This work presents some existence, non-existence and location results for the problem composed by the fourth-order fully nonlinear equation u(4) (x)+ f ( x, u (x) , u (x) , u (x) , u (x) ) = sp(x) for x ∈ [0, 1], where f : [0, 1] × R4 → R and p : [0, 1] → R are continuous functions and s is a real parameter, with the Lidstone boundary conditions u(0) = u(1) = u(0) = u(1) = 0. This problem model...

Let P be a convex polyhedron in R3. The skeleton of P is the graph whose vertices and edges are the vertices and edges of P , respectively. We prove that, if these vertices are on the unit-sphere, the skeleton is a (0.999 · π)-spanner. If the vertices are very close to this sphere, then the skeleton is not necessarily a spanner. For the case when the boundary of P is between two concentric sphe...

We consider a two-type oriented competition model on the first quadrant of the two-dimensional integer lattice. Each vertex of the space may contain only one particle of either Red type or Blue type. A vertex flips to the color of a randomly chosen southwest nearest neighbor at exponential rate 2. At time zero there is one Red particle located at (1, 0) and one Blue particle located at (0, 1). ...

ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...

In settings where R&D specialists work together on a technical project without physically being together, boundary objects are often used to facilitate understanding and collaboration (Carlile, 2002; Star & Griesemer, 1989). From a practice perspective, boundary objects refer to artifacts that are understood within their local setting, yet have enough common ground to facilitate the shared prac...

In this paper, by rst deriving a global version of gradient estimates, we obtain both upper and lower bound estimates for the heat kernel satisfying Neumann boundary conditions on a compact Riemannian manifold with nonconvex boundary .

The finite-size critical properties of the O(n) vector φ4 model, with longrange interaction decaying algebraically with the interparticle distance r like r−d−σ, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature Tc. We show that thi...

In the later part of the paper we shall assume in addition that p decays exponentially at −∞. The support properties of the potential imply that the right reflection coefficient r(k) admits a meromorphic continuation to the upper half-plane C+ = {k ∈ C, Im k > 0} with at most finitely many poles. The inverse problem under consideration consists of recovery of the potential p from the sequence {...

We consider the Dirichlet problem for a class of elliptic and parabolic equations in upper-half space $\mathbb{R}^d_+$, where coefficients are product $x_d^\alpha, \alpha \in (-\infty, 1),$ bounded uniformly matrix coefficients. Thus, singular or degenerate near boundary $\{x_d =0\}$ they may not locally integrable. The novelty work is that we find proper weights under which existence, uniquene...