A comparison of the physical-chemical properties of precipitated calcium carbonate (PCC), prepared by batch and semicontinuous processes, is presented. In both processes, PCC, was synthesized by carbonation of slaked lime. In the batch process the experiments were performed by varying the initial mass concentration and temperature, and the semicontinuous process was conducted by varying the ini...

In general, the value function associated with an exit time problem is a discontin-uous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton-Jacobi equation involving the proximal subdiierentials (superdiierentials) with subdiierential type (superdiierential type) mixed boundary condition. We also show that if t...

In general, the value function associated with an exit time problem is a discontinuous function. We prove that the lower (upper) semicontinuous envelope of the value function is a supersolution (subsolution) of the Hamilton–Jacobi equation involving the proximal subdifferentials (superdifferentials) with subdifferential-type (superdifferential-type) mixed boundary condition. We also show that i...

We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of ...

In this note we prove an explicit formula for the lower semicontinuous envelope of some functionals defined on real polyhedral chains. More precisely, denoting by H : R → [0,∞) an even, subadditive, and lower semicontinuous function with H(0) = 0, and by ΦH the functional induced by H on polyhedral m-chains, namely

We define the notions of lower and upper semicontinuity for functions from a metric space to the extended real line. We prove that a function is both lower and upper semicontinuous if and only if it is continuous. We also give several equivalent characterizations of lower semicontinuity. In particular, we prove that a function is lower semicontinuous if and only if its epigraph is a closed set....

In order to produce microalgal lipids that can be transformed to biodiesel fuel, effects of concentration of CO(2) aeration on the biomass production and lipid accumulation of Nannochloropsis oculata in a semicontinuous culture were investigated in this study. Lipid content of N. oculata cells at different growth phases was also explored. The results showed that the lipid accumulation from loga...