Remarks on Neumann boundary problems involving Jacobians

In this note, we explore the validity of Wente-type estimates for Neumann boundary problems involving Jacobians. We show in particular that such estimates do not in general hold under the same hypotheses on the data for Dirichlet boundary problems.     

Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data

Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+|x| ^p ) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superlinear convex gradient nonlinearity. If the corresponding control problem has a bounded diffusion with respect to the control, then our results apply to a larger class of solutions, namely those growing like O(1+|x| ^p ) at infinity. This latter case encompasses some equations related to backward stochastic differential equations.     

Fractional harmonic maps into manifolds in odd dimension n > 1

In this paper we consider critical points of the following nonlocal energy $$\begin{array}{ll}{\mathcal{L}}_n(u) = \int_{{I\!\!R}^n}| ({-\Delta})^{n/4} u(x)|^2 dx, \qquad(1)\end{array}$$ where ${u \in \dot{H}^{n/2}({I\!\!R}^n,{\mathcal{N}}), {\mathcal{N}} \subset {I\!\!R}^m}$ is a compact k dimensional smooth manifold without boundary and n > 1 is an odd integer. Such critical points are called n/2-harmonic maps into ${{\mathcal{N}}}$ . We prove that ${(-\Delta) ^{n/4} u\in L^p_{loc}({I\!\!R}^n)}$ for every p ≥  1 and thus ${u \in C^{0,\alpha}_{loc}({I\!\!R}^n)}$ , for every 0 < α < 1. The local Hölder continuity of n/2-harmonic maps is based on regularity results obtained in [4] for nonlocal Schrödinger systems with an antisymmetric potential and on some new 3-terms commutators estimates.     

Uncertain data envelopment analysis with imprecisely observed inputs and outputs

Data envelopment analysis (DEA) is a powerful analytical tool in operations research and management for measuring and estimating the efficiency of decision-making units. Both the inputs and the outputs are assumed to be known constants in the classical DEA models. However, in many cases, those data (e.g., carbon emissions and social benefit) cannot be measured in a precise way. Therefore, in this article, the inputs and outputs are considered as uncertain variables and a new uncertain DEA model is introduced. The sensitivity and stability of the new model are also analyzed. Finally, a numerical example of the new model is documented.     

A Pizzetti-type formula for the heat operator

We provide an asymptotic expansion of the integral mean of a smooth function over the Heat ball. Namely we generalize to the Heat operator the so-called Pizzetti’s Formula, which expresses the integral mean of a smooth function over an Euclidean ball in terms of a power series with respect to the radius of the ball having the iterated of the ordinary Laplace operator as coefficients. Similarly here, we express the heat integral mean as a power series with respect to the radius of the heat ball, whose coefficients are powers of a distorted heat operator. We also discuss sufficient conditions to have a finite sum. Received: 27 May 2005     

Pythium irregulare Fermentation to Produce Arachidonic Acid (ARA) and Eicosapentaenoic Acid (EPA) Using Soybean Processing Co-products as Substrates

Arachidonic acid (ARA) and eicosapentaenoic acid (EPA) were produced by Pythium irregulare fungus using soybean cotyledon fiber and soy skim, two co-products from soybean aqueous processing, as substrates in different fermentation systems. Parameters such as moisture content, substrate glucose addition, incubation time, and vegetable oil supplementation were found to be important in solid-state fermentation (SSF) of soybean fiber, which is to be used as animal feed with enriched long-chain polyunsaturated fatty acids (PUFA). Soybean fiber with 8 % (dwb) glucose supplementation for a 7-day SSF produced 1.3 mg of ARA and 1.6 mg of EPA in 1 g of dried substrate. When soy skim was used as substrate for submerged fermentation, total ARA yield of 125.7 mg/L and EPA yield of 92.4 mg/L were achieved with the supplementation of 7 % (w/v) soybean oil. This study demonstrates that the values of soybean fiber and soy skim co-products could be enhanced through the long-chain PUFA production by fermentation.     

Scanning probe microscope with interchangeable AFM-FFM and STM heads

Summary A scanning probe microscope operating in air with interchangeable atomic force-friction force (AFM-FFM) and electronic-tunnelling (STM) heads is presented. Our AFM operates in the so-called contact mode and utilizes the optical-lever detection method which allows simultaneous measurement of the topography as well as the lateral force. The set-up also contains an optical microscope to control both the sample and the probe laser spot on the cantilever. The experimental method to change from AFM to STM operation is based on the use of the probe laser beam and the optical microscope. The maximum scanning area is (24×24) μm² and it is well embraced in the optical-microscope visual field. The microscope attains atomic resolution in air in both AFM and STM configuration. Its performance is demonstrated on the surface of different samples. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Evaluation of Enzyme Activity and Fiber Content of Soybean Cotyledon Fiber and Distiller’s Dried Grains with Solubles by Solid State Fermentation

To increase the value of coproducts from corn ethanol fermentation and soybean aqueous processing, distiller??s dried grains with solubles (DDGS) and soybean cotyledon fiber were used as the substrates for solid state fermentation (SSF) to improve feed digestibility. Aspergillus oryzae, Trichoderma reesei, and Phanerochaete chrysosporium were chosen as they produce desirable enzymes and are widely used in SSF for feed. The results showed that the cellulase and xylanase activities were significantly increased after 7?days of fermentation, and cellulose and hemicellulose degradation was also greatly increased. When soybean fiber was used as SSF substrate, the maximum activities of the cellulase and xylanase were 10.3 and 84.2?IU/g substrate (dry weight basis) after SSF treatment, respectively. However, the enzyme activities were relatively low in DDGS, and the growth of the three fungi was poor. The fungi grew better when soybean cotyledon fiber was added to DDGS, and cellulase and xylanase activity increased with the increase of soybean fiber content. Porosity was identified as an important factor for SSF because the addition of inert soybean hull alone improved the fungi growth significantly. These data suggest that the nutritional value of DDGS and soybean cotyledon fiber as monogastric animal feed could be greatly enhanced by SSF treatment.