The research for new mineral oil substitutes focuses on vegetable oils known for their biodegradability and low toxicity. This paper focuses on the development and analysis of physicochemical and dielectric properties of a bio-based insulating liquid from castor oil. Castor oil is an inedible tropical resource. It has a good annual oil yield and is widely available in developing countries. Cold pressing of castor seeds is the most appropriate non-chemical process for extracting oil. A refining process was used to remove metal and chemical residues. Refined Castor Oil was filtered and degassed in order to minimize the dissolved gases, solid particles and moisture. A transesterification operation was performed to significantly reduce viscosity oil. Finally, obtained Castor Oil Methyl Esters (COME) are finally distilled in a rotary evaporator under vacuum to remove traces of water and methanol. Physicochemical properties as visual examination, relative density, kinematic viscosity, and acidity were measured in accord-ance with ASTM D6871. AC Breakdown voltage was performed according to IEC 60156, and had been analyzed using Weibull distribution. Processed Castor Oil (PCO) has low viscosity than certified transformer vegetable oils (BIOTEMP, FR3) and high Dielectric Strength (74.67 kV/2.5 mm). Partial Discharges characteristics including the Partial Discharge Inception Voltage and the Partial Discharge Propagation Voltage were also investigated according to the recommendations of IEC 61294. PCO has satisfactory properties for their use as an insulating oil for transformer.

Abstract:
En 1965 sont lancés en périphérie de Paris cinq projets de villes nouvelles dont Melun-Sénart est la cadette. La ville se voit refuser la création d’un centre-ville jusqu’en 1985. En 1986, Melun-Sénart devenu Sénart lance un concours d’idées pour se créer un centre. Les projets lauréats ne seront pas réalisés. L’aménageur de la ville propose un nouveau projet : le Carré Sénart. Ce carré de 1,4 km de c té est destiné à devenir un centre-ville. Il est subdivisé par une trame orthogonale dans laquelle s’insère notamment un nouveau centre commercial. Il accueille environ 10 millions de visiteurs par an et devient l’espace commun de la ville. Je propose de reconstruire la genèse du projet pour comprendre comment un projet de ville lancé par l’état a aujourd’hui un centre commercial pour centre-ville.

Abstract:
There is a one-to-one correspondence between natural numbers and rooted trees; the number is called the Matula number of the rooted tree. We show how a large number of properties of trees can be obtained directly from the corresponding Matula number.

Abstract:
In this paper we use the theory of viscosity solutions for Hamilton-Jacobi equations to study propagation phenomena in kinetic equations. We perform the hydrodynamic limit of some kinetic models thanks to an adapted WKB ansatz. Our models describe particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of monostable type. The scattering operator is supposed to satisfy a maximum principle. When the velocity space is bounded, we show, under suitable hypotheses, that the phase converges towards the viscosity solution of some constrained Hamilton-Jacobi equation which effective Hamiltonian is obtained solving a suitable eigenvalue problem in the velocity space. In the case of unbounded velocities, the non-solvability of the spectral problem can lead to different behavior. In particular, a front acceleration phenomena can occur. Nevertheless, we expect that when the spectral problem is solvable one can extend the convergence result.

Abstract:
A permutation is simsun if for all k, the subword of the one-line notation consisting of the k smallest entries does not have three consecutive decreasing elements. Simsun permutations were introduced by Simion and Sundaram, who showed that they are counted by the Euler numbers. In this paper we enumerate simsun permutations avoiding a pattern or a set of patterns of length 3. The results involve Motkzin, Fibonacci, and secondary structure numbers. The techniques in the proofs include generating functions, bijections into lattice paths and generating trees.

Abstract:
The Hosoya polynomial of a graph encompasses many of its metric properties, for instance the Wiener index (alias average distance) and the hyper-Wiener index. An expression is obtained that reduces the computation of the Hosoya polynomials of a graph with cut vertices to the Hosoya polynomial of the so-called primary subgraphs. The main theorem is applied to specific constructions including bouquets of graphs, circuits of graphs and link of graphs. This is in turn applied to obtain the Hosoya polynomial of several chemically relevant families of graphs. In this way numerous known results are generalized and an approach to obtain them is simplified. Along the way several misprints from the literature are corrected.

Abstract:
In this paper, we study propagation in a nonlocal reaction-diffusion-mutation model describing the invasion of cane toads in Australia. The population of toads is structured by a space variable and a phenotypical trait and the space-diffusivity depends on the trait. We use a Schauder topological degree argument for the construction of some travelling wave solutions of the model. The speed $c^*$ of the wave is obtained after solving a suitable spectral problem in the trait variable. An eigenvector arising from this eigenvalue problem gives the flavor of the profile at the edge of the front. The major difficulty is to obtain uniform $L^\infty$ bounds despite the combination of non local terms and an heterogeneous diffusivity.

Abstract:
In this paper we introduce a new bijection from the set of Dyck paths to itself. This bijection has the property that it maps statistics that appeared recently in the study of pattern-avoiding permutations into classical statistics on Dyck paths, whose distribution is easy to obtain. We also present a generalization of the bijection, as well as several applications of it to enumeration problems of statistics in restricted permutations.

Abstract:
We give a new interpretation of the derangement numbers d_n as the sum of the values of the largest fixed points of all non-derangements of length n-1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We provide analytic and bijective proofs of both results, as well as a new recurrence for the derangement numbers.

Abstract:
A permutation is defined to be cycle-up-down if it is a product of cycles that, when written starting with their smallest element, have an up-down pattern. We prove bijectively and analytically that these permutations are enumerated by the Euler numbers, and we study the distribution of some statistics on them, as well as on up-down permutations, on all permutations, and on a generalization of cycle-up-down permutations. The statistics include the number of cycles of even and odd length, the number of left-to-right minima, and the number of extreme elements.