Maximum principles for a class of nonlinear second order elliptic differential equations

In this paper we investigate maximum principles for functionals defined on solutions to special partial diff'erential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.     

Improved Dermal and Transdermal Delivery of Curcumin with SmartFilms and Nanocrystals

Poor aqueous solubility of active compounds is a major issue in today’s drug delivery. In this study the smartFilm-technology was exploited to improve the dermal penetration efficacy of a poorly soluble active compound (curcumin). Results were compared to the dermal penetration efficacy of curcumin from curcumin bulk suspensions and nanocrystals, respectively. The smartFilms enabled an effective dermal and transdermal penetration of curcumin, whereas curcumin bulk- and nanosuspensions were less efficient when the curcumin content was similar to the curcumin content in the smartFilms. Interestingly, it was found that increasing numbers of curcumin particles within the suspensions increased the passive dermal penetration of curcumin. The effect is caused by an aqueous meniscus that is created between particle and skin if the dispersion medium evaporates. The connecting liquid meniscus causes a local swelling of the stratum corneum and maintains a high local concentration gradient between drug particles and skin. Thus, leading to a high local passive dermal penetration of curcumin. The findings suggest a new dermal penetration mechanism for active compounds from nano-particulate drug delivery systems, which can be the base for the development of topical drug products with improved penetration efficacy in the future.     

Accurate Solution to Overdetermined Linear Equations with Errors Using L1 Norm Minimization

It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m × n) matrix A and the data vector b. This is in contrast to a least squares solution, where even one large error will typically cause a large error in x. In this paper we give necessary and sufficient conditions that the correct solution is obtained when there are some errors in A and b. Based on the sufficient condition, it is shown that if k rows of [A b] contain large errors, the correct solution is guaranteed if (m – n)/n 2k/, where > 0, is a lower bound of singular values related to A. Since m typically represents the number of measurements, this inequality shows how many data points are needed to guarantee a correct solution in the presence of large errors in some of the data. This inequality is, in fact, an upper bound, and computational results are presented, which show that the correct solution will be obtained, with high probability, for much smaller values of m – n.     

评价矿井突水危险性的关键层方法

将煤层底板至含水层间承载能力最大的一层岩层看作起阻水作用的关键岩层（简称关键层），并把它简化为薄板，利用板的理论解确定该岩层的破断跨距，用以评价底板突水的危险性．实例分析表明，这种预测突水危险性的方法是简明有效的．     

Segments and Hilbert schemes of points

Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order (as, for example, the degrevlex order) in the Hilbert scheme of points in Pⁿ. In this context, we look into the properties of several types of “segment” ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.     

Triphasic FE Modeling of the Skin Water Barrier

A skin–air model is developed to model the water barrier function of skin. The skin model is a porous solid saturated with a monovalent salt solution. The air model is a vapor diffusion model in non-moving air. In vivo measurements of water loss from human skin under varying ambient conditions are used to validate the model.     

Possibilities for human skin characterization based on strongly reduced Raman spectroscopic information

Loss‐of‐function mutations in the gene coding for filaggrin are the single most important risk factor for development of atopic dermatitis and associated allergic rhinitis and asthma. Filaggrin is enzymatically degraded to natural moisturizing factor (NMF) in the stratum corneum (SC). In vivo Raman spectra of human skin can be used to quantify the NMF concentration in SC and thereby identify carriers of a loss‐of‐function mutation in the gene coding for filaggrin, which results in decreased NMF content. Here, we demonstrate that strongly reduced Raman spectral information is sufficient to make this differentiation. This is an important step towards development of a dedicated diagnostic device of reduced complexity, size and cost as compared to current state‐of‐the‐art Raman equipment. A genetic algorithm was used to select the spectral regions needed to classify skin based on normal or reduced NMF content in SC. Using the NMF content based on full spectral information as gold standard, only four Raman regions were required to create a linear discriminant analysis model that can differentiate between skin with low NMF and skin with normal NMF with a prediction accuracy of 93 %. Copyright © 2013 John Wiley & Sons, Ltd.     

On Algebras of Invariants and Codimension 1 Luna Strata for Nonconnected Groups

In order to describe explicitly the algebra of invariants for a non-connected reductive subgroup G GL(V) we apply the method of strata. For this we describe codimension 1 strata of the quotient V//G and study the normality property of their closures. We find some criteria for k[V]^G to be polynomial or a hypersurface. Then we apply these results to complete the classification [Sh] of nonconnected simple groups G such that k[V]^G is polynomial.