Bochner's theorem: Difference between revisions

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{{Starbox begin
Emilia Shryock is my name but you can contact me anything you like. South Dakota is where me and my husband reside. To gather cash is what her family members and her appreciate. Bookkeeping is my occupation.<br><br>Here is my weblog; [http://www.lankaclipstv.com/user/SFergerso home std test kit]
| name=Delta Ophiuchi
}}
{{Starbox image
| image =
    <div style="position: relative">[[File:Ophiuchus IAU.svg|250px|alt=Diagram showing star positions and boundaries of the Ophiuchus constellation and its surroundings]]
    <div style="position: absolute; left: 79.7%; top: 36.6%;">[[File:Cercle rouge 100%.svg|12px]]</div>
    </div>
| caption=Location of δ Ophiuchi (circled)
}}
{{Starbox observe
| epoch    = J2000
| ra      = {{RA|16|14|20.73853}}<ref name=aaa474_2_653/>
| dec      = {{DEC|–03|41|39.5612}}<ref name=aaa474_2_653/>
| appmag_v = 2.75<ref name=clpl4_99/>
| constell = [[Ophiuchus]]
}}
{{Starbox character
| class    = M0.5&nbsp;III<ref name=araa11_29/>
| b-v      = +1.59<ref name=clpl4_99/>
| u-b      = +1.96<ref name=clpl4_99/>
| variable = Suspected<ref name=ibvs3791_1/>
}}
{{Starbox astrometry
| radial_v = –19.9<ref name=gcsrv/>
| prop_mo_ra  = –47.54<ref name=aaa474_2_653/>
| prop_mo_dec = –142.73<ref name=aaa474_2_653/>
| parallax = 19.06
| p_error  = 0.16
| parallax_footnote = <ref name=aaa474_2_653/>
| absmag_v = –0.90<ref name=an319_6_375/><!-- Av = 0.04 -->
}}
{{Starbox detail
| mass    = 1.5<ref name=tsuji2007/>
| radius  = 59<ref name=lang2006/>
| luminosity  =
| temperature = 3,679<ref name=aaa61_1_17/>
| metal_fe = 0.32<ref name=aaa61_1_17/>
| rotation =
| rotational_velocity = 7.0<ref name=aj135_1_209/>
| gravity  = 1.4<ref name=aaa61_1_17/>
| age      =
}}
{{Starbox catalog
| names = 1 Oph, [[Bonner Durchmusterung|BD]]-03 3903, [[Fifth Fundamental Catalogue|FK5]] 603, [[Henry Draper catalogue|HD]] 146051, [[Hipparcos catalogue|HIP]] 79593, [[Harvard Revised catalogue|HR]] 6056, [[Smithsonian Astrophysical Observatory|SAO]] 141052.<ref name=simbad/>
}}
{{Starbox end}}
 
'''Delta Ophiuchi''' (δ Oph, δ Ophiuchi) is a [[star]] in the [[constellation]] [[Ophiuchus]]. It has the traditional name '''Yed Prior'''. The star [[Epsilon Ophiuchi]], with which it forms a [[naked eye]] [[double star|optical double]], is ''Yed Posterior''. The [[apparent visual magnitude]] is 2.75,<ref name=clpl4_99/> making this a third-magnitude star and the [[List of stars in Ophiuchus|fourth brightest]] in the constellation. [[Parallax]] measurements from the [[Hipparcos]] spacecraft yield a distance estimate of around {{Convert|171|ly|pc|abbr=off|lk=on}} from [[Earth]].<ref name=aaa474_2_653/>
 
==Properties==
Delta Ophiuchi is 170 [[light year]]s from [[Earth]], while Epsilon is 108; hence they are a mere optical double. This star has a [[stellar classification]] of M0.5&nbsp;III,<ref name=araa11_29/> making this a [[red giant]] star that has undergone expansion of its outer envelope after exhausting the supply of hydrogen at its core. The measured [[angular diameter]] of this star, after correction for [[limb darkening]], is {{nowrap|10.47 ± 0.12 [[milliarcsecond|mas]]}}.<ref name=aaa431_773/> At the estimated distance of Delta Ophiuchi,<ref name=aaa474_2_653/> this yields a physical size of about 59 times the [[Solar radius|radius of the Sun]].<ref name=lang2006/> In spite of its enlarged size, this star has only 1.5 times the mass of the Sun and hence a much lower density.<ref name=tsuji2007/> The [[effective temperature]] of the outer atmosphere of Delta Ophiuchi is a relatively cool 3,679&nbsp;K,<ref name=aaa61_1_17/> which is what gives it the orange-red hue of an M-type star.<ref name=csiro/>
 
Yed Prior is listed as a suspected [[variable star]] that may change by 0.03 in visual magnitude.<ref name=ibvs3791_1/><ref name=simbad/> It has a low [[projected rotational velocity]] of {{nowrap|7.0 km s<sup>–1</sup>}}, which gives a minimum value for the [[azimuth]]al velocity along the star's equator.<ref name=aj135_1_209/> The abundance of elements other than hydrogen and helium, what astronomers term the star's [[metallicity]], is more than double the abundance in the Sun's photosphere.<ref name=aaa61_1_17/>
 
==Etymology==
The traditional name Yed is derived from [[Arabic language|Arabic]] meaning "the hand", and the two stars are the left hand of Ophiuchus (the Serpent Bearer) that holds the head of the serpent [[Serpens Caput]].
 
It was a member of the indigenous Arabic [[Asterism (astronomy)|asterism]] ''al-Nasaq al-Yamānī'', the "Southern Line" of ''al-Nasaqān'' the "Two Lines",<ref name=kunitzsch_smart2006/> along with [[Alpha Serpentis|α Ser]] (Unukalhai), [[Delta Serpentis|δ Ser]] (Qin, Tsin), [[Epsilon Serpentis|ε Ser]] (Ba, Pa),  [[Epsilon Ophiuchi|ε Oph]] (Yed Posterior), [[Zeta Ophiuchi|ζ Oph]] (Han) and [[Gamma Ophiuchi|γ Oph]] (Tsung Ching).<ref name=allen1963/>
 
According to the catalogue of stars in the ''Technical Memorandum 33-507 - A Reduced Star Catalog Containing 537 Named Stars'', ''al-Nasaq al-Yamānī'' or ''Nasak Yamani'' were the titles for two stars :[[Delta Serpentis|δ Ser]] as ''Nasak Yamani I'' and [[Epsilon Serpentis|ε Ser]] as ''Nasak Yamani II'' (exclude this star, [[Alpha Serpentis|α Ser]], [[Epsilon Ophiuchi|ε Oph]], [[Zeta Ophiuchi|ζ Oph]] and [[Gamma Ophiuchi|γ Oph]]{{Clarify|date=November 2013|Reason=Garbled phrasing conceals all meaning. What is this list doing here?}} ).<ref name=rhoads1971/>
 
In [[Chinese language|Chinese]], {{lang|zh|天市右垣}} ({{lang|zh-Latn|Tiān Shì Yòu Yuán}}), meaning ''[[Heavenly Market enclosure|Right Wall of Heavenly Market Enclosure]]'', refers to an asterism which is represent eleven old states in China which is marking the right borderline of the enclosure, consisting of δ Ophiuchi, [[Beta Herculis|β Herculis]], [[Gamma Herculis|γ Herculis]], [[Kappa Herculis|κ Herculis]], [[Gamma Serpentis|γ Serpentis]], [[Beta Serpentis|β Serpentis]], [[Alpha Serpentis|α Serpentis]], [[Delta Serpentis|δ Serpentis]], [[Epsilon Serpentis|ε Serpentis]], [[Epsilon Ophiuchi|ε Ophiuchi]] and [[Zeta Ophiuchi|ζ Ophiuchi]].<ref>{{zh icon}} ''中國星座神話'', written by 陳久金. Published by 台灣書房出版有限公司, 2005, ISBN 978-986-7332-25-7.</ref> Consequently, δ Ophiuchi itself is known as {{lang|zh|天市右垣九}} ({{lang|zh-Latn|Tiān Shì Yòu Yuán jiǔ}}, {{lang-en|the Ninth Star of Right Wall of Heavenly Market Enclosure}}), representing the state of '''[[Liang (state)|Liang]]''' (梁) (or ''Leang'').<ref>{{zh icon}} [http://www.lcsd.gov.hk/CE/Museum/Space/Research/StarName/c_research_chinengstars_t_z.htm 香港太空館 - 研究資源 - 亮星中英對照表], Hong Kong Space Museum. Accessed on line November 23, 2010.</ref><ref>{{zh icon}} [http://www.lcsd.gov.hk/CE/Museum/Space/Research/StarName/e_research_chinengstarzone_b.htm#HeavenlyMarketEnclosure English-Chinese Glossary of Chinese Star Regions, Asterisms and Star Name], Hong Kong Space Museum. Accessed on line November 23, 2010.</ref>
 
==References==
{{reflist|refs=
 
<ref name=aaa474_2_653>{{citation | first=F. | last=van Leeuwen |date=November 2007 | title=Validation of the new Hipparcos reduction | journal=Astronomy and Astrophysics | volume=474 | issue=2 | pages=653–664 | bibcode=2007A&A...474..653V | doi=10.1051/0004-6361:20078357 |arxiv = 0708.1752 }}</ref>
 
<ref name=simbad>{{citation | title=del Oph -- Variable Star | work=SIMBAD | publisher=Centre de Données astronomiques de Strasbourg | url=http://simbad.u-strasbg.fr/simbad/sim-basic?Ident=Delta+Ophiuchi | accessdate=2010-07-06 }}</ref>
 
<ref name=gcsrv>{{citation | last=Wilson | first=Ralph Elmer | year=1953 | title=General Catalogue of Stellar Radial Velocities | publisher=Carnegie Institution of Washington | location=Washington | bibcode=1953QB901.W495..... }}</ref>
 
<ref name=aaa61_1_17>{{citation | last=Oinas | first=V. | title=Neutral-ion anomaly in cool stars | journal=Astronomy and Astrophysics | volume=61 | issue=1 | pages=17&ndash;20 |date=October 1977 | bibcode=1977A&A....61...17O }}</ref>
 
<ref name=araa11_29>{{citation | last1=Morgan | first1=W. W. | last2=Keenan | first2=P. C. | title=Spectral Classification | journal=Annual Review of Astronomy and Astrophysics | volume=11 | page=29 | year=1973 | doi=10.1146/annurev.aa.11.090173.000333 | bibcode=1973ARA&A..11...29M }}</ref>
 
<ref name=clpl4_99>{{citation | display-authors=1 | last1=Johnson | first1=H. L. | last2=Iriarte | first2=B. | last3=Mitchell | first3=R. I. | last4=Wisniewskj | first4=W. Z. | title=UBVRIJKL photometry of the bright stars | journal=Communications of the Lunar and Planetary Laboratory | volume=4 | issue=99 | year=1966 | bibcode=1966CoLPL...4...99J }}</ref>
 
<ref name=aj135_1_209>{{citation | display-authors=1 | last1=Massarotti | first1=Alessandro | last2=Latham | first2=David W. | last3=Stefanik | first3=Robert P. | last4=Fogel | first4=Jeffrey | title=Rotational and Radial Velocities for a Sample of 761 HIPPARCOS Giants and the Role of Binarity | journal=The Astronomical Journal | volume=135 | issue=1 | pages=209–231 |date=January 2008 | doi=10.1088/0004-6256/135/1/209 | bibcode=2008AJ....135..209M }}</ref>
 
<ref name=aaa431_773>{{citation | last1=Richichi | pages=A. | last2=Percheron | first2=I. | last3=Khristoforova | first3=M. | title=CHARM2: An updated Catalog of High Angular Resolution Measurements | journal=Astronomy and Astrophysics | volume=431 | pages=773–777 |date=February 2005 | doi=10.1051/0004-6361:20042039 | bibcode=2005A&A...431..773R }}</ref>
 
<ref name=lang2006>{{citation | first1=Kenneth R. | last1=Lang | title=Astrophysical formulae | volume=1 | series=Astronomy and astrophysics library | edition=3 | publisher=Birkhäuser | year=2006 | isbn=3-540-29692-1 | url=http://books.google.com/books?id=OvTjLcQ4MCQC&pg=PA41 }}. The radius (R<sub>*</sub>) is given by:
:<math>\begin{align} 2\cdot R_*
& = \frac{(52.5\cdot 10.47\cdot 10^{-3})\ \text{AU}}{0.0046491\ \text{AU}/R_{\bigodot}} \\
& \approx 118\cdot R_{\bigodot}
\end{align}</math></ref>
 
<ref name=kunitzsch_smart2006>{{citation | last1=Kunitzsch | first1=P. | last2=Smart | first2=T. | year=2006 | title=A Dictionary of Modern Star names: A Short Guide to 254 Star names and Their Derivations | edition=Second Revised | publisher=Sky Publishing | location=Cambridge, MA | isbn=1-931559-44-9 | page=31 }}</ref>
 
<ref name=allen1963>{{citation | last=Allen | first=R. H. | year=1963 | authorlink=Richard Hinckley Allen | title=Star Names: Their Lore and Meaning | url=http://penelope.uchicago.edu/Thayer/E/Gazetteer/Topics/astronomy/_Texts/secondary/ALLSTA/Hercules*.html | accessdate=2010-12-12 | edition=Reprint | publisher=Dover Publications Inc | location=New York, NY | isbn=0-486-21079-0 | page=243 }}</ref>
 
<ref name=rhoads1971>{{citation | url=http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720005197_1972005197.pdf | first1=Jack W. | last1=Rhoads | title=Technical Memorandum 33-507-A Reduced Star Catalog Containing 537 Named Stars | publisher=Jet Propulsion Laboratory, California Institute of Technology | date=November 15, 1971 }}</ref>
 
<ref name=an319_6_375>{{citation | last1=Schmidt-Kaler | first1=T. | last2=Oestreicher | first2=M. O. | title=The luminosity index for M stars and the distance to the LMC | journal=Astronomische Nachrichten | volume=319 | issue=6 | pages=375–386 |date=October 1998 | bibcode=1998AN....319..375S }}</ref>
 
<ref name=tsuji2007>{{citation | last1=Tsuji | first1=Takashi | contribution=Isotopic abundances of Carbon and Oxygen in Oxygen-rich giant stars | title=Convection in Astrophysics, Proceedings of IAU Symposium #239 held 21-25 August, 2006 in Prague, Czech Republic | editor1-first=F. | editor1-last=Kupka | editor2-first=I. | editor2-last=Roxburgh | editor3-first=K. | editor3-last=Chan | pages=307–310 |date=May 2007 | doi=10.1017/S1743921307000622 | bibcode=2007IAUS..239..307T |arxiv = astro-ph/0610180 }}</ref>
 
<ref name=ibvs3791_1>{{citation | last1=Percy | first1=J. R. | last2=Shepherd | first2=C. W. | title=A Photometric Survey of Small-Amplitude Red Variables | journal=Information Bulletin on Variable Stars | volume=3792 | page=1 |date=October 1992 | bibcode=1992IBVS.3792....1P }}</ref>
 
<ref name=csiro>{{citation | title=The Colour of Stars | date=December 21, 2004 | work=Australia Telescope, Outreach and Education | publisher=Commonwealth Scientific and Industrial Research Organisation  | url=http://outreach.atnf.csiro.au/education/senior/astrophysics/photometry_colour.html | accessdate=2012-01-16 }}</ref>
 
}}
 
==External links==
* {{citation | accessdate=2012-02-07 | url=http://stars.astro.illinois.edu/sow/yedprior.html | title=Yed Prior | first1=James B. | last1=Kaler | work=Stars | publisher=University of Illinois }}
 
{{Stars of Ophiuchus}}
 
[[Category:Ophiuchus (constellation)]]
[[Category:Bayer objects|Ophiuchi, Delta]]
[[Category:M-type giants]]
[[Category:Stars with proper names]]

Latest revision as of 22:30, 2 September 2014

Emilia Shryock is my name but you can contact me anything you like. South Dakota is where me and my husband reside. To gather cash is what her family members and her appreciate. Bookkeeping is my occupation.

Here is my weblog; home std test kit