Extension of the sun-synchronous Orbit

Through careful consideration of the orbit perturbation force due to the oblate nature of the primary body a secular variation of the ascending node angle of a near-polar orbit can be induced without expulsion of propellant. Resultantly, the orbit perturbations can be used to maintain the orbit plane in, for example, a near-perpendicular (or at any other angle) alignment to the Sun-line throughout the full year of the primary body; such orbits are normally termed Sun-synchronous orbits [1, 2]. Sun-synchronous orbits about the Earth are typically near-circular Low-Earth Orbits (LEOs), with an altitude of less than 1500 km. It is normal to design a LEO such that the orbit period is synchronised with the rotation of the Earth‟s surface over a given period, such that a repeating ground-track is established. A repeating ground-track, together with the near-constant illumination conditions of the ground-track when observed from a Sun-synchronous orbit, enables repeat observations of a target over an extended period under similar illumination conditions [1, 2]. For this reason, Sun-synchronous orbits are extensively used by Earth Observation (EO) platforms, including currently the Environmental Satellite (ENVISAT), the second European Remote Sensing satellite (ERS-2) and many more. By definition, a given Sun-synchronous orbit is a finite resource similar to a geostationary orbit. A typical characterising parameter of a Sun-synchronous orbit is the Mean Local Solar Time (MLST) at descending node, with a value of 1030 hours typical. Note that ERS-1 and ERS-2 used a MLST at descending node of 1030 hours ± 5 minutes, while ENVISAT uses a 1000 hours ± 5 minutes MLST at descending node [3]. Following selection of the MLST at descending node and for a given desired repeat ground-track, the orbit period and hence the semi-major axis are fixed, thereafter assuming a circular orbit is desired it is found that only a single orbit inclination will enable a Sun-synchronous orbit [2]. As such, only a few spacecraft can populate a given repeat ground-track Sun-synchronous orbit without compromise, for example on the MLST at descending node. Indeed a notable feature of on-going studies by the ENVISAT Post launch Support Office is the desire to ensure sufficient propellant remains at end-of-mission for re-orbiting to a graveyard orbit to ensure the orbital slot is available for future missions [4]. An extension to the Sun-synchronous orbit is considered using an undefined, non-orientation constrained, low-thrust propulsion system. Initially the low-thrust propulsion system will be considered for the free selection of orbit inclination and altitude while maintaining the Sun-synchronous condition. Subsequently the maintenance of a given Sun-synchronous repeat-ground track will be considered, using the low-thrust propulsion system to enable the free selection of orbit altitude. An analytical expression will be developed to describe these extensions prior to then validating the analytical expressions within a numerical simulation of a spacecraft orbit. Finally, an analysis will be presented on transfer and injection trajectories to these orbits

Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables

[EN] Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A completely multiplicative sequence (b(n)) of complex numbers is said to be an l(1)-multiplier for H-infinity whenever Sigma(n vertical bar)a(n)b(n vertical bar) < infinity for every D is an element of H-infinity. We study the problem of describing such sequences (b(n)) in terms of the asymptotic decay of the subsequence (b(pj)), where p(j) denotes the j th prime number. Given a completely multiplicative sequence b = (b(n)) we prove (among other results): b is an l(1)-multiplier for H-infinity provided vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) < 1, and conversely, if b is an l(1)-multiplier for H-infinity, then vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) <= 1 (here b* stands for the decreasing rearrangement of b). Following an ingenious idea of Harald Bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk D-infinity (the open unit ball of l(infinity)) for which every bounded and holomorphic function f on D-infinity has an absolutely convergent monomial series expansion Sigma(alpha) partial derivative alpha f (0)/alpha! z alpha. Moreover, we study analogous problems in Hardy spaces of Dirichlet series and Hardy spaces of functions on the infinite dimensional polytorus T-infinity.The second, fourth and fifth authors were supported by MINECO and FEDER Project MTM2014-57838-C2-2-P. The fourth author was also supported by PrometeoII/2013/013. The fifth author was also supported by project SP-UPV20120700.Bayart, F.; Defant, A.; Frerick, L.; Maestre, M.; Sevilla Peris, P. (2017). Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables. Mathematische Annalen. 368(1-2):837-876. https://doi.org/10.1007/s00208-016-1511-1S8378763681-2Aleman, A., Olsen, J.-F., Saksman, E.: Fatou and brother Riesz theorems in the infinite-dimensional polydisc. arXiv:1512.01509Balasubramanian, R., Calado, B., Queffélec, H.: The Bohr inequality for ordinary Dirichlet series. Studia Math. 175(3), 285–304 (2006)Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Monatsh. Math. 136(3), 203–236 (2002)Bayart, F., Pellegrino, D., Seoane-Sepúlveda, J.B.: The Bohr radius of the $$n$$ n -dimensional polydisk is equivalent to $$\sqrt{(\log n)/n}$$ ( log n ) / n . Adv. Math. 264:726–746 (2014)Bohnenblust, H.F., Hille, E.: On the absolute convergence of Dirichlet series. Ann. Math. 32(3), 600–622 (1931)Bohr, H.: Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichlet–schen Reihen $$\sum \,\frac{a_n}{n^s}$$ ∑ a n n s . Nachr. Ges. Wiss. Göttingen, Math. Phys. Kl. 441–488 (1913)Bohr, H.: Über die gleichmäßige Konvergenz Dirichletscher Reihen. J. Reine Angew. Math. 143, 203–211 (1913)Cole, B.J., Gamelin., T.W.: Representing measures and Hardy spaces for the infinite polydisk algebra. Proc. Lond. Math. Soc. 53(1), 112–142 (1986)Davie, A.M., Gamelin, T.W.: A theorem on polynomial-star approximation. Proc. Am. Math. Soc. 106(2), 351–356 (1989)de la Bretèche, R.: Sur l’ordre de grandeur des polynômes de Dirichlet. Acta Arith. 134(2), 141–148 (2008)Defant, A., Frerick, L., Ortega-Cerdà, J., Ounaïes, M., Seip, K.: The Bohnenblust–Hille inequality for homogeneous polynomials is hypercontractive. Ann. Math. 174(1), 485–497 (2011)Defant, A., García, D., Maestre, M.: New strips of convergence for Dirichlet series. Publ. Mat. 54(2), 369–388 (2010)Defant, A., García, D., Maestre, M., Pérez-García, D.: Bohr’s strip for vector valued Dirichlet series. Math. Ann. 342(3), 533–555 (2008)Defant, A., Maestre, M., Prengel, C.: Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables. J. Reine Angew. Math. 634, 13–49 (2009)Dineen, S.: Complex Analysis on Infinite-dimensional Spaces. Springer Monographs in Mathematics. Springer-Verlag London Ltd, London (1999)Floret, K.: Natural norms on symmetric tensor products of normed spaces. Note Mat. 17(153–188), 1997 (1999)Harris, L. A.: Bounds on the derivatives of holomorphic functions of vectors. In: Analyse fonctionnelle et applications (Comptes Rendus Colloq. Analyse, Inst. Mat., Univ. Federal Rio de Janeiro, Rio de Janeiro, 1972), pp. 145–163. Actualités Aci. Indust., No. 1367. Hermann, Paris (1975)Hedenmalm, H., Lindqvist, P., Seip, K.: A Hilbert space of Dirichlet series and systems of dilated functions in $$L^2(0,1)$$ L 2 ( 0 , 1 ) . Duke Math. J. 86(1), 1–37 (1997)Helson, H., Lowdenslager, D.: Prediction theory and Fourier series in several variables. Acta Math. 99, 165–202 (1958)Hibert, D.: Gesammelte Abhandlungen (Band 3). Verlag von Julius Springer, Berlin (1935)Hilbert, D.: Wesen und Ziele einer Analysis der unendlichvielen unabhängigen Variablen. Rend. del Circolo Mat. di Palermo 27, 59–74 (1909)Kahane, J.-P.: Some Random Series of Functions, Volume 5 of Cambridge Studies in Advanced Mathematics, second edn. Cambridge University Press, Cambridge (1985)Konyagin, S.V., Queffélec, H.: The translation $$\frac{1}{2}$$ 1 2 in the theory of Dirichlet series. Real Anal. Exchange 27(1):155–175 (2001/2002)Maurizi, B., Queffélec, H.: Some remarks on the algebra of bounded Dirichlet series. J. Fourier Anal. Appl. 16(5), 676–692 (2010)Queffélec, H.: H. Bohr’s vision of ordinary Dirichlet series; old and new results. J. Anal. 3, 43–60 (1995)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet Series. HRI Lecture Notes Series, New Delhi (2013)Rudin, W.: Function Theory in Polydisks. W. A. Benjamin Inc, New York (1969)Toeplitz, O.: Über eine bei den Dirichletschen Reihen auftretende Aufgabe aus der Theorie der Potenzreihen von unendlichvielen Veränderlichen. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, pp. 417–432 (1913)Weissler, F.B.: Logarithmic Sobolev inequalities and hypercontractive estimates on the circle. J. Funct. Anal. 37(2), 218–234 (1980)Wojtaszczyk, P.: Banach Spaces for Analysts, Volume 25 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1991

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915

Harpgophytum procumbens for osteoarthritis and low back pain: A systematic review

BACKGROUND: The objective of this review is to determine the effectiveness of Harpagophytum procumbens preparations in the treatment of various forms of musculoskeletal pain. METHODS: Several databases and other sources were searched to identify randomized controlled trials, quasi-randomized controlled trials, and controlled clinical trials testing Harpagophytum preparations in adults suffering from pain due to osteoarthritis or low back pain. RESULTS: Given the clinical heterogeneity and insufficient data for statistical pooling, trials were described in a narrative way, taking into consideration methodological quality scores. Twelve trials were included with six investigating osteoarthritis (two were identical trials), four low back pain, and three mixed-pain conditions. CONCLUSIONS: There is limited evidence for an ethanolic Harpagophytum extract containing less than <30 mg harpagoside per day in the treatment of knee and hip osteoarthritis. There is moderate evidence of effectiveness for (1) the use of a Harpagophytum powder at 60 mg harpagoside in the treatment of osteoarthritis of the spine, hip and knee; (2) the use of an aqueous Harpagophytum extract at a daily dose of 100 mg harpagoside in the treatment of acute exacerbations of chronic non-specific low back pain; and (3) the use of an aqueous extract of Harpagophytum procumbens at 60 mg harpagoside being non-inferior to 12.5 mg rofecoxib per day for chronic non-specific low-back pain (NSLBP) in the short term. Strong evidence exists for the use of an aqueous Harpagophytum extract at a daily dose equivalent of 50 mg harpagoside in the treatment of acute exacerbations of chronic NSLBP

Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. This result is extended to complex Frechet spaces with a continuous norm and an unconditional Schauder decomposition, and also to complex Frechet spaces with an unconditional basis, which gives a partial positive answer to a problem posed by Bonet. We also solve a problem of Bes and Chan in the negative by presenting hypercyclic, but non-chaotic operators on \mathbb{C}^\mathbb{N}. We extend the main result to C_0-semigroups of operators. Finally, in contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator.This work was partially supported by ANR-Projet Blanc DYNOP, by the MEC and FEDER Projects MTM2007-64222 and MTM2010-14909, and by Generalitat Valenciana Project PROMETEO/2008/101.De La Rosa Penilla, M.; Frerick, L.; Grivaux, S.; Peris Manguillot, A. (2012). Frequent hypercyclicity, chaos, and unconditional Schauder decompositions. Israel Journal of Mathematics. 190(1):389-399. https://doi.org/10.1007/s11856-011-0210-6S3893991901S. Ansari, Existence of hypercyclic operators on topological vector spaces, Journal of Functional Analysis 148 (1997), 384–390.F. Bayart and S. Grivaux, Frequently hypercyclic operators, Transactions of the American Mathematical Society 358 (2006), 5083–5117.F. Bayart and S. Grivaux, Hypercyclicity and unimodular point spectrum, Journal of Functional Analysis 226 (2005), 281–300.F. Bayart and S. Grivaux, Invariant Gaussian measures for linear operators on Banach spaces and linear dynamics, Proceedings of the London Mathematical Society 94 (2007), 181–210.F. Bayart and É. Matheron, Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009.L. Bernal-González, On hypercyclic operators on Banach spaces, Proceedings of the American Mathematical Society 127 (1999), 1003–1010.J. Bès and A. Peris, Hereditarily hypercyclic operators, Journal of Functioanl Analysis 167 (1999), 94–112.J. Bonet, F. Martínez-Giménez and A. Peris, A Banach space wich admits no chaotic operator, The Bulletin of the London Mathematical Society 33 (2001), 196–198.M. De la Rosa, L. Frerick, S. Grivaux and A. Peris, Chaos on Fréchet spaces with unconditional basis, preprint.W. T. Gowers, A solution to Banach’s hyperplane problem, The Bulletin of the London Mathematical Society 26 (1994), 523–530.W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, Mathematische Annalen 307 (1997), 543–568.W. T. Gowers and B. Maurey, The unconditional basic sequence problem, Journal of the American Mathematical Society 6 (1993), 851–874.S. Grivaux, A new class of frequently hypercyclic operators, Indiana University Mathematics Journal, to appear.K. G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer-Verlag, Berlin, 2011.K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs, New Series, Vol. 20, Clarendon Press, Oxford, 2000.S. Shkarin, On the spectrum of frequently hypercyclic operators, Proceedings of the American Mathematical Society 137 (2009), 123–134

A systematic review on the effectiveness of complementary and alternative medicine for chronic non-specific low-back pain

The purpose of this systematic review was to assess the effects of spinal manipulative therapy (SMT), acupuncture and herbal medicine for chronic non-specific LBP. A comprehensive search was conducted by an experienced librarian from the Cochrane Back Review Group (CBRG) in multiple databases up to December 22, 2008. Randomised controlled trials (RCTs) of adults with chronic non-specific LBP, which evaluated at least one clinically relevant, patient-centred outcome measure were included. Two authors working independently from one another assessed the risk of bias using the criteria recommended by the CBRG and extracted the data. The data were pooled when clinically homogeneous and statistically possible or were otherwise qualitatively described. GRADE was used to determine the quality of the evidence. In total, 35 RCTs (8 SMT, 20 acupuncture, 7 herbal medicine), which examined 8,298 patients, fulfilled the inclusion criteria. Approximately half of these (2 SMT, 8 acupuncture, 7 herbal medicine) were thought to have a low risk of bias. In general, the pooled effects for the studied interventions demonstrated short-term relief or improvement only. The lack of studies with a low-risk of bias, especially in regard to SMT precludes any strong conclusions; however, the principal findings, which are based upon low- to very-low-quality evidence, suggest that SMT does not provide a more clinically beneficial effect compared with sham, passive modalities or any other intervention for treatment of chronic low-back pain. There is evidence, however, that acupuncture provides a short-term clinically relevant effect when compared with a waiting list control or when acupuncture is added to another intervention. Although there are some good results for individual herbal medicines in short-term individual trials, the lack of homogeneity across studies did not allow for a pooled estimate of the effect. In general, these results are in agreement with other recent systematic reviews on SMT, but in contrast with others. These results are also in agreement with recent reviews on acupuncture and herbal medicine. Randomized trials with a low risk of bias and adequate sample sizes are direly needed

SCIAMACHY Polarisation Sensitivity

In this paper we use the Mueller Matrix formalism to describe the transfer of polarised radiation through the SCIAMACHY instrument. Several features of the polarisation sensitivity are highlighted; in particular the so-called polarisation phase shift which introduces strong features in SCIAMACHY''s 315-400 nm channel