Fixed a bounded open set Ω of R , we completely characterize the weak* lower semicontinuity of functionals of the form F (u,A) = ess sup x∈A f(x, u(x), Du(x)) defined for every u ∈ W 1,∞(Ω) and for every open subset A ⊂ Ω. Without a continuity assumption on f(·, u, ξ) we show that the supremal functional F is weakly* lower semicontinuous if and only if it can be represented through a level conv...

In this work, we apply the Martin-Siggia-Rose path integral formalism to equations of a thin elastic plate. Using diagrammatic technique, obtain direct interaction approximation (DIA) describe evolutions correlation function and response fields. Consistent with previous results, show that DIA for plates can be derived from non-markovian stochastic process in weakly nonlinear limit, lead kinetic...

OBJECTIVE To compare signal intensity (SI) correction using scale and rescale slopes with SI correction using SIs of spleen and muscle for quantifying multiphase hepatic contrast enhancement with Gd-EOB-DTPA by assessing their correlation with T1 values generated from Look-Locker turbo-field-echo (LL-TFE) sequence data (ER-T1). MATERIALS AND METHODS Thirty patients underwent Gd-EOB-DTPA-enhan...

We investigated the corneal morphology of adult Mp/+ mice, which are heterozygous for the micropinna microphthalmia mutation, and identified several abnormalities, which implied that corneal epithelial maintenance was abnormal. The Mp/+ corneal epithelium was thin, loosely packed and contained goblet cells in older mice. Evidence also suggested that the barrier function was compromised. However...

Submodular functions are a broad class of set functions, which naturally arise in diverse areas such as economics, operations research and game theory. Many algorithms have been suggested for the maximization of these functions, achieving both strong theoretical guarantees and good practical performance. Unfortunately, once the function deviates from submodularity (even slightly), the known alg...