We investigate a class of singular m-point p-Laplacian boundary value problem on time scales with the sign changing nonlinearity. By using the well-known Schauder fixed point theorem and upper and lower solutions method, some new existence criteria for positive solutions of the boundary value problem are presented. These results are new even for the corresponding differential (T = R) and differ...

We consider collective choice with agents possessing strictly monotone, strictly convex and continuous preferences over a compact and convex constraint set contained in Rþ. If it is non-empty the core will lie on the efficient boundary of the constraint set and any policy not in the core is beaten by some policy on the efficient boundary. It is possible to translate the collective choice proble...

r–division approach pieces of size O(r) with boundary O( √ r) per piece (total boundary O(n/ √ r)) precompute APSP for all nodes on the boundary, space O(n/r); at query time, explore piece of v (say Pv) and piece of w (Pw) and find best connection pair ∂Pv × ∂Pw, piece sizes O(r) and O( √ r) connection pairs, total query time O(r) smoothly interpolates between SSSP and APSP (only separators use...

We consider affine analogues of the isoperimetric inequality in the sense of piecewise linear (PL) manifolds. Given a closed polygon P having n edges, embedded in R, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface embedded in R having P as its geometric boundary. More generally we obtain such bounds for a triangulated (locally flat) ...

Given a closed polygon P having n edges, embedded in R, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface embedded in R d having P as its geometric boundary. More generally we obtain such bounds for a triangulated (locally flat) PL surface having P as its boundary which is immersed in R and whose interior is disjoint from P . The most ...

A new viewpoint for the gauge hierarchy problem is proposed: compactification at a large scale, 1/R, leads to a low energy effective theory with supersymmetry softly broken at a much lower scale, α/R. The hierarchy is induced by an extremely small angle α which appears in the orbifold compactification boundary conditions. The same orbifold boundary conditions break Peccei-Quinn symmetry, leadin...

In this paper, we are concerned with the third-order quasilinear ordinary differential equation (Φp(u)) = f(t, u, u′, u′′), 0 < t < 1, with the nonlinear boundary conditions u(0) = 0, g(u′(0), u′′(0)) = A, h(u′(1), u′′(1)) = B or u(0) = C, L(u′(0), u′(1)) = 0, R(u′(0), u′(1), u′′(0), u′′(1)) = 0, where A,B, C ∈ R,Φp(u) = |u|p−2u(p > 1), f : [0, 1]× R → R is continuous, g, h, L : R → R, R : R → ...

We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive number R there exists a radially symmetric stationary solution with free boundary r = R and interior boundary r = ρ.The system depends on a positive parameter μ, and for a sequence of values μ2 < μ3 < · · · there also exist branches o...

We construct R-charged adS bubbles in D = 5, N = 8 supergravity. These bubbles are charecterised by four parameters. The asymptotic boundary of these solutions are deSitter times a circle. By comparing boundary energies, we study the possibility of a transition from certain class of black holes to these bubbles below a critical radius of the boundary circle. We argue that this may occur when fo...

In minimal non-critical string theory we show that the principal (r,s) ZZ brane can be viewed as the basic (1,1) ZZ boundary state tensored with the (r,s) Cardy boundary state. In this sense there exists only one ZZ boundary state, the basic (1,1) boundary state.