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- Mansoor A. Haider, Stephanos Venakides, Vassilis G. Papanicolaou
- SIAM Journal of Applied Mathematics
- 2000

We compute the transmission properties of two-dimensional (2-D) electromagnetic transverse magnetic (TM) waves that are normally incident on a Fabry--Perot structure with mirrors consisting of… (More)

We continue the study of the Floquet (spectral) theory of the beam equation, namely the fourth-order eigenvalue problem [a(x)u(x)] = λρ(x)u(x), -∞ < x < ∞, where the functions a and p are periodic… (More)

AbstractWe study the spectral theory of the fourth-order eigenvalue problem
$$\left[ {a(x)u''(x)} \right]^{\prime \prime } = \lambda \rho (x)u(x), - \infty< x< \infty ,$$
, where the functionsa and ϱ… (More)

The recovery of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of the corresponding transmission eigenvalues for which the corresponding… (More)

We propose a justification of Ewald's method of obtaining rapidly convergent series for the Green's function of the 3-dimensional Helmholtz equation. Our point of view enables us to extend the method… (More)

We develop techniques of computing the asymptotics of the expected number of coupons that a collector has to buy in order to find all N existing different coupons, as N → ∞. The probabilities… (More)

The “double Dixie cup problem” of [D.J. Newman and L. Shepp, Amer. Math. Monthly 67 (1960) 58–61] is a well-known variant of the coupon collector’s problem, where the object of study is the number T… (More)

SummaryUsing standard reflected Brownian motion (SRBM) and martingales we define (in the spirit of Stroock and Varadhan-see [S-V]) the probabilistic solution of the boundary value problem… (More)