Andromeda Galaxy: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
Newer edit →
 
I changed one number so it would be correct.
Line 1: Line 1:
{{Distinguish|Taurus (disambiguation)}}
== Fa9H3D Jordan 6 World Cup Brazil yyV3h7t4 ==
{{About|the surface and mathematical concept of a torus}}


[[File:Torus.png|thumb|A torus]]
Belle Vernon Area was ready for its WPIAL Class AAA semifinal test against New Castle in the playoffs at the Civic Arena in Pittsburgh. Guided by head coach Don Asmonga and his assistant, George Estok, the Leopards won the Section 3 championship. The squad was comprised of Bill Contza, Tom Parks, Randy Giannini, Greg Grimm, John Russell, Joe Tordy, Mike Breza, Rich Zuraw, Daoug Indoff, Walter Diethorn, Guy Bizzelle, Don Wassilchalk, Mark McManus and Dave Hoffman.<br><br>Under Reagan, unemployment first went up from 7.5 percent figure in January 1981, peaking at 10.8 percent at the end of 1982. In the last two years of his first term, it declined rapidly, reaching 7.2 percent on Election Day 1984. GDP growth in Reagan's first term averaged about 3 percent a year.<br><br>To get tickets for the Inauguration you can contact your local representatives and senators. They are allotted a certain amount of tickets and will distribute them as they wish. Otherwise, the Presidential Inaugural Committee, which is formed after the new president is chosen, handles inaugural galas, balls and the parade, and the itineraries and schedules have not yet been finalized.<br><br>"We need to find solutions," Panetta told his final Pentagon news briefing. "We can't just sit here and bitch; we can't just sit here and complain; we can't just sit here and blame others; we can't just sit here and point fingers at each other; we can't just sit here and try to get sound bytes; we can't just sit here and try to make points, political points."<br><br>A week earlier I had decided [http://www.larad.org/meetss.php??p=42168-cheap-Nike-Free-3.0-V2-Suede-Gray-Black-White-September-Releases-for-sale.html cheap Nike Free 3.0 V2 Suede Gray Black White September Releases for sale] to land an assignment that would give me an excuse to drink on an expense account. St. Patrick's Day was conveniently near enough that I was able to pitch a story this story to the most highly respected and popular magazine on the stands. Unfortunately, right before my pitch meeting I inadvertently exposed myself to a secretary, later being informed that it didn't look very inadvertent to witnesses, and that in fact she was the magazine's publisher. Several phone calls attempting to re spark interest in the story were met with attorney, forcing me to sell it to the makers of the functionally illiterate online offal you're now reading.<br><br>Nissan Motor Co., Ltd., Japan's second largest automotive company, is headquartered in Yokohama, Japan, and is part of [http://www.ti-cmc.org/commitss.php??p=67451-authentic-Nike-Shox-R4-White-Red-clearance-shoes-online.html authentic Nike Shox R4 White Red clearance shoes online] the Renault Nissan Alliance. Operating with more than 248,000 employees globally, Nissan provided customers with more than 4.9 million vehicles in 2012, generating revenue of 9.4 trillion yen ($US118.95 billion) in fiscal 2011. With a strong commitment to developing exciting and innovative products for all, Nissan delivers a comprehensive range of 64 models under the Nissan and Infiniti brands. The heat pump uses minimal power from the battery so it does not drain it's range as the older electric heater.<br><br>Social experimentation, which began in the 1920 facilitates the adoption of new forms of social organization and optimal management. Social experiments thus perform a cognitive function and fall within the sphere of social management. A social experiment must take into account the interests of the particular group of people who are the object of the experiment, this object being one of the participants in the experiment, and the investigator himself being part of the situation he is investigating. The content and procedures of social experimentation are also conditioned by [http://www.larad.org/meetss.php??p=47726-buy-authentic-Nike-Air-Max-Tn-Requin-Blue-White-Green-2014-Release-Dates-online.html buy authentic Nike Air Max Tn Requin Blue White Green 2014 Release Dates online] society legal and ethical norms.
[[File:Sphere-like degenerate torus.gif|thumb|As the distance to the axis of revolution decreases, the ring torus becomes a horn torus, then a spindle torus, and finally [[Degeneracy (mathematics)|degenerates]] into a sphere.]]
相关的主题文章:
In [[geometry]], a '''torus''' (pl. '''tori''') is a [[surface of revolution]] generated by revolving a [[circle]] in three-dimensional space about an axis [[coplanar]] with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a '''ring torus''' or simply ''torus'' if the ring shape is implicit.
<ul>
 
  <li>[http://www.ccms.cc/forum.php?mod=viewthread&tid=71813&extra= http://www.ccms.cc/forum.php?mod=viewthread&tid=71813&extra=]</li>
 
  <li>[http://www.wak3-up.de/index.php?site=forum_topic&topic=24486 http://www.wak3-up.de/index.php?site=forum_topic&topic=24486]</li>
 
  <li>[http://www.sjzhb.org/forum.php?mod=viewthread&tid=2150 http://www.sjzhb.org/forum.php?mod=viewthread&tid=2150]</li>
 
</ul>


When the axis is tangent to the circle, the resulting surface is called a '''horn torus'''; when the axis is a chord of the circle, it is called a '''spindle torus'''. A [[Degeneracy (mathematics)|degenerate]] case is when the axis is a diameter of the circle, which simply generates a [[sphere|2-sphere]]. The ring torus bounds a solid known as a '''toroid'''. The adjective '''toroidal''' can be applied to tori, toroids or, more generally, any ring shape as in [[toroidal inductors and transformers]]. Real-world examples of (approximately) toroidal objects include [[doughnut]]s, [[vada (food)|vadai]]s, [[inner tube]]s, [[bagels]], many [[lifebuoy]]s, [[O-ring]]s and [[vortex ring]]s.
== GEP4pI Brazil 6s V5rsCn0k ==


In [[topology]], a ring torus is [[Homeomorphism|homeomorphic]] to the Cartesian [[product topology|product]] of two [[circle]]s: ''S''<sup>1</sup>&nbsp;×&nbsp;''S''<sup>1</sup>, and the latter is taken to be the definition in that context. It is a compact 2-manifold of genus 1. The ring torus is one way to embed this space into three-dimensional [[Euclidean space]], but another way to do this is the Cartesian product of the embedding of ''S''<sup>1</sup> in the plane. This produces a geometric object called the [[Clifford torus]], surface in [[Four-dimensional space|4-space]].
Motives for leaking Stone's memoIf you think the current crisis over Shane Stone's memo to the PM has a familiar ring, you're right. In 1994, the Liberal Party commissioned private polling on John Hewson's standing with voters. The document was damning, but no one told the leader. It was leaked, and John Hewson never recovered. <br><br>However [political parties] may now and then answer popular ends, they are likely in the course of time and things, to become potent engines, by which cunning, ambitious, and unprincipled men will be enabled to subvert the power of the people and to usurp for themselves the reins of government, destroying afterwards the very engines which have lifted them to unjust dominion.<br><br>It is only a few days after the "not guilty" verdict in the George Zimmerman trial and I wonder just where the Voting Rights Act and the civil rights struggle is headed. I can acknowledge that indeed the South has changed as mentioned in a previous blog, but have we come that far? Will the work of civil rights pioneers Medgar Evers, Rosa Parks, Martin Luther King Jr., Malcom X, Fannie Lou Hamer and Presidents John F. Kennedy and Lyndon B. Johnson, go in vain? Johnson, who took office after Kennedy was assassinated, signed the Voting Rights Act into law on Aug. 6, 1965.<br><br>'It was a very nice finish, and I'm glad to be in the cool for a while because it's getting very hot out there now. I hit a decent drive down the last then hit a good hybrid rescue club onto the [http://www.calpath.org/memberss.php??p=9688-Stores-To-Buy-Michael-Jackson-King-of-Pop-Black-Black-Air-Force-1-Low.html Stores To Buy Michael Jackson King of Pop Black Black Air Force 1 Low] fringe, and managed to get down in two from there. So I'm very happy,' he said.<br><br>Paraguay's ousted President [http://www.larad.org/meetss.php??p=6711-Sale-Nike-Free-3.0-V4-WMS-511495-310-Volt-Black-Gray-Online.html Sale Nike Free 3.0 V4 WMS 511495-310 Volt Black Gray Online] Fernando Lugo, center, smiles during a Cabinet meeting in Asuncion, Paraguay, Tuesday, June 26, 2012. Lugo said Monday that he is aiming to return to power and will rally allies at home and abroad after a landslide congressional vote forced him from office in what he called a break with democracy. Lugo has symbolically created a parallel Cabinet, attacking the legitimacy of the government that replaced him. Pictured are Lugo's Foreign Minister Jorge Lara Castro, left, Rocio Casco, director of the Socialism Movement Party, PMAS, second left, and his Health Minister Esperanza Martinez, right. (AP Photo/Jorge Saenz)<br><br>Nudged by Leno in a notably sober first segment, Obama [http://www.mimaweb.org/imagess.php??p=2006-new-Nike-Air-Max-90-White-Blue-Black-2015-for-sale.html new Nike Air Max 90 White Blue Black 2015 for sale] reflected on the meaning of Gadhafi's death, a gruesome and chaotic demise recorded on cellphone video for all the world to see. The president argued that Gadhafi had had an opportunity to let Libya move on a path toward democracy peacefully.<br><br>Has a leadership personality, Deker said. never really different. She always carries herself as if she in a leadership role. She knows what to do, and she has everything planned out. She very organized, and knows what each person should be doing. The delegates at the Oregon FFA Association recently voted Rutledge in as vice president of the statewide organization.<br><br>For the first year or so, Mosby still had hopes of eventually moving on to Memphis. However, he finally gave up that desire. He once made a statement to Mr. Appling that he had found Bristol to be such a good place to live that he planned to make it home for the rest of his life. But that was not to be. Soon after the Civil War began, he enlisted in the service of the Confederacy. He left Bristol in early May 1861 and never returned here to live or practice law. His wife lived on here for a few months then she moved on to eastern Virginia.
相关的主题文章:
<ul>
 
  <li>[http://jxwar.com/forum.php?mod=viewthread&tid=126756&extra= http://jxwar.com/forum.php?mod=viewthread&tid=126756&extra=]</li>
 
  <li>[http://ziewang.com/forum.php?mod=viewthread&tid=1691582 http://ziewang.com/forum.php?mod=viewthread&tid=1691582]</li>
 
  <li>[http://telekomxchange.com/activity/p/93644/ http://telekomxchange.com/activity/p/93644/]</li>
 
</ul>


The word ''torus'' comes from the [[Latin]] word meaning [[cushion]].<ref>{{cite book|url = http://books.google.com/?id=GGoNQzt3I_IC&pg=PA16&lpg=PA16&dq=torus+Latin+word+for+a+cushion+of+this+shape | isbn = 978-0-323-01440-3 | page = 16 | author = Harold A. Stein ... | year = 2002 | publisher = Mosby | location = St. Louis | title = Fitting guide for rigid and soft contact lenses : a practical approach}}</ref>
== hS40LR Jordan 6 Brazil 3eTIQGxN ==


==Geometry==
Tom Fitton, [http://www.ti-cmc.org/commitss.php??p=62473-authentic-Nike-Air-Force-1-Low-Womens-Futura-Be-True-Team-Orange-site-online.html authentic Nike Air Force 1 Low Womens Futura Be True Team Orange site online] president of Judicial Watch said, "I know there's this pretend division between the Residence and the so called official part of the building, but just because your lawyers say something's OK doesn't mean it's OK. We expected this president to go above and beyond in terms of ethics and adhering to the law."<br><br>We meet a man in the shadows who depends on the indignity of [http://www.calpath.org/memberss.php??p=25489-Cheap-Mothers-Day.html Cheap Mothers Day] charity and who can't look people in the eyes. Why? His body, physical gifts, experience, relationships, religion, culture, family and the system itself all forced him to the fringe because he was born lame. Cowering in fear and shame, he hadn't questioned his position on the outside steps of the temple in years.<br><br>"Mitt Romney has, however, failed to recognize the very core of the American dilemma. He attacked Obama with twisted facts shortly after the announcement of the death of the US ambassador to Libya, Chris Stevens. He claimed that the US government had sympathized with the attackers in Benghazi. But not only was that factually wrong, it also demonstrated an alarmingly high level of foreign policy incompetence to his own party. None of this would [http://www.ti-cmc.org/commitss.php??p=34147-Wholesale-Free-TR-Twist-Wmns-Blue-Grey-White-.html Wholesale Free TR Twist Wmns Blue Grey White] matter, except that Romney wants Obama's job  and might even get it on Nov. 6."<br><br>Yanamala sees conspiracy to impose President's rule September 30, 2013 Doctors bid to barge into health varsityOctober 1, 2013 Jagan's tour to Krishna, Guntur put off October 1, 2013 Andhra Pradesh bifurcation unlikely, opines JACOctober 1, 2013 Mood upbeat in YSRC camp September 30, 2013 NGOs gearing up for Rythu Garjana on October 2September 30, 2013 Vijayawada Congress leaders hail Kiran as 'the new hero'September 29, 2013 APNGOs force closure of Vijayawada's Central government organisationsSeptember 29, 2013<br><br>Its ludicrous that the once renowned CBI has submitted to the special court, its inability to further proceed with the case citing insufficient evidence. The Jewish state has already lost the glare of its gilt only to pose a lack lustre outlook. The world out there is not going to buy anymore the story of Israel, as its leaning towards unjust provocations to stall the peace process. As such the day is not far off, when the flag of free Palestine will flutter pompously at the centre point of East Jerusalem. Since then all US Presidents, but JFK, were 'Christianist' converts from Judaism (Nazi collaborator Prescott Bush tribe) or have Jewsih blood, including Mr Obama! What is not mentioned is that all the US made bombs were delivered with US airplanes! Arab leaders have not served Arabs well; they need to know the facts. He was killed by Jew L. Rubinstein and covered up by Jews LBJ, Nixon, G. Ford, Warren 12 tribes. Since 1972 when China replaced US puppet Taiwan as 5th UN Veto power, the vast majority of UN Vetoes were cast by US and almost all were to stop UN from condemning genocide committing 'Chosen' Israel that recently used WMD s in 02 06 Lebanon (cluster, nuclear clad bunker buster bombs and civilian deaths) and 08 GAZA: white phosphorous, civilian killings and using children as human shields. When will the part Jew US Presidents be just to all, including American 'gentiles' (Jew word for all leprous others)? These US and Jew made Arab tragedies have been going on for 62 years! When US supports an evil Israel, the US is equally evil!.
[[File:torus cycles.png|thumb|right|A torus is the product of two circles, in this case the red circle is swept around axis defining the pink circle. ''R'' is the radius of the pink circle, ''r'' is the radius of the red one.]]
相关的主题文章:
{{multiple image
  <ul>
  | direction = vertical
 
| width    = 100
   <li>[http://satellite-delight.us/index.php?title=User:Bmuvbmkqjd#lit25v_Jordan_6_World_Cup_Brazil_dfblL22g http://satellite-delight.us/index.php?title=User:Bmuvbmkqjd#lit25v_Jordan_6_World_Cup_Brazil_dfblL22g]</li>
| footer   = Bottom-halves and cross-sections of the three classes
 
| image1    = Standard_torus-ring.png
   <li>[http://www.xiaoyuankeji8.com/shownews.asp?id=76 http://www.xiaoyuankeji8.com/shownews.asp?id=76]</li>
| alt1      = ring
 
| caption1  = Ring torus
   <li>[http://www.touchnet.tw/discuz/upload/forum.php?mod=viewthread&tid=62713&extra= http://www.touchnet.tw/discuz/upload/forum.php?mod=viewthread&tid=62713&extra=]</li>
| image2   = Standard_torus-horn.png
 
| alt2      = horn
</ul>
| caption2  = Horn torus
| image3   = Standard_torus-spindle.png
| alt3      = spindle
| caption3  = Spindle torus
}}
[[File:Toroidal coord.png|thumb|A diagram depicting the poloidal (θ) direction, represented by the red arrow, and the toroidal (ζ or φ) direction, represented by the blue arrow.]]


A torus can be defined [[parametric equation|parametric]]ally by:<ref>{{cite web|url=http://www.geom.uiuc.edu/zoo/toptype/torus/standard/eqns.html |title=Equations for the Standard Torus |publisher=Geom.uiuc.edu |date=1995-07-06 |accessdate=2012-07-21}}</ref>
== E3IRnB Buy Cheap Jordans 2014 WYO1eZTQ ==


:<math>x(\theta, \varphi) = (R + r \cos \varphi) \cos{\theta} </math>
Post crash helicopter fires have killed at least 73 people and injured at least 25 since [http://www.m3-consultancy.com.sg/indexs.php cheap jordans] Nov. 2, 1994, according to a USA TODAY review of autopsy reports and crash records. [http://www.seimitsu.sg/LegendBlue11s/‎ Legend Blue 11s] Although crash reports do not describe helicopter fuel [http://www.pigscanfly.com/frenchblue7s/ french blue 7s] components, none of the 46 helicopters in the crashes was required to have the sturdier tanks, USA TODAY found. <br><br>The 2 team because they lost to Maryland in the 2010 championship [http://www.qsamarine.com.sg/UploadedImg/Media/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] game. They finished 20 2 with losses to the Terps and the Tar [http://www.qsamarine.com.sg/UploadedImg/Media/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] Heels. (MDLaxManiac) 3. A designated team member pulls them in advance for each work order and ensures they are returned to their proper places after use. [http://www.pigscanfly.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] Not only has the improvement [http://www.m3-consultancy.com.sg/indexs.php cheap jordans] enhanced the efficiency and [http://www.oipc.ab.ca/jordan4oreo/ jordan 4 oreo] workflow of the punch cells, it has facilitated [http://www.trustedu.com/Jordan11LegendBlue/ Jordan 11 Legend Blue] maintenance and inventory improvements, as well.Metcam Turret Punch Tool CenterAccording to Metcam Quality Manager Richard Uber, one of the core benefits of the Kaizen initiatives is that workers on the production floor [http://www.pigscanfly.com/frenchblue7s/ french blue 7s] are the ones coming up with project ideas. Of the nine changes Metcam has implemented, only two were overseen by consultants hired in late 2013. <br><br>Recently Michelle Bachmannappeared on "Meet the Press" and revealed her findings to David Gregory. In her appearance [http://www.pigscanfly.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] she said, "It is shocking the revelations [http://www.trustedu.com/Jordan11LegendBlue/ Jordan 11 Legend Blue] of [http://www.icfrith.com.sg/jordan7frenchblue/ jordan 7 french blue] all the money that been spent There is a Congressional Research Service report that just was issued in February, and we discovered that secretly, unbeknownst to members of Congress, over $105 billion was hidden in the Obamacare [http://www.oipc.ab.ca/jordan4oreo/ jordan 4 oreo] legislation to fund the implementation of Obamacare. This [http://www.m3-consultancy.com.sg/LadyLiberty10s/ Lady Liberty 10s] is something that wasn known.".
:<math>y(\theta, \varphi) =  (R + r \cos \varphi) \sin{\theta}</math>
相关的主题文章：
:<math>z(\theta, \varphi) = r \sin \varphi </math>
  <ul>
 
  <li>[http://orcid.org/item/create_form/1 http://orcid.org/item/create_form/1]</li>
 
  <li>[http://www.dentech.net.gr/index.php?item/create_form/1 http://www.dentech.net.gr/index.php?item/create_form/1]</li>
 
  <li>[http://www.cleanenergyworld.org/index.php?item/create_form/1 http://www.cleanenergyworld.org/index.php?item/create_form/1]</li>
 
  <li>[http://www.kiwivapers.com/index.php?item/create_form/1 http://www.kiwivapers.com/index.php?item/create_form/1]</li>
 
  <li>[http://www.chrisadamsperfumes.com/index.php?item/create_form/1 http://www.chrisadamsperfumes.com/index.php?item/create_form/1]</li>
 
  </ul>


where
== 1Q8B6M buy jordans CVBxlJsH ==
:θ, φ are angles which make a full circle, starting at 0 and ending at 2π, so that their values start and end at the same point,
:''R'' is the distance from the center of the tube to the center of the torus,
:''r'' is the radius of the tube.


''R'' and ''r'' are also known as the "major radius" and "minor radius", respectively. The ratio of the two is known as the "[[aspect ratio]]". A doughnut has an aspect ratio of about 2 to 3.
On Friday, he rushed for more than 300 yards  the exact number remains a mystery depending on who you ask. But what made the number even more impressive was the opponent. It wasn't some paper defense like Uintah. Todd, MonticelloThere are many people that can and will be blamed for this accident. First, you have pilot error that could have caused the [http://www.nepaltribalart.com/frenchblue7s/index.html french blue 7s] crash. Second, there should have been someone in [http://www.stm-ce.com/jordan4oreo/ jordan 4 oreo] the control tower telling the pilot he was on the wrong runway. <br><br>Back [http://www.stm-ce.com/jordan4oreo/ jordan 4 oreo] in [http://www.m3-consultancy.com.sg/BullsOverBroadway10s/ Bulls Over Broadway 10s] New York, Radnor acknowledges that he has some growing up to do and [http://www.pigscanfly.com/cheapjordans/ cheap jordans] asks Reaser to go for a walk. However, he isn't quite done with Kenyon, as Magaro phones to confess to taking an overdose of pills and Radnor has to overcome his fear of flying to sit by his bedside. Having made his [http://www.oipc.ab.ca/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] peace with [http://www.seimitsu.sg/LegendBlue11s/‎ Legend Blue 11s] Olsen, Radnor returns east and snuggles with Reaser as she muses [http://www.stm-ce.com/jordan4oreo/ jordan 4 oreo] about how nice it will be for them to grow old together.. <br><br>Family and friends will assemble at the church at 12:45. At the funeral home. Services entrusted to the care of Franklin Hutcherson Funeral Home. I was only a couple of hundred metres offshore when I came up for a breath to my left. In the sea of black suited arms, legs and goggles, I saw something that was more comforting than the final exit buoys; more extraordinary than a hundred foot eel; [http://www.renocol-asia.sg/Jordan11LegendBlue/ Jordan 11 Legend Blue] more beautiful [http://www.oipc.ab.ca/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] than a pond lily. It was [http://www.qsamarine.com.sg/UploadedImg/Media/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] my husband's [http://www.m3-consultancy.com.sg/BullsOverBroadway10s/ Bulls Over Broadway 10s] face, mere inches from my own. <br><br>Overall, the portfolio is performing well from a credit perspective and we continue to feel good about ACSF prospects over the long term."Malon [http://www.qsamarine.com.sg/UploadedImg/Media/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] Wilkus, Chair and Chief Executive Officer commented, "We were pleased to announce a dividend of $0.28 per share for the third quarter. Our current annualized dividend represents a 7.5% yield on our NAV and an 8.6% yield on [http://www.oipc.ab.ca/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] our [http://www.oipc.ab.ca/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] September 30th closing share price. While we experienced depreciation this quarter, it is important to note that it was due to market spreads widening and not credit deterioration.
相关的主题文章：
<ul>
 
  <li>[http://centr-patriot.ru/index.php/component/xijc/?view=captcha http://centr-patriot.ru/index.php/component/xijc/?view=captcha]</li>
 
  <li>[http://www.chrisadamsperfumes.com/index.php?item/create_form/1 http://www.chrisadamsperfumes.com/index.php?item/create_form/1]</li>
 
  <li>[http://www.cleanenergyworld.org/index.php?item/create_form/1 http://www.cleanenergyworld.org/index.php?item/create_form/1]</li>
 
  <li>[http://www.marenostrumresort.com/en/index.php?item/create_form/1 http://www.marenostrumresort.com/en/index.php?item/create_form/1]</li>
 
  <li>[http://hhstyle.pl/index.php?item/create_form/1 http://hhstyle.pl/index.php?item/create_form/1]</li>
 
</ul>


An [[implicit function|implicit]] equation in [[Cartesian coordinates]] for a torus radially symmetric about the ''z''-[[Coordinate axis|axis]] is
== l2tFYQ cheap jordans 2014 CNVS7MUU ==


:<math>\left(R - \sqrt{x^2 + y^2}\right)^2 + z^2 = r^2,</math>
Mitch Daniels has put Indiana on a path to financial prosperity. Here comes the government. States all across America are facing unprecedented budget crises. The heyday of the Roman war chariot was about 1,500 years ago, but [http://www.asiastar.com/jordan4oreo/ jordan 4 oreo] they may be coming back. Hopefully they won be used to subjugate neighboring nations. But the excitement of careening around a dirt track in a flimsy looking, two wheeled cart a la Ben Hur, sans biological horses, seems to be calling to some modern gear [http://www.pigscanfly.com/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] heads. <br><br>As I seem to recall, Mr. Obama ran for office freely. As the winner of the requisite number electoral votes, he gained the right to assume office but he could have decided against it had he chosen to do so. IS was kicked [http://www.trustedu.com/abouts.html cheap jordans] out of al Qaida in May after disobeying [http://www.m3-consultancy.com.sg/LadyLiberty10s/ Lady Liberty 10s] its leader, Ayman al Zawahiri. So far, IS has not publicly responded to al Qaida's [http://www.trustedu.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] calls to reunite  the most recent on Oct. 17 from al Qaida in the Arabian Peninsula, the Yemen based offshoot [http://www.trustedu.com/abouts.html cheap jordans] that denounced the [http://www.asiastar.com/jordan4oreo/ jordan 4 oreo] airstrikes and called on rival militant [http://www.pigscanfly.com/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] groups to stop their infighting and together train their sights [http://www.trustedu.com/Jordan11LegendBlue/ Jordan 11 Legend Blue] on the West.. <br><br>Season 8 of "American Idol" is commonly referred to as "Battle of the Davids," as rocker David Cook [http://www.trustedu.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] and teen pop cutie David Archuleta went neck and neck throughout the entire competition. The rock star ultimately prevailed in 2008 with his raw voice and acoustic renditions of timeless hits from all genres. [http://www.trustedu.com/Jordan11LegendBlue/ Jordan 11 Legend Blue] As the show ended, Cook released his first single "Time [http://www.pigscanfly.com/frenchblue7s/ french blue 7s] of My Life," which went platinum in 2008. <br><br>It doesn't get any easier for the Utes from this point forward. Utah goes on the road this week to face eighth ranked UCLA. [http://www.trustedu.com/abouts.html cheap jordans] Four of the Utes' remaining eight opponents [http://www.trustedu.com/Jordan11LegendBlue/ Jordan 11 Legend Blue] are currently ranked 16th or higher [http://www.trustedu.com/Jordan11LegendBlue/ Jordan 11 Legend Blue] (and two more opponents are getting votes in the polls).
相关的主题文章：
<ul>
 
  <li>[http://www.chrisadamsperfumes.com/index.php?item/create_form/1 http://www.chrisadamsperfumes.com/index.php?item/create_form/1]</li>
 
  <li>[http://www.ibizstore.com/item/create_form/1 http://www.ibizstore.com/item/create_form/1]</li>
 
  <li>[http://www.aurosiksha.org/login/index.php?item/create_form/1 http://www.aurosiksha.org/login/index.php?item/create_form/1]</li>
 
  <li>[http://en.muzeumprahy.cz/index.php?item/create_form/1 http://en.muzeumprahy.cz/index.php?item/create_form/1]</li>
 
  <li>[http://e-learning.tsu.ge/login/index.php?item/create_form/1 http://e-learning.tsu.ge/login/index.php?item/create_form/1]</li>
 
</ul>


or the solution of ''f''(''x'', ''y'', ''z'') = 0, where
== hhw3re cheap jordans nzyZ9V0O ==


:<math> f(x,y,z) = \left(R - \sqrt{x^2 + y^2}\right)^2 + z^2 - r^2.</math>
Some have questioned using completion as a method of evaluation. [http://www.renocol-asia.sg/indexs.html cheap jordans] Kevin Carey, director of the Education Policy Program at the New America Foundation, wrote that judging courses that require such little effort to enroll in by their completion rates reflects how the traditional [http://yourmota.co.uk/jordan7frenchblue/ jordan 7 french blue] college mindset continues to dominate and limit the public understanding of what higher education can and should mean. [http://www.seimitsu.sg/LegendBlue11s/‎ Legend Blue 11s] This year, in an interview on the completion rates, Keller encouraged reframing the discussion around such courses. <br><br>Stones River Mall to host fun filled family event Aug. 2More than a photographer: Richard [http://www.renocol-asia.sg/jordan4oreo/ jordan 4 oreo] Claude ShacklettPark [http://www.seimitsu.sg/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] View Meadows Family Night Photo GalleryA mother's love is still the greatest gift of allWELLNESS SPOTLIGHT: What is Sibling Denial?MRS. MURFREESBORO: We should all enjoy our family when we have the chanceRead to [http://www.seimitsu.sg/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] Succeed's Me and My Family literature night [http://www.seimitsu.sg/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] a successBURRISS: Reporters need survival skills given political climateLOGUE: Pedophiles keep slipping into education systemWOODY: Athletes owe it to fans to speak upView AllI am taking a [http://www.renocol-asia.sg/jordan4oreo/ jordan 4 oreo] teacher training course at my mosque right now and am astounded at how little I know about the art and science of teaching. <br><br>If you have enjoyed this column, may I suggest you scroll down this page and press the SUBSCRIBE box? It's FREE. Thank you for your patronage. Schwab, Jr. Large portions of the Republican agenda passed [http://www.stm-ce.com/LadyLiberty10s/ Lady Liberty 10s] because Williams kept his promise to bring those matters [http://www.seimitsu.sg/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] to the floor, which is a vast improvement over former Speaker Jimmy Naifeh. Naifeh understood that many Democrats from rural districts [http://www.renocol-asia.sg/jordan4oreo/ jordan 4 oreo] agree with Republicans on social issues and Second Amendment rights, and that even with a Democratic majority in [http://www.renocol-asia.sg/Jordan11LegendBlue/ Jordan 11 Legend Blue] the House, pro life [http://www.renocol-asia.sg/jordan4oreo/ jordan 4 oreo] bills, gun bills, and other conservative matters would pass the House with solid votes in favor. Members who played ball with the Speaker [http://www.seimitsu.sg/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] were given the money for their district to help them [http://www.renocol-asia.sg/Jordan11LegendBlue/ Jordan 11 Legend Blue] get re elected regardless of party..
相关的主题文章：
<ul>
 
  <li>[http://www.sipqjh2.com/E_GuestBook.asp http://www.sipqjh2.com/E_GuestBook.asp]</li>
 
  <li>[http://www.sipqjh2.com/E_GuestBook.asp http://www.sipqjh2.com/E_GuestBook.asp]</li>
 
  <li>[http://www.cacenglish.com/index.php?item/create_form/1 http://www.cacenglish.com/index.php?item/create_form/1]</li>
 
  <li>[http://www.interconnectingautomation.com/onlinecourses/index.php?item/create_form/1 http://www.interconnectingautomation.com/onlinecourses/index.php?item/create_form/1]</li>
 
  <li>[http://www.luvstruck.co.za/s/index.php?item/create_form/1 http://www.luvstruck.co.za/s/index.php?item/create_form/1]</li>
 
</ul>


Algebraically eliminating the square root gives a [[quartic equation]],
== gXts78 jordans PajOBp3q ==
:<math> (x^2+y^2+z^2 + R^2 - r^2)^2 = 4R^2(x^2+y^2).  \,\!</math>


The three different classes of standard tori correspond to the three possible relative sizes of ''r'' and ''R''. When ''R'' > ''r'', the surface will be the familiar ring torus. The case ''R'' = ''r'' corresponds to the horn torus, which in effect is a torus with no "hole". The case ''R'' < ''r'' describes the self-intersecting spindle torus. When ''R'' = 0, the torus degenerates to the sphere.
This system took the idea of pilot injection  squirting a small amount of fuel into the cylinder [http://www.m3-consultancy.com.sg/jordan4oreo/ jordan 4 oreo] to 'prime' the combustion chamber for the main ignition process  and refined it still further. In this instance, the main injection is divided into a series of smaller injections, allowing smoother, more gradual combustion that utilises fuel more efficiently. The electronic control units, [http://www.icfrith.com.sg/Jordan11LegendBlue/ Jordan 11 Legend Blue] therefore, have to be astonishingly precise. <br><br>Each speaker has multiple inputs, [http://www.pigscanfly.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] a built in [http://www.pigscanfly.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] amplifier, multiple tweeters and a subwoofer to bring out the bass. [http://www.m3-consultancy.com.sg/jordan4oreo/ jordan 4 oreo] Altek Lansing also designs the system so that each speaker can play a different song if desired. The cost [http://www.icfrith.com.sg/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] of using Wi Fi to create multi room audio systems depends on the cost of the [http://www.trustedu.com/jordan7frenchblue/ jordan 7 french blue] Wi Fi speakers you purchase.. <br><br>On December 5, 2002, Rabinovitz communicated with bankruptcy counsel Herbert S. Weinberg [http://www.m3-consultancy.com.sg/jordan4oreo/ jordan 4 oreo] and made a decision that a [http://www.pigscanfly.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] petition be filed in the Federal Bankruptcy Court on behalf of Millennium. On December 9, 2002, after the preparation of that petition, Weinberg sent a facsimile letter to Mahlowitz also demanding that Mahlowitz voluntarily discharge the attachment or [http://www.icfrith.com.sg/Jordan11LegendBlue/ Jordan 11 Legend Blue] else a bankruptcy proceeding would be filed on behalf of [http://www.trustedu.com/jordan7frenchblue/ jordan 7 french blue] Millennium. <br><br>The Phantom Lightweight version of the Tactical Pants came out in 2011, three years after [http://www.pigscanfly.com/cheapjordans/ cheap jordans] the [http://www.icfrith.com.sg/Jordan10BullsOverBroadway/ Jordan 10 Bulls Over Broadway] release of the "Original". This model has the same fit and features of the original pant [http://www.pigscanfly.com/Jordan10LadyLiberty/ Jordan 10 Lady Liberty] but in a 6.5 oz (much lighter) polyester/cotton mini [http://www.m3-consultancy.com.sg/jordan4oreo/ jordan 4 oreo] ripstop fabric. We looked at both the full on pants and shorts.
 
相关的主题文章：
When ''R'' ≥ ''r'', the [[interior (topology)|interior]]
<ul>
 
 
:<math>\left(R - \sqrt{x^2 + y^2}\right)^2 + z^2 < r^2</math>
  <li>[http://www.sipqjh2.com/E_GuestBook.asp http://www.sipqjh2.com/E_GuestBook.asp]</li>
 
 
of this torus is [[diffeomorphism|diffeomorphic]] (and, hence, homeomorphic) to a [[Cartesian product|product]] of an [[disc (mathematics)|Euclidean open disc]] and a circle.
  <li>[http://www.kiwivapers.com/index.php?item/create_form/1 http://www.kiwivapers.com/index.php?item/create_form/1]</li>
 
 
The [[surface area]] and interior [[volume]] of this torus are easily computed using [[Pappus's centroid theorem]] giving<ref>{{Mathworld|Torus|Torus}}</ref>
  <li>[http://www.pkunity.com/guestbook.asp http://www.pkunity.com/guestbook.asp]</li>
 
 
:<math>A = 4 \pi^2 R r = \left( 2\pi r \right) \left(2 \pi R \right) </math>
  <li>[http://www.pkunity.com/guestbook.asp http://www.pkunity.com/guestbook.asp]</li>
:<math>V = 2 \pi^2 R r^2 = \left ( \pi r ^2 \right ) \left( 2 \pi R \right).</math>
 
 
  <li>[http://blog.jinbo.net/jamie/index.php?item/create_form/1 http://blog.jinbo.net/jamie/index.php?item/create_form/1]</li>
These formulas are the same as for a cylinder of length 2π''R'' and radius ''r'', created by cutting the tube and unrolling it by straightening out the line running around the center of the tube. The losses in surface area and volume on the inner side of the tube exactly cancel out the gains on the outer side.
 
 
</ul>
As a torus is the product of two circles, a modified version of the [[spherical coordinate system]] is sometimes used. In traditional spherical coordinates there are three measures, ''R'', the distance from the center of the coordinate system, and θ and φ, angles measured from the center point. As a torus has, effectively, two center points, the centerpoints of the angles are moved; φ measures the same angle as it does in the spherical system, but is known as the "toroidal" direction. The center point of θ is moved to the center of ''r'', and is known as the "poloidal" direction. These terms were first used in a discussion of the Earth's magnetic field, where "poloidal" was used to denote "the direction toward the poles".<ref>{{cite web |url=http://dictionary.oed.com/cgi/entry/50183023?single=1&query_type=word&queryword=poloidal&first=1&max_to_show=10 |title= Oxford English Dictionary Online |accessdate=2007-08-10 |work=poloidal |publisher=Oxford University Press|pages= |language= |archiveurl= |archivedate= |quote= }}</ref> In modern use these terms are more commonly used to discuss [[magnetic confinement fusion]] devices.
 
==Topology==
[[Topology|Topologically]], a '''torus''' is a closed [[surface]] defined as the [[product topology|product]] of two [[circle]]s: ''S''<sup>1</sup>&nbsp;×&nbsp;''S''<sup>1</sup>. This can be viewed as lying in [[complex coordinate space|'''C'''<sup>2</sup>]] and is a subset of the [[3-sphere]] ''S''<sup>3</sup> of radius [[square root of 2|{{sqrt|2}}]]. This topological torus is also often called the [[Clifford torus]]. In fact, ''S''<sup>3</sup> is [[Foliation|filled out]] by a family of nested tori in this manner (with two degenerate circles), a fact which is important in the study of ''S''<sup>3</sup> as a [[fiber bundle]] over ''S''<sup>2</sup> (the [[Hopf bundle]]).
 
The surface described above, given the [[relative topology]] from [[real coordinate space|'''R'''<sup>3</sup>]], is [[homeomorphic]] to a topological torus as long as it does not intersect its own axis. A particular homeomorphism is given by [[Stereographic projection|stereographically projecting]] the topological torus into '''R'''<sup>3</sup> from the north pole of ''S''<sup>3</sup>.
 
The torus can also be described as a [[quotient space|quotient]] of the [[Cartesian plane]] under the identifications
:(''x'', ''y'') ~ (''x''+1, ''y'') ~ (''x'', ''y''+1).
Or, equivalently, as the quotient of the [[unit square]] by pasting the opposite edges together, described as a [[fundamental polygon]] ''ABA''<sup>−1</sup>''B''<sup>−1</sup>.
 
[[File:Inside-out torus (animated, small).gif|thumb|Turning a punctured torus inside-out]]
The [[fundamental group]] of the torus is just the [[direct product of groups|direct product]] of the fundamental group of the circle with itself:
 
:<math>\pi_1(\mathbf{T}^2) = \pi_1(S^1) \times \pi_1(S^1) \cong \mathbf{Z} \times \mathbf{Z}.</math>
 
Intuitively speaking, this means that a [[loop (topology)|closed path]] that circles the torus' "hole" (say, a circle that traces out a particular latitude) and then circles the torus' "body" (say, a circle that traces out a particular longitude) can be deformed to a path that circles the body and then the hole.  So, strictly 'latitudinal' and strictly 'longitudinal' paths commute. This might be imagined as two shoelaces passing through each other, then unwinding, then rewinding.
 
If a torus is punctured and turned inside out then another torus results, with lines of latitude and longitude interchanged.
 
The first [[homology group]] of the torus is [[isomorphic]] to the fundamental group (this follows from [[Hurewicz theorem]] since the fundamental group is [[abelian group|abelian]]).
 
==Two-sheeted cover==
The 2-torus double-covers the 2-sphere, with four [[ramification point]]s.  Every [[conformal structure]] on the 2-torus can be represented as a two-sheeted cover of the 2-sphere.  The points on the torus corresponding to the ramification points are the [[Weierstrass point]]s.  In fact, the conformal type of the torus is determined by the [[cross-ratio]] of the four points.
 
==''n''-dimensional torus==
[[File:Clifford-torus.gif|thumb|A stereographic projection of a [[Clifford torus]] in four dimensions performing a simple rotation through the ''xz''-plane.]]
 
The torus has a generalization to higher dimensions, the ''n''-'''dimensional torus''', often called the ''n''-'''torus''' or '''hypertorus'''<ref>As in ''[[The Road to Reality]]''.</ref> for short.  (This is one of two different meanings of the term "''n''-torus".) Recalling that the torus is the product space of two circles, the ''n''-dimensional torus is the product of ''n'' circles. That is:
 
:<math>\mathbf{T}^n = \underbrace{S^1 \times \cdots \times S^1}_n.</math>
 
The 1-torus is just the circle: '''T'''<sup>1</sup>&nbsp;=&nbsp;''S''<sup>1</sup>. The torus discussed above is the 2-torus, '''T'''<sup>2</sup>. And similar to the 2-torus, the ''n''-torus, '''T'''<sup>''n''</sup> can be described as a quotient of '''R'''<sup>''n''</sup> under integral shifts in any coordinate. That is, the ''n''-torus is '''R'''<sup>''n''</sup> modulo the [[group action|action]] of the integer [[lattice (group)|lattice]] '''Z'''<sup>''n''</sup> (with the action being taken as vector addition). Equivalently, the ''n''-torus is obtained from the ''n''-dimensional [[hypercube]] by gluing the opposite faces together.
 
An ''n''-torus in this sense is an example of an ''n-''dimensional [[Compact space|compact]] [[manifold]]. It is also an example of a compact [[abelian group|abelian]] [[Lie group]]. This follows from the fact that the [[unit circle]] is a compact abelian Lie group (when identified with the unit [[complex number]]s with multiplication). Group multiplication on the torus is then defined by coordinate-wise multiplication.
 
Toroidal groups play an important part in the theory of [[compact Lie group]]s. This is due in part to the fact that in any compact Lie group ''G'' one can always find a [[maximal torus]]; that is, a closed [[subgroup]] which is a torus of the largest possible dimension. Such maximal tori ''T'' have a controlling role to play in theory of connected ''G''. Toroidal groups are examples of [[protorus|protori]], which (like tori) are compact connected abelian groups, which are not required to be [[manifold]]s.
 
[[Automorphism]]s of ''T'' are easily constructed from automorphisms of the lattice '''Z'''<sup>''n''</sup>, which are classified by [[invertible matrix|invertible]] [[integral matrices]] of size ''n'' with an integral inverse; these are just the integral matrices with determinant ±1. Making them act on '''R'''<sup>''n''</sup> in the usual way, one has the typical '''toral automorphism''' on the quotient.
 
The [[fundamental group]] of an ''n''-torus is a [[free abelian group]] of rank ''n''.  The ''k''-th [[homology group]] of an ''n''-torus is a free abelian group of rank ''n'' [[binomial coefficient|choose]] ''k''. It follows that the [[Euler characteristic]] of the ''n''-torus is 0 for all ''n''.  The [[cohomology ring]] ''H''<sup>•</sup>('''T'''<sup>''n''</sup>,&nbsp;'''Z''') can be identified with the [[exterior algebra]] over the '''Z'''-[[module (mathematics)|module]] '''Z'''<sup>''n''</sup> whose generators are the duals of the ''n'' nontrivial cycles.
 
===Configuration space===
[[File:Moebius Surface 1 Display Small.png|thumb|The configuration space of 2 not necessarily distinct points on the circle is the [[orbifold]] quotient of the 2-torus, '''T'''<sup>2</sup>/''S''<sub>2</sub>, which is the [[Möbius strip]].]]
<!-- Deleted image removed: [[File:Topological III by Robert R. Wilson, at Harvard University.JPG|upright|thumb|The configuration space of 3 not necessarily distinct points on the circle, '''T'''<sup>3</sup>/''S''<sub>3</sub> is the above orbifold.]] -->
As the ''n''-torus is the ''n''-fold product of the circle, the ''n''-torus is the [[configuration space]] of ''n'' ordered, not necessarily distinct points on the circle. Symbolically, '''T'''<sup>''n''</sup> = (''S''<sup>1</sup>)<sup>''n''</sup>. The configuration space of ''unordered'', not necessarily distinct points is accordingly the [[orbifold]] '''T'''<sup>''n''</sup>/''S<sub>n</sub>'', which is the quotient of the torus by the [[symmetric group]] on ''n'' letters (by permuting the coordinates).
 
For ''n'' = 2, the quotient is the [[Möbius strip]], the edge corresponding to the orbifold points where the two coordinates coincide. For ''n'' = 3 this quotient may be described as a solid torus with cross-section an [[equilateral triangle]], with a twist; equivalently, as a [[triangular prism]] whose top and bottom faces are connected with a 1/3 twist (120°): the 3-dimensional interior corresponds to the points on the 3-torus where all 3 coordinates are distinct, the 2-dimensional face corresponds to points with 2 coordinates equal and the 3rd different, while the 1-dimensional edge corresponds to points with all 3 coordinates identical.
 
These orbifolds have found significant [[Orbifold#Music theory|applications to music theory]] in the work of Dmitri Tymoczko and collaborators (Felipe Posada and Michael Kolinas, et al.), being used to model [[triad (music)|musical triad]]s.<ref>{{Cite journal | first = Dmitri | last = Tymoczko | journal = [[Science (journal)|Science]]  | date = 7 July 2006 | volume = 313 | pages = 72–74 | doi = 10.1126/science.1126287 | url = http://www.brainmusic.org/EducationalActivitiesFolder/Tymoczko_chords2006.pdf | title = The Geometry of Musical Chords | issue = 5783 | pmid = 16825563 | postscript = <!--None--> }}</ref><ref>Tony Phillips, ''[http://www.ams.org/mathmedia/archive/10-2006-media.html Tony Phillips' Take on Math in the Media],'' [[American Mathematical Society]], October 2006</ref>
 
==Flat torus==
{| class=wikitable align=right width=480
|[[File:Torus from rectangle.gif|240px]]<BR>In three dimensions, one can bend a rectangle into a torus, but doing this typically stretches the surface, as seen by the distortion of the checkered pattern
|[[Image:Duocylinder ridge animated.gif|240px]]<BR>Seen in [[stereographic projection]] a 4D '''flat torus''' can be projected into 3-dimensions and rotated on a fixed axis
|}
The flat torus is a torus with the metric inherited from its representation as the [[quotient space|quotient]], '''R'''<sup>2</sup>/'''Z'''<sup>2</sup>, of the [[Cartesian plane]] under the identifications (''x'',&#8239;''y'') ~ (''x''+1,&#8239;''y'') ~ (''x'',&#8239;''y''+1). This gives it the structure of a [[Riemannian manifold]].
 
This metric can also be realised by specific embeddings of the familiar 2-torus into Euclidean 4-space or higher dimensions.  Its surface has zero [[Gaussian curvature]] everywhere.  Its surface is "flat" in the same sense that the surface of a cylinder is "flat". In 3 dimensions one can bend a flat sheet of paper into a cylinder without stretching the paper, but you cannot then bend this cylinder into a torus without stretching the paper (unless you give up some regularity and differentiability conditions, see below).  In 4 dimensions one can (mathematically).
 
A simple 4 dimensional Euclidean embedding is as follows:
 
:(''x'',&#8239;''y'',&#8239;''z'',&#8239;''w'') = (''R''&#8239;cos''u'', ''R''&#8239;sin''u'', ''P''&#8239;cos''v'', ''P''&#8239;sin''v'')
 
where ''R'' and ''P'' are constants determining the aspect ratio. It is [[diffeomorphic]] to a regular torus but not [[isometry|isometric]].  It can not be isometrically embedded into Euclidean 3-space.  [[map (mathematics)|Mapping]] it into ''3''-space requires you to stretch it, in which case it looks like a regular torus, for example, the following map
 
:(''x'',&nbsp;''y'',&nbsp;''z'') = ((''R'' + ''P''sin(''v''))cos(''u''),&nbsp;(''R'' + ''P''sin(''v''))sin(''u''),&nbsp;''P''cos(''v'')).
 
A flat torus partitions the [[3-sphere]] into two [[congruence (geometry)|congruent]] solid tori subsets with the aforesaid flat torus surface as their common [[boundary (topology)|boundary]].
 
In April 2012, an embedding of a flat torus into three dimensions was found.<ref>{{cite web|last=Filippelli |first=Gianluigi |url=http://docmadhattan.fieldofscience.com/2012/04/flat-torus-in-three-dimensional-space.html |title=Doc Madhattan: A flat torus in three dimensional space |doi=10.1073/pnas.1118478109 |publisher=Docmadhattan.fieldofscience.com |date=2012-04-27 |accessdate=2012-07-21}}</ref><ref>{{cite web|url=http://www.sci-news.com/othersciences/mathematics/article00279.html |title=Mathematicians Produce First-Ever Image of Flat Torus in 3D &#124; Mathematics |publisher=Sci-News.com |date=2012-04-18 |accessdate=2012-07-21}}</ref><ref>{{cite web|url=http://www2.cnrs.fr/en/2027.htm |title=Mathematics : first-ever image of a flat torus in 3D - CNRS Web site - CNRS |date= |accessdate=2012-07-21}}</ref><ref>{{cite web|url=http://math.univ-lyon1.fr/~borrelli/Hevea/Presse/index-en.html |title=Flat tori finally visualized! |publisher=Math.univ-lyon1.fr |date=2012-04-18 |accessdate=2012-07-21}}</ref> It is similar in structure to a [[fractal]] as it is constructed by repeatedly corrugating a normal torus. Like fractals, it has no defined Gaussian curvature. However, unlike fractals, it does have defined [[surface normals]].  These infinitely recursive corrugations are a pathology only necessary for embedding into three dimensions. They are not an intrinsic feature of the flat torus.
 
==''n''-fold torus==
In the theory of [[surface]]s there is another object, the ''n''-fold torus.  Instead of the product of ''n'' circles, an ''n''-fold torus is the [[connected sum]] of ''n'' 2-tori.  To form a connected sum of two surfaces, remove from each the interior of a disk and "glue" the surfaces together along the disks' boundary circles.  To form the connected sum of more than two surfaces, sum two of them at a time until they are all connected.  In this sense, an ''n''-torus resembles the surface of ''n'' doughnuts stuck together side by side, or a [[sphere|2-sphere]] with ''n'' handles attached.
 
An ordinary torus is a 1-fold torus, a 2-fold torus is called a [[double torus]], a 3-fold torus a [[triple torus]], and so on.  The ''n''-fold torus is said to be an "[[orientability|orientable surface]]" of "[[Genus (mathematics)|genus]]" ''n'', the genus being the number of handles.  The 0-fold torus is the [[sphere|2-sphere]].
 
The [[classification theorem]] for surfaces states that every [[compact space|compact]] [[connected space|connected]] surface is either a sphere, an ''n''-fold torus with ''n'' > 0, or the connected sum of ''n'' [[projective plane]]s (that is, projective planes over the [[real numbers]]) with ''n'' > 0.
 
{| class=wikitable
|- align=center
|[[File:Double torus illustration.png|160px]]<br>[[double torus]]
|[[File:Triple torus illustration.png|240px]]<br>[[triple torus]]
|}
 
==Toroidal polyhedra==
{{Details|Toroidal polyhedron}}
[[File:Hexagonal torus.png|thumb|A [[toroidal polyhedron]] with 6&#8239;×&#8239;4&nbsp;=&nbsp;24 quadrilateral faces.]]
Polyhedra with the topological type of a torus are called [[toroidal polyhedra]], and satisfy a modified version of the [[polyhedron formula]], ''E''−''F''−''V'' = 0.
 
The term "toroidal polyhedron"<!-- just a typo?  was: polydron --> is also used for higher genus polyhedra and for immersions of toroidal polyhedra.
 
{{Expand section|date=April 2010}}
 
==Automorphisms==
The [[homeomorphism group]] (or the subgroup of diffeomorphisms) of the torus is studied in [[geometric topology]]. Its [[mapping class group]] (the group of connected components) is isomorphic to the group GL(''n'',&nbsp;'''Z''') of invertible integer matrices, and can be realized as linear maps on the universal covering space '''R'''<sup>''n''</sup> that preserve the standard lattice '''Z'''<sup>''n''</sup> (this corresponds to integer coefficients) and thus descend to the quotient.
 
At the level of homotopy and homology, the mapping class group can be identified as the action on the first homology (or equivalently, first cohomology, or on the [[fundamental group]], as these are all naturally isomorphic; also the first [[cohomology group]] generates the [[algebra cohomology|cohomology algebra]]):
 
:<math>\operatorname{MCG}(\mathbf{T}^n) = \operatorname{Aut}(\pi_1(X)) = \operatorname{Aut}(\mathbf{Z}^n) = \operatorname{GL}(n,\mathbf{Z}).</math>
 
Since the torus is an [[Eilenberg–MacLane space]] ''K''(''G'',&nbsp;1), its homotopy equivalences, up to homotopy, can be identified with automorphisms of the fundamental group); that this agrees with the mapping class group reflects that all homotopy equivalences can be realized by homeomorphisms – every homotopy equivalence is homotopic to a homeomorphism – and that homotopic homeomorphisms are in fact isotopic (connected through homeomorphisms, not just through homotopy equivalences). More tersely, the map Homeo('''T'''<sup>''n''</sup>) → SHE('''T'''<sup>''n''</sup>) is [[n-connected|1-connected]] (isomorphic on path-components, onto fundamental group). This is a "homeomorphism reduces to homotopy reduces to algebra" result.
 
Thus the [[short exact sequence]] of the mapping class group splits (an identification of the torus as the quotient of '''R'''<sup>''n''</sup> gives a splitting, via the linear maps, as above):
:<math>1 \to \operatorname{Homeo}_0(\mathbf{T}^n) \to \operatorname{Homeo}(\mathbf{T}^n) \to \operatorname{MCG}(\mathbf{T}^n) \to 1,</math>
so the homeomorphism group of the torus is a [[semidirect product]],
:<math>\operatorname{Homeo}(\mathbf{T}^n) \cong \operatorname{Homeo}_0(\mathbf{T}^n) \rtimes \operatorname{GL}(n,\mathbf{Z}).</math>
 
The mapping class group of higher genus surfaces is much more complicated, and an area of active research.
 
==Coloring a torus==
<!--Chromatic number-->
If a torus is divided into regions, then it is always possible to color the regions with no more than seven colors so that neighboring regions have different colors. (Contrast with the [[four color theorem]] for the [[plane (mathematics)|plane]].)
[[File:Projection color torus.png|480px|thumb|center|This construction shows the torus divided into the maximum of seven regions, every one of which touches every other.]]
 
==Cutting a torus==
A standard torus (specifically, a ring torus) can be cut with ''n'' planes into at most
:<math>\tfrac{1}{6}(n^3 + 3n^2 + 8n)</math>
parts.<ref>{{MathWorld|urlname=TorusCutting|title=Torus Cutting}}</ref>
 
The initial terms of this sequence for ''n'' starting from 1 are:
:2, 6, 13, 24, 40, … {{OEIS|id=A003600}}.
 
==See also==
{{col-begin}}
{{col-break}}
*[[Algebraic torus]]
*[[Annulus (mathematics)]]
*[[Bagel]]
*[[Clifford torus]]
*[[Complex torus]]
*[[Doughnut]]
*[[Dupin cyclide]]
*[[Elliptic curve]]
*[[Irrational cable on a torus]]
*[[Joint European Torus]]
*[[Loewner's torus inequality]]
*[[Maximal torus]]
{{col-break}}
{{Portal|Mathematics}}
*[[Period lattice]]
*[[Sphere]]
*[[Spiric section]]
*[[Surface]]
*[[Toric lens]]
*[[Toric section]]
*[[Toric variety]]
*[[Toroid (geometry)]]
*[[Toroidal and poloidal]]
*[[Torus knot]]
*[[Umbilic torus]]
*[[Villarceau circles]]
{{col-end}}
 
==Notes==
* ''NOCIONES DE GEOMETRIA ANALITICA Y ALGEBRA LINEAL'', ISBN 978-970-10-6596-9, Author: Kozak Ana Maria, Pompeya Pastorelli Sonia, Verdanega Pedro Emilio, Editorial: McGraw-Hill, ''Edition 2007'', 744 pages, language; Spanish
* Allen Hatcher. [http://www.math.cornell.edu/~hatcher/AT/ATpage.html Algebraic topology]. Cambridge University Press, 2002. ISBN 0-521-79540-0.
* V.V. Nikulin, I.R.Shafarevich. Geometries and Groups. Springer, 1987. ISBN 3-540-15281-4, ISBN 978-3-540-15281-1.
*[http://www.mathcurve.com/surfaces/tore/tore.shtml "Tore (notion géométrique)" at Encyclopédie des Formes Mathématiques Remarquables]
 
==References==
<references/>
 
==External links==
{{Commons|Torus}}
* [http://www.cut-the-knot.org/shortcut.shtml#torus Creation of a torus] at [[cut-the-knot]]
* [http://www.dr-mikes-maths.com/4d-torus.html "4D torus"] Fly-through cross-sections of a four dimensional torus.
* [http://www.visumap.net/index.aspx?p=Resources/RpmOverview "Relational Perspective Map"] Visualizing high dimensional data with flat torus.
* [http://www.geometrygames.org/TorusGames/ "Torus Games"] Free downloadable games for Windows and Mac OS X that highlight the topology of a torus.
* [http://tofique.fatehi.us/Mathematics/Polydoes/polydoes.html Polydos]
* {{cite web|last=Séquin|first=Carlos|title=Topology of a Twisted Torus - Numberphile|url=http://www.youtube.com/watch?v=3_VydFQmtZ8|publisher=[[Brady Haran]]|accessdate=27 January 2014|format=video}}
{{Use dmy dates|date=January 2011}}
 
[[Category:Surfaces]]

Revision as of 02:34, 5 March 2014

Fa9H3D Jordan 6 World Cup Brazil yyV3h7t4

Belle Vernon Area was ready for its WPIAL Class AAA semifinal test against New Castle in the playoffs at the Civic Arena in Pittsburgh. Guided by head coach Don Asmonga and his assistant, George Estok, the Leopards won the Section 3 championship. The squad was comprised of Bill Contza, Tom Parks, Randy Giannini, Greg Grimm, John Russell, Joe Tordy, Mike Breza, Rich Zuraw, Daoug Indoff, Walter Diethorn, Guy Bizzelle, Don Wassilchalk, Mark McManus and Dave Hoffman.

Under Reagan, unemployment first went up from 7.5 percent figure in January 1981, peaking at 10.8 percent at the end of 1982. In the last two years of his first term, it declined rapidly, reaching 7.2 percent on Election Day 1984. GDP growth in Reagan's first term averaged about 3 percent a year.

To get tickets for the Inauguration you can contact your local representatives and senators. They are allotted a certain amount of tickets and will distribute them as they wish. Otherwise, the Presidential Inaugural Committee, which is formed after the new president is chosen, handles inaugural galas, balls and the parade, and the itineraries and schedules have not yet been finalized.

"We need to find solutions," Panetta told his final Pentagon news briefing. "We can't just sit here and bitch; we can't just sit here and complain; we can't just sit here and blame others; we can't just sit here and point fingers at each other; we can't just sit here and try to get sound bytes; we can't just sit here and try to make points, political points."

A week earlier I had decided cheap Nike Free 3.0 V2 Suede Gray Black White September Releases for sale to land an assignment that would give me an excuse to drink on an expense account. St. Patrick's Day was conveniently near enough that I was able to pitch a story this story to the most highly respected and popular magazine on the stands. Unfortunately, right before my pitch meeting I inadvertently exposed myself to a secretary, later being informed that it didn't look very inadvertent to witnesses, and that in fact she was the magazine's publisher. Several phone calls attempting to re spark interest in the story were met with attorney, forcing me to sell it to the makers of the functionally illiterate online offal you're now reading.

Nissan Motor Co., Ltd., Japan's second largest automotive company, is headquartered in Yokohama, Japan, and is part of authentic Nike Shox R4 White Red clearance shoes online the Renault Nissan Alliance. Operating with more than 248,000 employees globally, Nissan provided customers with more than 4.9 million vehicles in 2012, generating revenue of 9.4 trillion yen ($US118.95 billion) in fiscal 2011. With a strong commitment to developing exciting and innovative products for all, Nissan delivers a comprehensive range of 64 models under the Nissan and Infiniti brands. The heat pump uses minimal power from the battery so it does not drain it's range as the older electric heater.

Social experimentation, which began in the 1920 facilitates the adoption of new forms of social organization and optimal management. Social experiments thus perform a cognitive function and fall within the sphere of social management. A social experiment must take into account the interests of the particular group of people who are the object of the experiment, this object being one of the participants in the experiment, and the investigator himself being part of the situation he is investigating. The content and procedures of social experimentation are also conditioned by buy authentic Nike Air Max Tn Requin Blue White Green 2014 Release Dates online society legal and ethical norms. 相关的主题文章:

GEP4pI Brazil 6s V5rsCn0k

Motives for leaking Stone's memoIf you think the current crisis over Shane Stone's memo to the PM has a familiar ring, you're right. In 1994, the Liberal Party commissioned private polling on John Hewson's standing with voters. The document was damning, but no one told the leader. It was leaked, and John Hewson never recovered.

However [political parties] may now and then answer popular ends, they are likely in the course of time and things, to become potent engines, by which cunning, ambitious, and unprincipled men will be enabled to subvert the power of the people and to usurp for themselves the reins of government, destroying afterwards the very engines which have lifted them to unjust dominion.

It is only a few days after the "not guilty" verdict in the George Zimmerman trial and I wonder just where the Voting Rights Act and the civil rights struggle is headed. I can acknowledge that indeed the South has changed as mentioned in a previous blog, but have we come that far? Will the work of civil rights pioneers Medgar Evers, Rosa Parks, Martin Luther King Jr., Malcom X, Fannie Lou Hamer and Presidents John F. Kennedy and Lyndon B. Johnson, go in vain? Johnson, who took office after Kennedy was assassinated, signed the Voting Rights Act into law on Aug. 6, 1965.

'It was a very nice finish, and I'm glad to be in the cool for a while because it's getting very hot out there now. I hit a decent drive down the last then hit a good hybrid rescue club onto the Stores To Buy Michael Jackson King of Pop Black Black Air Force 1 Low fringe, and managed to get down in two from there. So I'm very happy,' he said.

Paraguay's ousted President Sale Nike Free 3.0 V4 WMS 511495-310 Volt Black Gray Online Fernando Lugo, center, smiles during a Cabinet meeting in Asuncion, Paraguay, Tuesday, June 26, 2012. Lugo said Monday that he is aiming to return to power and will rally allies at home and abroad after a landslide congressional vote forced him from office in what he called a break with democracy. Lugo has symbolically created a parallel Cabinet, attacking the legitimacy of the government that replaced him. Pictured are Lugo's Foreign Minister Jorge Lara Castro, left, Rocio Casco, director of the Socialism Movement Party, PMAS, second left, and his Health Minister Esperanza Martinez, right. (AP Photo/Jorge Saenz)

Nudged by Leno in a notably sober first segment, Obama new Nike Air Max 90 White Blue Black 2015 for sale reflected on the meaning of Gadhafi's death, a gruesome and chaotic demise recorded on cellphone video for all the world to see. The president argued that Gadhafi had had an opportunity to let Libya move on a path toward democracy peacefully.

Has a leadership personality, Deker said. never really different. She always carries herself as if she in a leadership role. She knows what to do, and she has everything planned out. She very organized, and knows what each person should be doing. The delegates at the Oregon FFA Association recently voted Rutledge in as vice president of the statewide organization.

For the first year or so, Mosby still had hopes of eventually moving on to Memphis. However, he finally gave up that desire. He once made a statement to Mr. Appling that he had found Bristol to be such a good place to live that he planned to make it home for the rest of his life. But that was not to be. Soon after the Civil War began, he enlisted in the service of the Confederacy. He left Bristol in early May 1861 and never returned here to live or practice law. His wife lived on here for a few months then she moved on to eastern Virginia. 相关的主题文章:

hS40LR Jordan 6 Brazil 3eTIQGxN

Tom Fitton, authentic Nike Air Force 1 Low Womens Futura Be True Team Orange site online president of Judicial Watch said, "I know there's this pretend division between the Residence and the so called official part of the building, but just because your lawyers say something's OK doesn't mean it's OK. We expected this president to go above and beyond in terms of ethics and adhering to the law."

We meet a man in the shadows who depends on the indignity of Cheap Mothers Day charity and who can't look people in the eyes. Why? His body, physical gifts, experience, relationships, religion, culture, family and the system itself all forced him to the fringe because he was born lame. Cowering in fear and shame, he hadn't questioned his position on the outside steps of the temple in years.

"Mitt Romney has, however, failed to recognize the very core of the American dilemma. He attacked Obama with twisted facts shortly after the announcement of the death of the US ambassador to Libya, Chris Stevens. He claimed that the US government had sympathized with the attackers in Benghazi. But not only was that factually wrong, it also demonstrated an alarmingly high level of foreign policy incompetence to his own party. None of this would Wholesale Free TR Twist Wmns Blue Grey White matter, except that Romney wants Obama's job and might even get it on Nov. 6."

Yanamala sees conspiracy to impose President's rule September 30, 2013 Doctors bid to barge into health varsityOctober 1, 2013 Jagan's tour to Krishna, Guntur put off October 1, 2013 Andhra Pradesh bifurcation unlikely, opines JACOctober 1, 2013 Mood upbeat in YSRC camp September 30, 2013 NGOs gearing up for Rythu Garjana on October 2September 30, 2013 Vijayawada Congress leaders hail Kiran as 'the new hero'September 29, 2013 APNGOs force closure of Vijayawada's Central government organisationsSeptember 29, 2013

Its ludicrous that the once renowned CBI has submitted to the special court, its inability to further proceed with the case citing insufficient evidence. The Jewish state has already lost the glare of its gilt only to pose a lack lustre outlook. The world out there is not going to buy anymore the story of Israel, as its leaning towards unjust provocations to stall the peace process. As such the day is not far off, when the flag of free Palestine will flutter pompously at the centre point of East Jerusalem. Since then all US Presidents, but JFK, were 'Christianist' converts from Judaism (Nazi collaborator Prescott Bush tribe) or have Jewsih blood, including Mr Obama! What is not mentioned is that all the US made bombs were delivered with US airplanes! Arab leaders have not served Arabs well; they need to know the facts. He was killed by Jew L. Rubinstein and covered up by Jews LBJ, Nixon, G. Ford, Warren 12 tribes. Since 1972 when China replaced US puppet Taiwan as 5th UN Veto power, the vast majority of UN Vetoes were cast by US and almost all were to stop UN from condemning genocide committing 'Chosen' Israel that recently used WMD s in 02 06 Lebanon (cluster, nuclear clad bunker buster bombs and civilian deaths) and 08 GAZA: white phosphorous, civilian killings and using children as human shields. When will the part Jew US Presidents be just to all, including American 'gentiles' (Jew word for all leprous others)? These US and Jew made Arab tragedies have been going on for 62 years! When US supports an evil Israel, the US is equally evil!. 相关的主题文章:

E3IRnB Buy Cheap Jordans 2014 WYO1eZTQ

Post crash helicopter fires have killed at least 73 people and injured at least 25 since cheap jordans Nov. 2, 1994, according to a USA TODAY review of autopsy reports and crash records. Legend Blue 11s Although crash reports do not describe helicopter fuel french blue 7s components, none of the 46 helicopters in the crashes was required to have the sturdier tanks, USA TODAY found.

The 2 team because they lost to Maryland in the 2010 championship Jordan 10 Bulls Over Broadway game. They finished 20 2 with losses to the Terps and the Tar Jordan 10 Bulls Over Broadway Heels. (MDLaxManiac) 3. A designated team member pulls them in advance for each work order and ensures they are returned to their proper places after use. Jordan 10 Lady Liberty Not only has the improvement cheap jordans enhanced the efficiency and jordan 4 oreo workflow of the punch cells, it has facilitated Jordan 11 Legend Blue maintenance and inventory improvements, as well.Metcam Turret Punch Tool CenterAccording to Metcam Quality Manager Richard Uber, one of the core benefits of the Kaizen initiatives is that workers on the production floor french blue 7s are the ones coming up with project ideas. Of the nine changes Metcam has implemented, only two were overseen by consultants hired in late 2013.

Recently Michelle Bachmannappeared on "Meet the Press" and revealed her findings to David Gregory. In her appearance Jordan 10 Lady Liberty she said, "It is shocking the revelations Jordan 11 Legend Blue of jordan 7 french blue all the money that been spent There is a Congressional Research Service report that just was issued in February, and we discovered that secretly, unbeknownst to members of Congress, over $105 billion was hidden in the Obamacare jordan 4 oreo legislation to fund the implementation of Obamacare. This Lady Liberty 10s is something that wasn known.". 相关的主题文章：

1Q8B6M buy jordans CVBxlJsH

On Friday, he rushed for more than 300 yards the exact number remains a mystery depending on who you ask. But what made the number even more impressive was the opponent. It wasn't some paper defense like Uintah. Todd, MonticelloThere are many people that can and will be blamed for this accident. First, you have pilot error that could have caused the french blue 7s crash. Second, there should have been someone in jordan 4 oreo the control tower telling the pilot he was on the wrong runway.

Back jordan 4 oreo in Bulls Over Broadway 10s New York, Radnor acknowledges that he has some growing up to do and cheap jordans asks Reaser to go for a walk. However, he isn't quite done with Kenyon, as Magaro phones to confess to taking an overdose of pills and Radnor has to overcome his fear of flying to sit by his bedside. Having made his Jordan 10 Lady Liberty peace with Legend Blue 11s Olsen, Radnor returns east and snuggles with Reaser as she muses jordan 4 oreo about how nice it will be for them to grow old together..

Family and friends will assemble at the church at 12:45. At the funeral home. Services entrusted to the care of Franklin Hutcherson Funeral Home. I was only a couple of hundred metres offshore when I came up for a breath to my left. In the sea of black suited arms, legs and goggles, I saw something that was more comforting than the final exit buoys; more extraordinary than a hundred foot eel; Jordan 11 Legend Blue more beautiful Jordan 10 Lady Liberty than a pond lily. It was Jordan 10 Bulls Over Broadway my husband's Bulls Over Broadway 10s face, mere inches from my own.

Overall, the portfolio is performing well from a credit perspective and we continue to feel good about ACSF prospects over the long term."Malon Jordan 10 Bulls Over Broadway Wilkus, Chair and Chief Executive Officer commented, "We were pleased to announce a dividend of $0.28 per share for the third quarter. Our current annualized dividend represents a 7.5% yield on our NAV and an 8.6% yield on Jordan 10 Lady Liberty our Jordan 10 Lady Liberty September 30th closing share price. While we experienced depreciation this quarter, it is important to note that it was due to market spreads widening and not credit deterioration. 相关的主题文章：

l2tFYQ cheap jordans 2014 CNVS7MUU

Mitch Daniels has put Indiana on a path to financial prosperity. Here comes the government. States all across America are facing unprecedented budget crises. The heyday of the Roman war chariot was about 1,500 years ago, but jordan 4 oreo they may be coming back. Hopefully they won be used to subjugate neighboring nations. But the excitement of careening around a dirt track in a flimsy looking, two wheeled cart a la Ben Hur, sans biological horses, seems to be calling to some modern gear Jordan 10 Bulls Over Broadway heads.

As I seem to recall, Mr. Obama ran for office freely. As the winner of the requisite number electoral votes, he gained the right to assume office but he could have decided against it had he chosen to do so. IS was kicked cheap jordans out of al Qaida in May after disobeying Lady Liberty 10s its leader, Ayman al Zawahiri. So far, IS has not publicly responded to al Qaida's Jordan 10 Lady Liberty calls to reunite the most recent on Oct. 17 from al Qaida in the Arabian Peninsula, the Yemen based offshoot cheap jordans that denounced the jordan 4 oreo airstrikes and called on rival militant Jordan 10 Bulls Over Broadway groups to stop their infighting and together train their sights Jordan 11 Legend Blue on the West..

Season 8 of "American Idol" is commonly referred to as "Battle of the Davids," as rocker David Cook Jordan 10 Lady Liberty and teen pop cutie David Archuleta went neck and neck throughout the entire competition. The rock star ultimately prevailed in 2008 with his raw voice and acoustic renditions of timeless hits from all genres. Jordan 11 Legend Blue As the show ended, Cook released his first single "Time french blue 7s of My Life," which went platinum in 2008.

It doesn't get any easier for the Utes from this point forward. Utah goes on the road this week to face eighth ranked UCLA. cheap jordans Four of the Utes' remaining eight opponents Jordan 11 Legend Blue are currently ranked 16th or higher Jordan 11 Legend Blue (and two more opponents are getting votes in the polls). 相关的主题文章：

hhw3re cheap jordans nzyZ9V0O

Some have questioned using completion as a method of evaluation. cheap jordans Kevin Carey, director of the Education Policy Program at the New America Foundation, wrote that judging courses that require such little effort to enroll in by their completion rates reflects how the traditional jordan 7 french blue college mindset continues to dominate and limit the public understanding of what higher education can and should mean. Legend Blue 11s This year, in an interview on the completion rates, Keller encouraged reframing the discussion around such courses.

Stones River Mall to host fun filled family event Aug. 2More than a photographer: Richard jordan 4 oreo Claude ShacklettPark Jordan 10 Lady Liberty View Meadows Family Night Photo GalleryA mother's love is still the greatest gift of allWELLNESS SPOTLIGHT: What is Sibling Denial?MRS. MURFREESBORO: We should all enjoy our family when we have the chanceRead to Jordan 10 Bulls Over Broadway Succeed's Me and My Family literature night Jordan 10 Bulls Over Broadway a successBURRISS: Reporters need survival skills given political climateLOGUE: Pedophiles keep slipping into education systemWOODY: Athletes owe it to fans to speak upView AllI am taking a jordan 4 oreo teacher training course at my mosque right now and am astounded at how little I know about the art and science of teaching.

If you have enjoyed this column, may I suggest you scroll down this page and press the SUBSCRIBE box? It's FREE. Thank you for your patronage. Schwab, Jr. Large portions of the Republican agenda passed Lady Liberty 10s because Williams kept his promise to bring those matters Jordan 10 Bulls Over Broadway to the floor, which is a vast improvement over former Speaker Jimmy Naifeh. Naifeh understood that many Democrats from rural districts jordan 4 oreo agree with Republicans on social issues and Second Amendment rights, and that even with a Democratic majority in Jordan 11 Legend Blue the House, pro life jordan 4 oreo bills, gun bills, and other conservative matters would pass the House with solid votes in favor. Members who played ball with the Speaker Jordan 10 Bulls Over Broadway were given the money for their district to help them Jordan 11 Legend Blue get re elected regardless of party.. 相关的主题文章：

gXts78 jordans PajOBp3q

This system took the idea of pilot injection squirting a small amount of fuel into the cylinder jordan 4 oreo to 'prime' the combustion chamber for the main ignition process and refined it still further. In this instance, the main injection is divided into a series of smaller injections, allowing smoother, more gradual combustion that utilises fuel more efficiently. The electronic control units, Jordan 11 Legend Blue therefore, have to be astonishingly precise.

Each speaker has multiple inputs, Jordan 10 Lady Liberty a built in Jordan 10 Lady Liberty amplifier, multiple tweeters and a subwoofer to bring out the bass. jordan 4 oreo Altek Lansing also designs the system so that each speaker can play a different song if desired. The cost Jordan 10 Bulls Over Broadway of using Wi Fi to create multi room audio systems depends on the cost of the jordan 7 french blue Wi Fi speakers you purchase..

On December 5, 2002, Rabinovitz communicated with bankruptcy counsel Herbert S. Weinberg jordan 4 oreo and made a decision that a Jordan 10 Lady Liberty petition be filed in the Federal Bankruptcy Court on behalf of Millennium. On December 9, 2002, after the preparation of that petition, Weinberg sent a facsimile letter to Mahlowitz also demanding that Mahlowitz voluntarily discharge the attachment or Jordan 11 Legend Blue else a bankruptcy proceeding would be filed on behalf of jordan 7 french blue Millennium.

The Phantom Lightweight version of the Tactical Pants came out in 2011, three years after cheap jordans the Jordan 10 Bulls Over Broadway release of the "Original". This model has the same fit and features of the original pant Jordan 10 Lady Liberty but in a 6.5 oz (much lighter) polyester/cotton mini jordan 4 oreo ripstop fabric. We looked at both the full on pants and shorts. 相关的主题文章：

Retrieved from "https://en.formulasearchengine.com/index.php?title=Andromeda_Galaxy&oldid=285578"