u̇(t) = −∇xf(u(t), r(t)), u(t0) = u0 where f(x, r) is the exponential penalty function associated with the linear program min{c′x : Ax ≤ b}, and r(t) decreases to 0 as t goes to ∞. We show that for each initial condition (t0, u0) the solution u(t) is defined on the whole interval [t0,∞) and, under suitable hypothesis on the rate of decrease of r(t), we establish the convergence of u(t) towards a...

Let R(∂) be a matrix whose entries are linear partial differential operators, with constant coefficients. Let Ω be a non-empty, open, bounded, convex set. We consider the homogeneous system R(∂)f = 0 in a neighborhood of Ω, subject to the boundary condition f = g in a neighborhood of ∂Ω. For a given smooth function g, we give a criterion for the (unique) existence of a smooth solution f to this...

We consider the Schrödinger map initial-value problem { ∂tφ = φ×∆φ on R × R; φ(0) = φ0, where φ : R × R → S →֒ R is a smooth function. In all dimensions d ≥ 2, we prove that the Schrödinger map initial-value problem admits a unique global smooth solution φ ∈ C(R : H∞ Q ), Q ∈ S, provided that the data φ0 ∈ H∞ Q is smooth and satisfies the smallness condition ‖φ0−Q‖Ḣd/2 ≪ 1. We prove also that th...

for some r-dimensional vector of functions m(zi, θ) of the observable data vector zi and possible parameter value θ in some parameter space Θ. Assuming that θ0 is the unique solution of this population moment equation (equivalent to identification when only (*) is imposed), a method-of-moments estimator θ̂ is defined as a solution (or near-solution) of a sample analogue to (*), replacing the pop...

Let (R, g(t)), 0 ≤ t ≤ T , n ≥ 3, be a standard solution of the Ricci flow with radially symmetric initial data g0. We will extend a recent existence result of P. Lu and G. Tian and prove that for any t0 ∈ [0, T ) there exists a solution of the corresponding harmonic map flow φt : (R, g(t)) → (R, g(t0)) satisfying ∂φt/∂t = ∆g(t),g(t0)φt of the form φt(r, θ) = (ρ(r, t), θ) in polar coordinates i...

The Historical R-tree is a spatio-temporal access method aimed at the retrieval of window queries in the past. The concept behind the method is to keep an R-tree for each timestamp in history, but allow consecutive trees to share branches when the underlying objects do not change. New branches are only created to accommodate updates from the previous timestamp. Although existing implementations...

The Green’s function approach for treating quantum transport in nano devices requires the solution of nonlinear matrix equations of the form X + (C∗ + iηD∗)X−1(C + iηD) = R + iηP , where R and P are Hermitian, P + λD∗ + λ−1D is positive definite for all λ on the unit circle, and η → 0. For each fixed η > 0, we show that the required solution is the unique stabilizing solution Xη. Then X∗ = limη...

We study black-hole-like solutions ( spacetimes with singularities ) of Einstein field equations in 3+ 1 and 2+ 2-dimensions. In the 3+ 1-dim case, it is shown how the horizon of the standard black hole solution at r = 2GNM can be displaced to the location r = 0 of the point massM source, when the radial gauge function is chosen to have an ultra-violet cutoff R(r = 0) = 2GNM if, and only if, on...