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Laurent,

doi:10.1016/s0025-5610(97)00043-9

Cited by 6 publications

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“…Secondly, in order to efficiently reflect the X-ray photons from 0.5 to 80 keV the mirror surface will be coated with multilayers [3]. To efficiently and simultaneously detect the X-ray over such a very large energy band, two detectors, one on top of the other one, are foreseen at the focus of the mirrors [4]. Around the focal plane camera there is also an efficient anticoincidence system to obtain very low background [4].…”

Section: Introductionmentioning

confidence: 99%

“…To efficiently and simultaneously detect the X-ray over such a very large energy band, two detectors, one on top of the other one, are foreseen at the focus of the mirrors [4]. Around the focal plane camera there is also an efficient anticoincidence system to obtain very low background [4]. Similarly, a pre-collimator and a proton diverter are mounted in front and behind the mirror module, respectively [5].…”

Section: Introductionmentioning

confidence: 99%

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Simbol-X: a formation flight mission with an unprecedented imaging capability in the 0.5-80 keV energy band

Tagliaferri

Ferrando

Duigou

et al. 2017

International Conference on Space Optics — ICSO 2008

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The discovery of X-ray emission from cosmic sources in the 1960s has opened a new powerful observing window on the Universe. In fact, the exploration of the X-ray sky during the 70s-90s has established X-ray astronomy as a fundamental field of astrophysics. Today, the emission from astrophysical sources is by large best known at energies below 10 keV. The main reason for this situation is purely technical since grazing incidence reflection has so far been limited to the soft X-ray band. Above 10 keV all the observations have been obtained with collimated detectors or coded mask instruments. To make a leap step forward in Xray astronomy above 10 keV it is necessary to extend the principle of focusing X ray optics to higher energies, up to 80 keV and beyond. To this end, ASI and CNES are presently studying the implementation of a X-ray mission called Simbol-X.Taking advantage of emerging technology in mirror manufacturing and spacecraft formation flying, Simbol-X will push grazing incidence imaging up to ~ 80 keV and beyond, providing a strong improvement both in sensitivity and angular resolution compared to all instruments that have operated so far above 10 keV. This technological breakthrough will open a new highenergy window in astrophysics and cosmology. Here we will address the problematic of the development for such a distributed and deformable instrument. We will focus on the main performances of the telescope, like angular resolution, sensitivity and source localization. We will also describe the specificity of the calibration aspects of the payload distributed over two satellites and therefore in a not "frozen" configuration.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simbol-X: a formation flight mission with an unprecedented imaging capability in the 0.5-80 keV energy band

Tagliaferri

Ferrando

Duigou

et al. 2017

International Conference on Space Optics — ICSO 2008

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Deriving Finite Sphere Packings

Arkus¹,

Manoharan²,

Brenner³

2011

SIAM J. Discrete Math.

120

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Abstract. Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for deriving all packings of n spheres in R 3 satisfying minimal rigidity constraints (≥ 3 contacts per sphere and ≥ 3n − 6 total contacts). We derive such packings for n ≤ 10, and provide a preliminary set of maximum contact packings for 10 < n ≤ 20. The resultant set of packings has some striking features, among them: (i) all minimally-rigid packings for n ≤ 9 have exactly 3n − 6 contacts, (ii) non-rigid packings satisfying minimal rigidity constraints arise for n ≥ 9, (iii) the number of ground states (i.e. packings with the maximum number of contacts) oscillates with respect to n, (iv) for 10 ≤ n ≤ 20 there are only a small number of packings with the maximum number of contacts, and for 10 ≤ n < 13 these are all commensurate with the HCP lattice. The general method presented here may have applications to other related problems in mathematics, such as the Erdös repeated distance problem and Euclidean distance matrix completion problems.

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On Lagrangian Relaxation of Quadratic Matrix Constraints

Anstreicher¹,

Wolkowicz²

2000

SIAM J. Matrix Anal. & Appl.

108

107

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Abstract. Quadratically constrained quadratic programs (QQPs) play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Lagrangian relaxations often provide good approximate solutions to these hard problems. Such relaxations are equivalent to semidefinite programming relaxations.For several special cases of QQP, e.g., convex programs and trust region subproblems, the Lagrangian relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper we consider a certain QQP where the quadratic constraints correspond to the matrix orthogonality condition XX T = I. For this problem we show that the Lagrangian dual based on relaxing the constraints XX T = I and the seemingly redundant constraints X T X = I has a zero duality gap. This result has natural applications to quadratic assignment and graph partitioning problems, as well as the problem of minimizing the weighted sum of the largest eigenvalues of a matrix. We also show that the technique of relaxing quadratic matrix constraints can be used to obtain a strengthened semidefinite relaxation for the max-cut problem.Key words. Lagrangian relaxations, quadratically constrained quadratic programs, semidefinite programming, quadratic assignment, graph partitioning, max-cut problems AMS subject classifications. 49M40, 52A41, 90C20, 90C27 PII. S0895479898340299 1. Introduction. Quadratically constrained quadratic programs (QQPs) play an important modeling role for many diverse problems. They often provide a much improved model compared to the simpler linear relaxation of a problem. However, very large linear models can be solved efficiently, whereas QQPs are in general NP-hard and numerically intractable. Lagrangian relaxations often provide good approximate solutions to these hard problems. Moreover these relaxations can be shown to be equivalent to semidefinite programming (SDP) relaxations, and SDP problems can be solved efficiently, i.e., they are polynomial time problems; see, e.g., [31].SDP relaxations provide a tractable approach for finding good bounds for many hard combinatorial problems. The best example is the application of SDP to the max-cut problem, where a 87% performance guarantee exists [11,12]. Other examples include matrix completion problems [23,22], as well as graph partitioning problems and the quadratic assignment problem (references given below).In this paper we consider several quadratically constrained quadratic (nonconvex) programs arising from hard combinatorial problems. In particular, we look at the orthogonal relaxations of the quadratic assignment and graph partitioning problems. We show that the resulting well-known eigenvalue bounds for these problems can be obtained from the Lagrangian dual of the orthogonally constrained relaxations,

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Cited by 6 publications

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Simbol-X: a formation flight mission with an unprecedented imaging capability in the 0.5-80 keV energy band

Simbol-X: a formation flight mission with an unprecedented imaging capability in the 0.5-80 keV energy band

Deriving Finite Sphere Packings

On Lagrangian Relaxation of Quadratic Matrix Constraints

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