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Now showing items 1-6 of 6

#### Diffusion on curved, periodic surfaces

(American Physical Society, 1999-07)

We present a simulation algorithm for a diffusion on a curved surface given by the equation [omega](r)50. The algorithm is tested against analytical results known for diffusion on a cylinder and a sphere, and applied to the diffusion on the P, D, and G periodic nodal surfaces. It should find application in an interpretation ...

#### On minimal parabolic functions and time-homogenous parabolic h-transforms

(American Mathematical Society, 1999-03-29)

Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin
semi-infinite tubes D [is an element of the subset of real numbers to the power of] d of variable width and minimal harmonic functions h corresponding to the boundary point of D "at ...

#### A counterexample to the "hot spots" conjecture

(Princeton University and Institute for Advanced Study, 1999-01)

We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected
planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with
Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict
maximum at an interior point ...

#### Stochastic bifurcation models

(Institute of Mathematical Statistics, 1999-01)

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.

#### Cutting Brownian Paths

(American Mathematical Society, 1999-01)

Let Z [subscript] t be two-dimensional Brownian motion. We say that a straight line
L is a cut line if there exists a time t [is an element of the set] (0, 1) such that the trace of {Z [subscript] s : 0 [is less than or equal to] s < t} lies on one side of L and the trace of {Z [subscript] s : t < s < 1} lies on the other ...

#### On the "hot spots" conjecture of J. Rauch

(Academic Press (Elsevier), 1999-05-10)

We will state several rigorous versions of J. Rauch's "hot spots" conjecture, review some known
results, and prove the conjecture under some additional assumptions. Let us, however,
first observe that the conclusion cannot hold for all initial conditions.