Search results for "NUMBER"
showing 10 items of 3939 documents
A Symplectic Kovacic's Algorithm in Dimension 4
2018
Let $L$ be a $4$th order differential operator with coefficients in $\mathbb{K}(z)$, with $\mathbb{K}$ a computable algebraically closed field. The operator $L$ is called symplectic when up to rational gauge transformation, the fundamental matrix of solutions $X$ satisfies $X^t J X=J$ where $J$ is the standard symplectic matrix. It is called projectively symplectic when it is projectively equivalent to a symplectic operator. We design an algorithm to test if $L$ is projectively symplectic. Furthermore, based on Kovacic's algorithm, we design an algorithm that computes Liouvillian solutions of projectively symplectic operators of order $4$. Moreover, using Klein's Theorem, algebraic solution…
N-order rational solutions to the Johnson equation depending on 2N - 2 parameter
2017
International audience; We construct rational solutions of order N depending on 2N-2 parameters. They can be written as a quotient of 2 polynomials of degree 2N(N+1) in x, t and 2N(N+1) in y depending on 2N-2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x,y) and their evolution according to time and parameters a1,a2,a3,b1,b2,b3.
Multi-parametric families solutions to the Burgers equation
2021
We construct 2N real parameter solutions to the Burgers' equation in terms of determinant of order N and we call these solutions, N order solutions. We deduce general expressions of these solutions in terms of exponentials and study the patterns of these solutions in functions of the parameters for N = 1 until N = 4.
Bounds on the density of sources of ultra-high energy cosmic rays from the Pierre Auger Observatory
2013
We derive lower bounds on the density of sources of ultra-high energy cosmic rays from the lack of significant clustering in the arrival directions of the highest energy events detected at the Pierre Auger Observatory. The density of uniformly distributed sources of equal intrinsic intensity was found to be larger than similar to (0.06 – 5) x 10(-4) Mpc(-3) at 95% CL, depending on the magnitude of the magnetic defections. Similar bounds, in the range (0.2 – 7) x 10(-4) Mpc(-3), were obtained for sources following the local matter distribution.
Muons in air showers at the Pierre Auger Observatory
2015
We present the first hybrid measurement of the average muon number in air showers at ultrahigh energies, initiated by cosmic rays with zenith angles between 62° and 80°. The measurement is based on 174 hybrid events recorded simultaneously with the surface detector array and the fluorescence detector of the Pierre Auger Observatory. The muon number for each shower is derived by scaling a simulated reference profile of the lateral muon density distribution at the ground until it fits the data. A 1019eV shower with a zenith angle of 67°, which arrives at the surface detector array at an altitude of 1450 m above sea level, contains on average (2.68±0.04±0.48(sys))×107 muons with energies large…
Influence of vessel characteristics and atmospheric processes on the gas and particle phase of ship emission plumes: in situ measurements in the Medi…
2020
A total of 252 emission plumes of ships operating in the Mediterranean Sea and around the Arabian Peninsula were investigated using a comprehensive dataset of gas- and submicron-particle-phase properties measured during the 2-month shipborne AQABA (Air Quality and Climate Change in the Arabian Basin) field campaign in summer 2017. The post-measurement identification of the corresponding ship emission events in the measured data included the determination of the plume sources (up to 38 km away) as well as the plume ages (up to 115 min) and was based on commercially available historical records of the Automatic Identification System. The dispersion lifetime of chemically inert C…
Comparison between 2 Different Composite Nd3+:YVO4 Crystals in a Fibre Coupled Diode Pumped Laser
2008
International audience; We detail the performances of two composite Nd3+YVO4crystals, realised with two different sticking techniques. We tested them inside a fibre coupled diode end pumped laser.
Ultraviolet optical properties of silica controlled by hydrogen trapping at Ge-related defects
2007
We studied the effects induced by the ultraviolet-laser and -lamp exposure sequences on the twofold coordinated germanium (=Ge{sup {center_dot}}{sup {center_dot}}) and the H(II) center (=Ge{sup {center_dot}}-H) in silica. The H(II) centers, generated after the first laser irradiation stage by the trapping of atomic hydrogen H{sup 0} at the (=Ge{sup {center_dot}}{sup {center_dot}}), are destroyed by the subsequent lamp exposure with efficiency depending on photon energy. The H(II) photodestruction is activated from {approx}4 eV, and its cross section is here quantitatively measured, so giving the absorption profile of this center. Consistent with the observed correlated recovering of (=Ge{su…
ESPRESSO highlights the binary nature of the ultra-metal-poor giant HE 0107-5240
2020
Context. The vast majority of the known stars of ultra low metallicity ([Fe=H] >-4:5) are known to be enhanced in carbon, and belong to the 'low-carbon band' (A(C) = log(C=H) + 12 7:6). It is generally, although not universally, accepted that this peculiar chemical composition reflects the chemical composition of the gas cloud out of which these stars were formed. The first ultra-metalpoor star discovered, HE 0107-5240, is also enhanced in carbon and belongs to the 'low-carbon band'. It has recently been claimed to be a long-period binary, based on radial velocity measurements. It has also been claimed that this binarity may explain its peculiar composition as being due to mass transfer fro…
Spectral density estimate for alpha-stable p-adic processes
2012
International audience