Pre-Symmetry Sets of 3D shapes

The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surface M in 3-space (resp. smooth closed curve in 2D) is the set of pairs of points which contribute to the symmetry set, that is, the closure of the set of pairs of distinct points p and q in M, for which there exists a sphere (resp. a circle) tangent to M at p and at q. The aim of this paper is to address problems related to the smoothness and the singularities of the pre-symmetry sets of 3D shapes. We show that the pre-symmetry set of a smooth surface in 3-space has locally the structure of the graph of a function from R^2 to R^2, in many cases of interest.Comment: ACM-class: I.2; I.5; I.4; J.2. Latex, 3 grouped figures. The final version will appear in the proceedings of the First International Workshop on Deep Structure, Singularities and Computer Vision, Maastricht June 200

Level sets of functions and symmetry sets of smooth surface sections

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We also analyse the cases coming from degenerate critical points, corresponding to elliptic cusps of Gauss on a surface, where the differentiability is now reduced to C^[s/4]. However in all our applications to symmetry sets of families of plane curves, we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in Mathematics of Surfaces. Lecture Notes in Computer Science (2005

Reproductive biology of the common torpedo, Torpedo torpedo (Linnaeus, 1758) (Pisces, Torpedinidae) from the coast of Senegal (Eastern Tropical Atlantic)

Among the five species of genus Torpedo recorded from the coast of Senegal, the common torpedo, Torpedo torpedo is that most cornrnonly caught in the area. Adult males and fernales studied were over 300 mm and 310 mm total length (TL), respectively, with the largest male and the largest female recorded being 445 mm and 550 mm TL respectively. Size at birth was between 102 and 125 mm TL (mean 112.12 mm; s.e.m. 5.58). Weight of eggs ranged frorn 6.2 to 8.0 g (rnean: 7.07; s.e.m. 0.5). Gestation lasts longer, from 6 to 8 rnonths, than in the Mediterranean specimens. A calculated chernical balance of development based on rnean dry weights of the fully developed fetuses and ripe oocytes was 1.58 for T. torpedo. This value shows that this torpedinid is not a pure lecithotrophic species, and the role of the rnother during gestation is not negligible. The fecundity (s.1.) of T. torpedo ranges from 5 to 28 in Senegalese specimens as cornpared to 1 to 9 in Mediterranean specirnens. Male ernbryos and fully developed fetuses are more nurnerous than fernales. Among the free-living specimens, nurnber of males and fernales is practically the same. The cornrnon torpedos from the coast of Senegal are larger and the eggs are heavier than Mediterranean specirnens. Key words: Pisces, Torpedinidae, Torpedo torpedo, Reproductive biology, Senegal, Eastern Tropical Atlantic.Among the five species of genus Torpedo recorded from the coast of Senegal, the common torpedo, Torpedo torpedo is that most cornrnonly caught in the area. Adult males and fernales studied were over 300 mm and 310 mm total length (TL), respectively, with the largest male and the largest female recorded being 445 mm and 550 mm TL respectively. Size at birth was between 102 and 125 mm TL (mean 112.12 mm; s.e.m. 5.58). Weight of eggs ranged frorn 6.2 to 8.0 g (rnean: 7.07; s.e.m. 0.5). Gestation lasts longer, from 6 to 8 rnonths, than in the Mediterranean specimens. A calculated chernical balance of development based on rnean dry weights of the fully developed fetuses and ripe oocytes was 1.58 for T. torpedo. This value shows that this torpedinid is not a pure lecithotrophic species, and the role of the rnother during gestation is not negligible. The fecundity (s.1.) of T. torpedo ranges from 5 to 28 in Senegalese specimens as cornpared to 1 to 9 in Mediterranean specirnens. Male ernbryos and fully developed fetuses are more nurnerous than fernales. Among the free-living specimens, nurnber of males and fernales is practically the same. The cornrnon torpedos from the coast of Senegal are larger and the eggs are heavier than Mediterranean specirnens. Key words: Pisces, Torpedinidae, Torpedo torpedo, Reproductive biology, Senegal, Eastern Tropical Atlantic.Among the five species of genus Torpedo recorded from the coast of Senegal, the common torpedo, Torpedo torpedo is that most cornrnonly caught in the area. Adult males and fernales studied were over 300 mm and 310 mm total length (TL), respectively, with the largest male and the largest female recorded being 445 mm and 550 mm TL respectively. Size at birth was between 102 and 125 mm TL (mean 112.12 mm; s.e.m. 5.58). Weight of eggs ranged frorn 6.2 to 8.0 g (rnean: 7.07; s.e.m. 0.5). Gestation lasts longer, from 6 to 8 rnonths, than in the Mediterranean specimens. A calculated chernical balance of development based on rnean dry weights of the fully developed fetuses and ripe oocytes was 1.58 for T. torpedo. This value shows that this torpedinid is not a pure lecithotrophic species, and the role of the rnother during gestation is not negligible. The fecundity (s.1.) of T. torpedo ranges from 5 to 28 in Senegalese specimens as cornpared to 1 to 9 in Mediterranean specirnens. Male ernbryos and fully developed fetuses are more nurnerous than fernales. Among the free-living specimens, nurnber of males and fernales is practically the same. The cornrnon torpedos from the coast of Senegal are larger and the eggs are heavier than Mediterranean specirnens. Key words: Pisces, Torpedinidae, Torpedo torpedo, Reproductive biology, Senegal, Eastern Tropical Atlantic

Numerical Analysis of Three-dimensional Acoustic Cloaks and Carpets

We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous isotropic concentric layers is further proposed based on the effective medium theory. This cloak is characterised by a low reflection and good efficiency over a large bandwidth for both near and far fields, which approximates the ideal cloak with a inhomogeneous and anisotropic distribution of material parameters. The latter suffers from singular material parameters on its inner surface. This singularity depends upon the sharpness of corners, if the cloak has an irregular boundary, e.g. a polyhedron cloak becomes more and more singular when the number of vertices increases if it is star shaped. We thus analyse the acoustic response of a non-singular spherical cloak designed by blowing up a small ball instead of a point, as proposed in [Kohn, Shen, Vogelius, Weinstein, Inverse Problems 24, 015016, 2008]. The multilayered approximation of this cloak requires less extreme densities (especially for the lowest bound). Finally, we investigate another type of non-singular cloaks, known as invisibility carpets [Li and Pendry, Phys. Rev. Lett. 101, 203901, 2008], which mimic the reflection by a flat ground.Comment: Latex, 21 pages, 7 Figures, last version submitted to Wave Motion. OCIS Codes: (000.3860) Mathematical methods in physics; (260.2110) Electromagnetic theory; (160.3918) Metamaterials; (160.1190) Anisotropic optical materials; (350.7420) Waves; (230.1040) Acousto-optical devices; (160.1050) Acousto-optical materials; (290.5839) Scattering,invisibility; (230.3205) Invisibility cloak

Intercultural Competence Gains from Study Abroad in India

Participation in a study abroad program to Zambia with intentional intercultural activities embedded in the course curriculum has been shown to enhance cultural competence as measured by the Intercultural Development Inventory (IDI®) (Krishnan, Masters, Holgate, Wang & Calahan, 2017). The purpose of this study was to assess whether a new program to India, developed using a. similar model, was effective in increasing student intercultural competence and to compare student outcomes with the previous program to evaluate possible differences in outcomes related to the destination country. Participants included 21 students who participated in the SLHS in India study abroad program, and 20 students who have not travelled abroad. Quantitative data included a pre- and post-program administration of the IDI® for both groups. Qualitative data included pre-departure and final reflection papers completed by participants in the intervention group. Results indicated a significant increase in intercultural competence in the intervention group and no change in score in the control group participants. The increase in group score is similar to increases seen in students who had travelled to Zambia. Results indicate that an intensive, service learning study abroad program can be a mechanism for students to enhance intercultural competence, possibly regardless of destination country

Focusing: coming to the point in metamaterials

The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We analyze the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virtual sphere and displays a heterogeneous refractive index n(r) which is proportional to the inverse of 1+r^2. The latter is described by a homogeneous, but negative, refractive index. It has been suggested that the fisheye makes a perfect lens without negative refraction [Leonhardt, Philbin arxiv:0805.4778v2]. However, we point out that the definition of super-resolution in such a heterogeneous medium should be computed with respect to the wavelength in a homogenized medium, and it is perhaps more adequate to talk about a conjugate image rather than a perfect image (the former does not necessarily contains the evanescent components of the source). We numerically find that both the Maxwell fisheye and a thick silver slab lens lead to a resolution close to lambda/3 in transverse magnetic polarization (electric field pointing orthogonal to the plane). We note a shift of the image plane in the latter lens. We also observe that two sources lead to multiple secondary images in the former lens, as confirmed from light rays travelling along geodesics of the virtual sphere. We further observe resolutions ranging from lambda/2 to nearly lambda/4 for magnetic dipoles of varying orientations of dipole moments within the fisheye in transverse electric polarization (magnetic field pointing orthogonal to the plane). Finally, we analyse the Eaton lens for which the source and its image are either located within a unit disc of air, or within a corona 1<r<2 with refractive index $n(r)=\sqrt{2/r-1}$. In both cases, the image resolution is about lambda/2.Comment: Version 2: 22 pages, 11 figures. More figures added, additional cases discussed. Misprints corrected. Keywords: Maxwell fisheye, Eaton lens; Non-Euclidean geometry; Stereographic projection; Transformation optics; Metamaterials; Perfect lens. The last version appears at J. Modern Opt. 57 (2010), no. 7, 511-52

Effet de differentes sources de phosphate sur le rendement du riz sur sols acides

Le rendement du riz paddy reste faible ( 2 t ha-1) et l'efficience agronomique relative (> 40 %), par rapport à PT durant les deux premières années. L'usage d'une source de P contenant S, Al et Fe comme le SS à 60 kg P ha-1 combinée à des résidus de matière organique a été recommandée pour une riziculture plus productive et durable.Mots clés : Sols acides, hyperdystric ferralsol, engrais phosphatés, riziculture, Man

Qualité pastorale des ressources herbagères de la réserve de biosphère du Ferlo (Nord-Sénégal)

La strate herbac&#233;e des phytoc&#233;noses sah&#233;liennes joue un r&#244;le de grande importance dans l&#8217;alimentation du b&#233;tail. Ainsi, la connaissance de la production de fourrage &#171; qualifi&#233; &#187; permet de mieux suivre le fonctionnement des groupements herbac&#233;s. Cette &#233;tude &#233;value la production et appr&#233;cie la qualit&#233; pastorale des herbages de la r&#233;serve de biosph&#232;re du Ferlo (Nord S&#233;n&#233;gal). Un inventaire floristique de la v&#233;g&#233;tation herbac&#233;e a &#233;t&#233; effectu&#233; sur 201 placettes en zone tampon et en zone de transition de la r&#233;serve de biosph&#232;re. Le cort&#232;ge floristique, le recouvrement et la contribution sp&#233;cifique de la strate herbac&#233;e ont &#233;t&#233; &#233;tablis. La production de phytomasse herbac&#233;e au maximum de la v&#233;g&#233;tation par la r&#233;colte int&#233;grale est estim&#233;e &#224; 3,3 tonnes de MS/ha. L&#8217;indice global de qualit&#233; (IGQ) des parcours de la r&#233;serve de biosph&#232;re est de 56,4%. Huit esp&#232;ces (Schoenefeldia gracilis Kunth., Eragrostis tremula Hochst., Pennisetum pedicellatum Trin., Andropogon gayanus Kunth., Zornia glochidiata Reichb. Ex DC., Andropogon pseudapricus Stapf., Schizychirium exile Stapf. et Senna mimosoides L.) d&#233;terminent &#224; 91% la valeur pastorale des herbages. La production de fourrage &#171; qualifi&#233; &#187; est estim&#233;e &#224; 1,86 tonne de MS/ha et la capacit&#233; de charge &#224; 0,41 UBT/ha/an.Mots cl&#233;s: fourrage herbager - valeur pastorale - capacit&#233; de charg