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The Morse boundary of a proper geodesic metric space is a generalization of the Gromov boundary of a hyperbolic space. It is a quasi-isometry invariant to study "hyperbolic directions" in the space. T...
We consider a long Lorentz tube with absorbing boundaries. Particles are injected to the tube from the left end. We compute the equilibrium density pro les in two cases: the semi-in nite tube (in whi...
We study the boundary of an open smooth complex algebraic variety $U$. We ask when the cohomology of the geometric boundary $Z=X\setminus U$ in a smooth compactification $X$ is pure with respect to th...
Abstract: We study the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary q...
Based on empirical evidence, quantum eigenvalue equations appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimens...
The hydromagnetic steady flow of a viscous incompressible conducting fluid in a circular vertical pipe with slip at the permeable boundaries is investigated. Analytical solutions are constructed for t...
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t 7→ a + bt, a ≥ 0, b ∈ R, by a reflecting Brownian motion.
Let p be a real number greater than one and let 􀀀 be a connected graph of bounded degree. We show that the p-Royden boundary of 􀀀 with the p-harmonic boundary removed is a F-set. We...
We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is giv...
In 2000, Croke and Kleiner showed that a CAT(0) group G can admit more than one boundary. This contrasted with the situation for word hyperbolic groups, where it was well-known that each such group a...
Any discrete action of a group on a locally compact Hadamard space extends to a topological action on the virtual boundary. Croke and Kleiner introduced a class of so-called admissible actions and as...
Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary $\partial V$ for a standard conformally stationary spacetime V = ...
We consider the one-dimensional totally asymmetric simple exclusion model (TASEP model) with open boundary conditions and present the analytical computations leading to the exact formula for distance...
Let X be a smooth compact manifold with boundary. For smooth foliations on the boundary of X admitting a resolution’ in terms of a fibra-tion, we construct a pseudodifferential calculus generalizing ...
We study some spectral properties of a simple two-dimensional model for small angle defects in crystals and alloys. Starting from a periodic potential V : R2 → R, we let V#(x, y) = V (x, y) in the rig...

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