Parabolic equations with measure data in Orlicz spaces

We prove an existence result for solutions of nonlinear parabolic equations with measure data in Orlicz–Sobolev spaces.     

A General Multiresolution Method for Fitting Functions on the Sphere

In [7], Lyche and Schumaker have described a method for fitting functions of class C ¹ on the sphere which is based on tensor products of quadratic polynomial splines and trigonometric splines of order three associated with uniform knots. In this paper, we present a multiresolution method leading to C ²-functions on the sphere, using tensor products of polynomial and trigonometric splines of odd order with arbitrary simple knot sequences. We determine the decomposition and reconstruction matrices corresponding to the polynomial and trigonometric spline spaces. We describe the general tensor product decomposition and reconstruction algorithms in matrix form which are convenient for the compression of surfaces. We give the different steps of the computer implementation of these algorithms and, finally, we present a test example.     

Antibacterial and antioxidant properties of mixed linkage beta-oligosaccharides from extracted β-glucan hydrolysed by Penicillium occitanis EGL lichenase

The aim of this study was first to ascertain the chemical composition and the physicochemical properties of cereal extracted β-glucan from barley flour. Secondly, to assess the antioxidant properties and the antibacterial properties of extracted β-glucan hydrolysates. The proximate composition, FT-IR and scanning electron microscopy of extracted β-Glucan were studied. Hydrolysates from extracted β-glucan, obtained by lichenase EG_L from Penicillium occitanis, were a mixed linkage beta-oligosaccharides (MLBO) of trisaccharides and tetrasaccharides. MLBO showed a DPPH radical scavenger with IC50 about 1.8 ± 0.01 mg/mL whereas the IC50 of extracted β-glucan was about 5 ± 0.01 mg/mL. MLBO showed a high antioxidative capacity (175 μmol/mL α-tocopherol equivalents) at 5 mg/mL. The antimicrobial activity was confirmed against all tested bacteria especially at 20 mg/mL of MLBO while no inhibition was observed for all the strains used after the addition of either EG_L or extracted β-glucan.     

Simultaneous analysis of polychlorinated biphenyls and organochlorine pesticides in water by headspace solid-phase microextraction with gas chromatography-tandem mass spectrometry

Headspace solid-phase microextraction combined with gas chromatography-ion trap tandem mass spectrometry (HS-SPME-GC-ITMS-MS) method has been developed and studied for the simultaneous determination of 15 organochlorine pesticides (OCPs) and 20 polychlorinated biphenyls (PCBs) in aqueous samples. To perform the HS-SPME polydimethylsiloxane (PDMS) (7, 30 and 100 microm film thickness) and polydimethylsiloxane-divinylbenzene (PDMS-DVB) fibers were initially compared on the basis of their absorption capacities for the selected compounds, and PDMS 100 microm film thickness was selected to accomplish the rests of essays. The influence of various parameters on OCPs and PCBs extraction efficiency by HS-SPME was thoroughly studied using GC-electron capture detector (ECD). Parameters such as collision induced dissociation (CID) resonant excitation amplitude and RF storage level were optimized to increase specificity and sensibility for ITMS-MS analysis. The performance of proposed HS-SPME-GC-ITMS-MS methodology with respect to linearity, reproducibility and limit of detection (LOD) was evaluated by water spiked with target compounds. The linear range of most compounds was found to be between 0.01 and 1 ng mL(-1) and the limits of detection were between 0.4 and 26 pg mL(-1). The reproducibility of the method (n = 6), expressed as relative standard deviation (RSD), was between 5 and 21%. Finally, developed procedure was applied to determine selected OCPs and PCBs in river water samples in concentration below 0.1 ng mL(-1) can be easily carried out with ultra-selectivity and precision.     

The first chromate containing both Cr<Subscript>2</Subscript>O<Subscript>7</Subscript> and Cr<Subscript>3</Subscript>O<Subscript>10</Subscript> groups,bis(1,3-bis(4-piperidinium)propane) dichromate trichromate monohydrate: Synthesis and crystal structure

A new organic-inorganic hybrid material (C₁₃H₂₈N₂)₂[Cr₂O₇][Cr₃O₁₀]·H₂O (1) was synthesized by slow solvent evaporation at room temperature, and its crystal structure was determined by single crystal X-ray diffraction. This compound crystallizes in the monoclinic space group P2₁/c. The asymmetric unit contains two crystallographically independent 1,3-bis(4-piperidinium)propane, (H₂bppp)²⁺ cations (A and B), one trichromate Cr₃O ₁₀ ^2? anion, one dichromate Cr₂O ₇ ^2? anion, and one water molecule. All these entities are interconnected into a complicated two-dimensional hydrogen bonded network via N–H?O and O–H?O hydrogen bonds. Furthermore, this structure is stabilized by a large number of C–H?O interactions, thus establishing a three-dimensional network structure. This compound appears to be the first example of chromates containing both Cr₂O₇ and Cr₃O₁₀ groups.     

A blind image watermarking using multiresolution visibility map

A perceptual pyramid watermarking method is proposed. The key idea is to use the contrast sensitivity of the human visual system (HVS) to determine “invisible” regions where watermark energy can be adjusted providing an invisible and robust watermark. These invisibles regions are obtained by computing a “visibility map” at each level of the Gaussian pyramid (GP). The watermark is weighted by the local contrast and a global scaling factor. The embedding process is performed by modifying the values in some levels of the Laplacian Pyramid (LP) using the spread spectrum technique. Afterwards, the watermarked image can be constructed from the levels of the LP. For watermark detection, a blind detection scheme using the threshold-correlation based technique is proposed. Finally, the performances of the watermarking method are evaluated in terms of invisibility and robustness using some quality metrics and different attacks of Stirmark such as Gaussian noise, low-pass filtering, Jpeg compression and cropping. This evaluation is performed for the choice of some parameters of the watermarking system depending on performances such as invisibility and robustness. The design of our watermarking technique can finally be formulated as an optimisation problem where the objective is to guarantee a trade-off between invisibility and robustness.     

First,Second, and Third Change of Rings Theorems for Gorenstein Homological dimensions

In this article, we investigate the change of rings theorems for the Gorenstein dimensions over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we extend the well-known first, second, and third change of rings theorems for the classical projective and injective dimensions to the Gorenstein projective and injective dimensions, respectively. Each of the results established in this article for the Gorenstein projective dimension is a generalization of a G-dimension of a finitely generated module M over a noetherian ring R.     

C 1 Quadratic and C 2 Quartic Macro-Elements on a Modified Morgan-Scott Triangulation

In this paper, we construct a quadratic composite finite element of class C ¹ and quartic composite finite element of class C ² on a new triangulation τ ₁₀ which is obtained by splitting each triangle of a given triangulation τ into ten smaller subtriangles. These new elements can be used for constructing spline spaces with local basis that can be applied for solving some Hermite interpolation problems with optimal approximation order.