Study of dielectric properties of composite insulators for use in medium voltage overhead lines

The dielectric properties of composite insulator materials based on silicone are studied as a function of ageing factors (temperature, UV). Our study includes composite insulators used in the Tunisian Electricity and Gas Company STEG networks (medium voltage overhead lines). Macroscopic characterization using conventional normalized test was performed at the Center of Measurement Tests of El Omrane (Tunis). In the other hand, samples taken from treated insulator are investigated by dielectric spectroscopy technique. The measurement was carried out according to the same ageing factors. So the correlation between the results of standardized tests and those obtained by laboratory characterization is possible. The results of our measurements show the existence of significant dielectric losses in the case of samples that have been aged under temperature and UV radiation. We attribute these losses to the rate of added filler during material elaboration. The dielectric losses increase respectively with time and ageing factors. This increase is remarkable at the vicinity of industrial frequencies.     

Average Growth of the Spectral Function on a Riemannian Manifold

We study average growth of the spectral function of the Laplacian on a Riemannian manifold. Two types of averaging are considered: with respect to the spectral parameter and with respect to a point on a manifold. We obtain as well related estimates of the growth of the pointwise ζ-function along vertical lines in the complex plane. Some examples and open problems regarding almost periodic properties of the spectral function are also discussed.     

Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process

Abstract

We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the Euler process and the proposed quantizations. We show in particular that at every discretization step t_k of the Euler scheme, this error is bounded by the cumulative quantization errors induced by the Euler operator, from times t₀ = 0 to time t_k. For numerics, we restrict our analysis to the one-dimensional setting and show how to compute the optimal grids using a Newton–Raphson algorithm. We then propose a closed formula for the companion weights and the transition probabilities associated to the proposed quantizations. This allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework. Numerical tests are carried out for the Brownian motion and for the pricing of European options in a local volatility model. A comparison with the Monte Carlo simulations shows that the proposed method may sometimes be more efficient (w.r.t. both computational precision and time complexity) than the Monte Carlo method.     

Multi-asset American Options and Parallel Quantization

We present a parallel implementation of the optimal quantization method on a grid computing. Its purpose is to price instantaneously multidimensional American options. Numerical tests are proceeded with variable number of processors, from 4 to 128. Finally a spatial extrapolation of Richardson–Romberg is introduced to speed up the convergence rate and stabilize the results.     

Apparent diffusion coefficient of intervertebral discs related to matrix composition and integrity

While tremendous work has been performed to characterize degenerative disc disease through gross morphologic, biochemical, and histologic grading schemes, the development of an accurate and noninvasive diagnostic tool is required to objectively detect changes in the matrix with aging and disc degeneration. In the present study, quantitative magnetic resonance was used to determine if the quality of the nutritional supply to the intervertebral disc at various ages and levels of degeneration could be assessed through measurement of the apparent diffusion coefficients (ADCs). Modifications of the nucleus pulposus matrix content, specifically of water and glycosaminoglycan contents, with age and disc degeneration, were reflected in correlating changes in the ADCs. From unforced stepwise linear regression analyses, relations were established showing that decreases in glycosaminoglycan or water contents in the nucleus pulposus resulted in direct decreases in the ADCs. Relations obtained for the ADCs of the nucleus pulposus were direction dependent, in conformity with the anisotropic diffusion in the intervertebral discs. Changes in matrix integrity, as evidenced by the percentage of denatured collagen, were also detected in the nucleus pulposus with a low positive correlation to the ADC along the height of the disc and an inverse statistically significant regression to the ADC along the anterior to posterior axis of the disc. Correlations between the matrix content and integrity of the annulus fibrosus and its ADCs were not as evident, with only the ADC in the lateral direction of the disc of the anterior annulus fibrosus able to reflect changes in matrix content. The information obtained by the ADCs, particularly of the nucleus pulposus, can potentially be used in combination with quantitative T1, T2, and MT parameters to noninvasively obtain a quantitative assessment of the disc matrix composition and structural integrity.     

Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method

Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.     

Hyperplane Sections of Grassmannians and the Number of MDS Linear Codes

We obtain some effective lower and upper bounds for the number of (n,k)-MDS linear codes over _q. As a consequence, one obtains an asymptotic formula for this number. These results also apply for the number of inequivalent representations over _q of the uniform matroid or, alternately, the number of _q-rational points of certain open strata of Grassmannians. The techniques used in the determination of bounds for the number of MDS codes are applied to deduce several geometric properties of certain sections of Grassmannians by coordinate hyperplanes.     

Flexible RuII Schiff Base Complexes: G-Quadruplex DNA Binding and Photo-Induced Cancer Cell Death

A series of new Ru^II Schiff base complexes built on the salphen moiety has been prepared. This includes four flexible monometallic Ru^II compounds and six rigid bimetallic analogues that contain Ni^II, Pd^II or Pt^II cations into the salphen complexation site. Steady state luminescence titrations illustrated the capacity of the compounds to photoprobe G-quadruplex (G4) DNA. Moreover, the vast array of the Schiff base structural changes allowed to extensively assess the influence of the ligand surface, flexibility and charge on the interaction of the compounds with G4 DNA. This was achieved thanks to circular dichroism melting assays and bio-layer interferometry studies that pointed up high affinities along with good selectivities of Ru^II Schiff base complexes for G4 DNA. In cellulo studies were carried out with the most promising compounds. Cellular uptake with location of the compounds in the nucleus as well as in the nucleolus was observed. Cell viability experiments were performed with U2OS osteosarcoma cells in the dark and under light irradiation which allowed the measurements of IC₅₀ values and photoindexes. They showed the substantial role played by light irradiation in the activity of the drugs in addition to the low cytotoxicity of the molecules in the dark. Altogether, the reported results emphasize the promising properties of Ru^II Schiff base complexes as a new class of candidates for developing potential G4 DNA targeting diagnostic or therapeutic compounds.     

Pairing of α-Fused BODIPY: Towards Panchromatic n-Type Semiconducting Materials

A chemical strategy to efficiently perform the dimerization of α-fused boron-dipyrromethene (BODIPY) is reported. The straightforward synthesis of one of these dimers is described and its properties have been investigated through UV/Vis spectroscopy, cyclic voltammetry, differential scanning calorimetry, and charge-carrier mobility measurements by using organic field-effect transistors and space–charge-limited current diodes. The results allow a chemical strategy to decrease the tendency of α-fused BODIPY to crystallize, to increase its light-harvesting properties, and to promote isotropic charge carriers transport. Moreover, the disclosed approach is also a way to maintain the deep LUMO level of α-fused BODIPY; thus making this class of materials highly desirable for optoelectronic applications.     

Unraveling the Composition of Rembrandt's Impasto through the Identification of Unusual Plumbonacrite by Multimodal X‐ray Diffraction Analysis

Rembrandt (1606–1669) is renowned for his impasto technique, involving his use of lead white paint with outstanding rheological properties. This paint was obtained by combining lead white pigment (a mixture of cerussite PbCO₃ and hydrocerussite Pb₃(CO₃)₂(OH)₂) with an organic binding medium, but the exact formulation used by Rembrandt remains a mystery. A powerful combination of high‐angle and high‐lateral resolution x‐ray diffraction was used to investigate several microscopic paint samples from four Rembrandt masterpieces. A rare lead compound, plumbonacrite (Pb₅(CO₃)₃O(OH)₂), was detected in areas of impasto. This can be considered a fingerprint of Rembrandt's recipe and is evidence of the use of an alkaline binding medium, which sheds a new light on Rembrandt's pictorial technique.