We study the uniqueness of weak solutions for Dirichlet problems with variable exponent and non-standard growth conditions. First, we provide two uniqueness results under ellipticity type hypotheses. Next, we provide a uniqueness result when the operator driving the problem is in the form of the divergence of a monotone map. Finally, we derive a fourth uniqueness result under homogeneity type h...

We analyze the asymptotic performance of ensembles of random binning Slepian-Wolf codes, where each type class of the source might have a different coding rate. In particular, we first provide the exact encoder excess rate exponent as well as the decoder error exponent. Then, using the error exponent expression, we determine the optimal rate function, namely, the minimal rate for each type clas...

PURPOSE Variable ventilation is superior to control mode ventilation in a number of circumstances. The nature of the breathing file used to deliver the variable rate and tidal volume has not been formally examined. METHODS We compared two different noise files in a randomized prospective trial of variable ventilation. Pigs were anesthetized, intubated, and mechanically ventilated. Oleic acid ...

We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type modular inequality in variable L spaces if and only if the variable exponent p(x) ∼ const.

We show that the Hardy-Littlewood maximal operator and a class of CalderónZygmund singular integrals satisfy the strong type modular inequality in variable Lp spaces if and only if the variable exponent p(x) ∼ const.

A generalized antithetic time series theory for exponentially derived antithetic random variables is developed. The correlation function between a generalized gamma distributed random variable and its pth exponent is derived. We prove that the correlation approaches minus one as the exponent approaches zero from the left and the shape parameter approaches infinity.