We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S . We determine HF(Σg × S , s;C) completely in the case c1(s) = 0, which for g ≥ 3 was previously unknown. We show that in this case HF∞ is closely related to the cohomology of a the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF (Σg ×S , ...

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially dependent diffusion coefficient of the form D(x)∼|x|^{c}, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At long times, t...

where p, q, e ∈ C t0,∞ , with p t > 0 and 0 < α ≤ β being constants. By a solution of 1.1 , wemean a function y t ∈ C1 Ty,∞ , , where Ty ≥ t0 depends on the particular solution, which has the property p t |y′ t |α−1y′ t ∈ C1 Ty,∞ and satisfies 1.1 . We restrict our attention to the nontrivial solutions y t of 1.1 only, that is, to solutions y t such that sup{|y t | : t ≥ T} > 0 for all T ≥ Ty ....

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

This article studies the regularity of the solution of the radiosity equation on polyhedral surfaces in R . We examine the localized equation near the vertices and characterize the smoothness of their solution in terms of weighted Sobolev spaces. We also consider the effect of shadows and prove local C1 regularity in the case of a piecewise C1 emissivity function.

Consider the linear nonhomogeneous fixed-point equation R D = N � i=1 Ci Ri + Q, where (Q, N , C1, C2, . . .) is a random vector with N ∈ {0, 1, 2, 3, . . .} ∪ {∞}, Ci ≥ 0 for all i ∈ N, P(|Q| > 0) > 0, and {Ri }i∈N is a sequence of i.i.d. random variables independent of (Q, N , C1, C2, . . .) having the same distribution as R. It is known that R will have a heavy-tailed distribution under seve...