Geometric Solution to the Angles-Only Initial Orbit Determination Problem

Initial orbit determination (IOD) from line-of-sight (i.e., bearing) measurements is a classical problem in astrodynamics. Indeed, there are many well-established methods for performing the IOD task when given three line-of-sight observations at known times. Interestingly, and in contrast to these existing methods, concepts from algebraic geometry may be used to produce a purely geometric solution. This idea is based on the fact that bearings from observers in general position may be used to directly recover the shape and orientation of a three-dimensional conic (e.g., a Keplerian orbit) without any need for knowledge of time. In general, it is shown that five bearings at unknown times are sufficient to recover the orbit -- without the use of any type of initial guess and without the need to propagate the orbit. Three bearings are sufficient for purely geometric IOD if the orbit is known to be (approximately) circular. The method has been tested over different scenarios, including one where extra observations make the system of equations over-determined.Comment: 31 pages excluding back matter, 14 figure

Identities for hyperelliptic P-functions of genus one, two and three in covariant form

We give a covariant treatment of the quadratic differential identities satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of genera 1, 2 and 3

Nonlinear dynamics of wind waves: multifractal phase/time effects

International audienceIn addition to the bispectral coherence method, phase/time analysis of analytic signals is another promising avenue for the investigation of phase effects in wind waves. Frequency spectra of phase fluctuations obtained from both sea and laboratory experiments follow an F-? power law over several decades, suggesting that a fractal description is appropriate. However, many similar natural phenomena have been shown to be multifractal. Universal multifractals are quantified by two additional parameters: the Lévy index 0 ? 2 for the type of multifractal and the co-dimension 0 C1 1 for intermittence. The three parameters are a full statistical measure the nonlinear dynamics. Analysis of laboratory flume data is reported here and the results indicate that the phase fluctuations are 'hard multifractal' (? > 1). The actual estimate is close to the limiting value ? = 2, which is consistent with Kolmogorov's lognormal model for turbulent fluctuations. Implications for radar and sonar backscattering from the sea surface are briefly considered

Punctual Hilbert Schemes and Certified Approximate Singularities

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots, x\_n]^N$, we present a Newton iteration on an extended deflated system that locally converges, under regularity conditions, to a small deformation of $f$ such that this deformed system has an exact singular root. The iteration simultaneously converges to the coordinates of the singular root and the coefficients of the so called inverse system that describes the multiplicity structure at the root. We use $$\alpha$$-theory test to certify the quadratic convergence, and togive bounds on the size of the deformation and on the approximation error. The approach relies on an analysis of the punctual Hilbert scheme, for which we provide a new description. We show in particular that some of its strata can be rationally parametrized and exploit these parametrizations in the certification. We show in numerical experimentation how the approximate inverse system can be computed as a starting point of the Newton iterations and the fast numerical convergence to the singular root with its multiplicity structure, certified by our criteria.Comment: International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Franc

Asymmetry of wind waves studied in a laboratory tank

International audienceAsymmetry of wind waves was studied in laboratory tank tinder varied wind and fetch conditions using both bispectral analysis of wave records and third-order statistics of the surface elevation. It is found skewness S (the normalized third-order moment of surface elevation describing the horizontal asymmetry waves) varies only slightly with the inverse wave u*/Cm (where u* is the air friction velocity and Cm is phase speed of the dominant waves). At the same time asymmetry A, which is determined from the Hilbert transform of the wave record and characterizes the skewness of the rate of change of surface elevation, increase consistently in magnitude with the ratio u*/Cm. This suggests that nonlinear distortion of the wave profile determined by the degree of wind forcing and is a sensitive indicator of wind-wave interaction processes. It is shown that the asymmetric profile of waves can described within the frameworks of the nonlinear nonspectral concept (Plate, 1972; Lake and Yuen, 197 according to which the wind-wave field can be represented as a coherent bound-wave system consisting mainly of dominant component w. and its harmonics propagating with the same speed C. , as observed by Ramamonjiaris and Coantic (1976). The phase shift between o). harmonics is found and shown to increase with the asymmetry of the waves

Sufentanil sublingual tablet system. From rationale of use to clinical practice

The control of post-operative pain in Italy and other western countries is still suboptimal. In recent years, the Sufentanil Sublingual Tablet System (SSTS; Zalviso; AcelRx Pharmaceuticals, Redwood City, CA, USA), which is designed for patient-controlled analgesia (PCA), has entered clinical practice. SSTS enables patients to manage moderate-to-severe acute pain during the first 72 postoperative hours directly in the hospital setting. However, the role of SSTS within the current framework of options for the management of post-operative pain needs to be better established. This paper presents the position on the use of SSTS of a multidisciplinary group of Italian Experts and provides protocols for the use of this device

Quantum discrete Dubrovin equations

The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the lattice at a constant time-level) evolutions are considered. In the classical limit, the temporal equations reduce to the (classical) discrete Dubrovin equations as given in a previous publication. The reconstruction of the original dynamical variables in terms of the Sklyanin variables is also achieved.Comment: 25 page

РАЗРАБОТКА КОМПЛЕКСА МАСС-СПЕКТРОМЕТРИЧЕСКИХ С ИНДУКТИВНО СВЯЗАННОЙ ПЛАЗМОЙ МЕТОДИК ОПРЕДЕЛЕНИЯ СОДЕРЖАНИЯ ИЗОТОПА ТЕХНЕЦИЙ-99 В УРАНОВЫХ МАТЕРИАЛАХ

The methods for the quantitative determination of technetium isotope (99Tc) in uranium materials based on inductively coupled plasma mass-spectrometry are described. The results of the investigation of uranium matrix effect on the analytical signal of 99Tc for two mass-spectrometer models are presented. Different approaches for the quantification of 99Tc in uranium materials are investigated including direct analysis and analysis with preliminary uranium separation. The methods for the quantification of 99Tc consisting of chromatographic separation of uranium and 99Tc using UTEVA and TEVA resins with consequent ICP-MS detection were developed. The detection limits of the developed methods are within the range of 0.0006 to 0.02 ng/g U. The choice of optimum conditions for quantitative determination of 99Tc by direct ICP-MS analysis allowed avoiding «tough» ICP-MS operating conditions which consist in high forward power equal to 1600 W. The developed methods require much less time and effort compared to radiometry methods. The introduction of the developed methods allow improving the existing standards for the quality control of the uranium materials in nuclear industry.Keywords: Inductively coupled plasma mass-spectrometry, technetium isotope, uranium fluorides, uranium oxides, chromatographic separation(Russian)DOI: http://dx.doi.org/10.15826/analitika.2013.17.4.005S.L. Ivanov1, N.V. Kuzmina1, A.Yu. Leykin2, A.V. Prosviryakova1, A.V. Saprygin1,3 1Open Joint Stock Company «Ural Electochemical Integrated Plant (JSC «UEIP»), Novouralsk, Russian Federation2Moscow representative office INTERTECH Corporation, Moscow, Russian Federation3FSAEI HPE «Ural Federal University named after the first President of Russia B.N. Yeltsin», Ekaterinburg, Russian FederationОписан комплекс методик определения содержания изотопа технеций-99 (99Тс) в урановых материалах, основанный на методе масс-спектрометрии с индуктивно связанной плазмой. Приведены результаты исследования матричного влияния урана на аналитический сигнал 99Тс для двух моделей масс-спектрометров. Исследованы возможности метода для определения содержания 99Тс в различных вариантах: с предварительным отделением урана и прямого анализа. Разработанные масс-спектрометрические методики, основанные на экстракционно-хроматографическом разделении урана и 99Тс на смолах UTEVA и TEVA (Eichrom Technologies), отличаются низкими пределами обнаружения (0.0006-0.02 нг/г). Предлагаемые условия прямого масс-спектрометрического определения содержания 99Тс позволяют отказаться от «жестких» условий работы масс-спектрометров, требующих установления высокой мощности высокочастотного генератора (1600 Вт). Основными достоинствами разработанного комплекса являются значительное сокращение длительности и трудоемкости выполнения анализа по сравнению с радиометрическими методиками. Внедрение разработанных методик позволит усовершенствовать комплекс методик, используемых в системе контроля качества урановых материалов, действующих на предприятиях атомной отрасли.Ключевые слова:масс-спектрометрия с индуктивно связанной плазмой, изотоп технеций-99, фториды урана, оксиды урана, экстракционно-хроматографическое разделениеDOI: http://dx.doi.org/10.15826/analitika.2013.17.4.00

Abelian functions associated with a cyclic tetragonal curve of genus six

We develop the theory of Abelian functions defined using a tetragonal curve of genus six, discussing in detail the cyclic curve y^4 = x^5 + λ[4]x^4 + λ[3]x^3 + λ[2]x^2 + λ[1]x + λ[0]. We construct Abelian functions using the multivariate sigma-function associated with the curve, generalizing the theory of theWeierstrass℘-function. We demonstrate that such functions can give a solution to the KP-equation, outlining how a general class of solutions could be generated using a wider class of curves. We also present the associated partial differential equations satisfied by the functions, the solution of the Jacobi inversion problem, a power series expansion for σ(u) and a new addition formula

Using online adverts to increase the uptake of cervical screening amongst "real Eastenders": an opportunistic controlled trial.

BACKGROUND: Cervical screening uptake has increased as a result of occurrences of cervical cancer in TV 'soap operas' and in real life celebrities such as Jade Goody. Media analysis at the time of Jade Goody's death suggested the NHS did not take sufficient advantage of this opportunity to improve cervical screening rates. Google AdWords has been used to recruit and raise awareness of health but we were not aware of its use to supplement media events. METHODS: This was an opportunistic service evaluation to accompany a cervical cancer storyline in Eastenders (a TV 'soap opera'). We ran an AdWords campaign based on keywords such as 'Eastenders', and 'cervical cancer' in a one mile radius in East London, linked to one webpage giving details of 10 practices and other links on cervical cancer. We recorded costs of adverts and setting up the webpage. We used routine statistics from Tower Hamlets, City and Hackney, and Newham Primary Care Trusts (PCTs) of the number of smears, eligible populations, and coverage by practice by month from September 2010 to January 2012 to compare the ten intervention practices with controls. RESULTS: Eight people per day in the target area viewed the project webpage. The cost of setting up the website and running Google AdWords was £1320 or £1.88 per person viewing the webpage. Unlike Jade Goody's death, there was no major impact from the Eastenders' storyline on Google searches for cervical cancer. There was considerable monthly variation in the number of smear tests in the 3 PCTs. The AdWords campaign may have had some effect on smear rates but this showed, at best, a marginal statistical difference. Assuming a 'real' effect, the intervention may have resulted in 110 'extra' women being screened but there was no change in coverage. CONCLUSIONS: Although the Eastenders storyline seemed to have no effect on interest in cervical cancer or screening, the AdWords campaign may have had some effect. Given the small scale exploratory nature of the study this was not statistically significant but the relatively modest cost of advertising suggests a larger study may be worthwhile. An outline of a possible study is described