclidean space $\R^m$. It is shown that (i) localisation implies vanishing
Berg, Michiel van den +3 more
core
On guided electromagnetic waves in photonic crystal waveguides [PDF]
Amer. Math. Soc. Transl. v. 231, AMS, 2010, pp. 99-108, 2009 The paper addresses the issue of existence and confinement of electromagnetic modes guided by linear defects in photonic crystals. Sufficient condition are provided for existence of such waves near a given spectral location. Confinement to the guide is achieved due to a photonic band gap in the bulk dielectric medium.
arxiv
Stability of Travelling Wave Solutions to the Sine-Gordon Equation [PDF]
arXiv, 2010 We give a geometric proof of spectral stability of travelling kink wave solutions to the sine-Gordon equation. For a travelling kink wave solution of speed $c \neq \pm 1$, the wave is spectrally stable. The proof uses the Maslov index as a means for determining the lack of real eigenvalues.
arxiv