A relative completeness theorem

Archiv der Mathematik - We prove a relative n-completeness theorem asserting that a complex space Y that fibers over a complex space X of dimension less than n is n-complete provided that Y admits...     

Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise

In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation ${{\rm d}X(t) = {\rm div} \left[\frac{\nabla X(t)}{|\nabla X(t)|}\right]{\rm d}t + X(t){\rm d}W(t) {\rm in} (0, \infty) \times \mathcal{O},}$ where ${\mathcal{O}}$ is a bounded and open domain in ${\mathbb{R}^N, N \geqq 1}$ and W(t) is a Wiener process of the form ${W(t) = \sum^{\infty}_{k = 1}\mu_{k}e_{k}\beta_{k}(t), e_{k} \in C^{2}(\overline{\mathcal{O}}) \cap H^{1}_{0}(\mathcal{O}),}$ and ${\beta_{k}, k \in \mathbb{N}}$ are independent Brownian motions. This is a stochastic diffusion equation with a highly singular diffusivity term. One main result established here is that for all initial conditions in ${L^2(\mathcal{O})}$ , it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality. Thus, one obtains a stochastic version of the (minimal) total variation flow. The new approach developed here also allows us to prove the finite time extinction of solutions in dimensions ${1\leqq N \leqq3}$ , which is another main result of this work.     

Optimal harvesting for periodic age-dependent population dynamics with logistic term

We prove an asymptotic behavior result for an age-dependent population dynamics with logistic term and periodic vital rates. We investigate next an optimal harvesting problem related to a periodic age-structured model with logistic term. Existence of an optimal control and necessary optimality conditions are established. A conceptual algorithm to approximate the optimal pair is derived and some numerical experiments are presented.     

A PDE variational approach to image denoising and restoration

In this paper we discuss a general variational model for image restoration based on the minimization of a convex functional of gradient under minimal growth conditions. This approach is related to minimization in bounded variation norm and has a smoothing effect on degraded image while preserving the edge features.     

Statistically q‐deformed and tau‐deformed systems

Two classes of statistically deformed systems are known in literature. They are, respectively, the q‐deformed systems (Lavagno and Narayana Swamy, Phys Rev E 2002, 65, 036101) and the κ‐deformed systems (Kaniadakis and Scarfone, Physica A 2002, 305, 69). In this article, a new class, i.e., the tau‐deformed systems, is introduced. For each of these systems, a consistent thermodynamics may be developed. A summary of the main similarities between the thermodynamic properties of q‐deformed and tau‐deformed systems is presented. The deformation outlined in this article is radically different from the nonextensive Tsallis statistics, where the structure of the entropy is rather arbitrary deformed via the logarithmic function. In contrast, the theory of tau‐deformed systems is developed on a purely physical basis. However, one finally shows that the tau‐systems may be described by using a new form of deformed logarithmic function. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Carleman Estimates and Controllability of Linear Stochastic Heat Equations

   Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat equation (with Dirichlet boundary conditions in the bounded domain D ⊂ R ^d and multiplicative noise):

From Mesomorphic Phosphine Oxide to Clustomesogens Containing Molybdenum and Tungsten Octahedral Cluster Cores

New clustomesogens (i.e., metal atom clusters containing liquid crystalline (LC) materials) have been obtained by grafting neutral cyanobiphenyl (CB)‐ or cholesteryl‐containing tailor‐made dendritic mesomorphic triphenylphosphine oxide ligands on luminescent (M₆Clⁱ₈)⁴⁺ octahedral cluster cores (M=Mo, W). The LC properties were studied by a combination of polarizing optical microscopy (POM), differential scanning calorimetry (DSC), and X‐ray powder diffraction analyses. While the organic ligands showed various mesophase types ranging from nematic, SmA columnar (SmA_Col), SmA, and SmC phases, it turned out that the corresponding clustomesogens formed layered phases (SmA) over a wide range of temperatures that depend on the nature and density of mesogenic groups employed. Intrinsic luminescence properties of the cluster precursors are preserved over the entire range of LC phase existence.     

Phytochemical Content and Antioxidant Activity of Malus domestica Borkh Peel Extracts

Apple is an important dietary source of carotenoids and phenolic compounds, and its regular consumption is associated with several health benefits. The aim of this study was to evaluate the phytochemical composition of fresh peels of four red-skinned (“Champion”, “Generos”, “Idared”, “Florina”) and two yellow-skinned (“Golden Delicious”, “Reinette Simirenko”) apple varieties. Antioxidant activity of apple peel extracts was determined by ferric reducing antioxidant power (FRAP) and ABTS radical scavenging capacity assays. Total carotenoid and polyphenolic contents were determined spectrophotometrically, while the profile of individual carotenoids and anthocyanins (in red-skinned varieties) was analyzed using high-performance liquid chromatography coupled to a photodiode array detector (HPLC-PDA). Carotenoid composition was specific for each variety, and total carotenoid content was slightly higher in yellow-skinned apple peels compared to red-skinned varieties. In contrast, total phenolic content was higher in the peels of red-skinned cultivars. Anthocyanin profile was predominated by cyanidin-3-O-galactoside. Antioxidant potential followed the trend of the total polyphenolic content, being highest in “Florina”, as measured by both FRAP and ABTS assays. Our results demonstrated apple peels have high phytochemical content with diverse compositions, and their regular consumption can be an excellent source of antioxidants.