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  • zeros
  • If the coefficients a_j are positive and the poles b_j are distinct, then r must switch from +inf to -inf as x passes through each pole, and it follows that r has exactly N-1 real zeros lying between the poles and also one more real zero lying to the right of all the poles. (mathworks.com)
  • In complex analysis, zeros of holomorphic functions and meromorphic functions play a particularly important role because of the duality between zeros and poles. (wikipedia.org)
  • This characterization of zeros and poles implies that zeros and poles are isolated, that is, every zero or pole has a neighbourhood that does not contain any other zero and pole. (wikipedia.org)
  • Because of the order of zeros an poles being defined as a non-negative number n and the symmetry between them, it is often useful to consider a pole of order n as a zero of order -n and a zero of order n as a pole of order -n. (wikipedia.org)
  • A meromorphic function may have infinitely many zeros and poles. (wikipedia.org)
  • If f is a function that is meromorphic on the whole Riemann sphere, then it has a finite number of zeros and poles, and the sum of the orders of its poles equals the sum of the orders of its zeros. (wikipedia.org)
  • Every rational function is meromorphic on the whole Riemann sphere, and, in this case, the sum of orders of the zeros or of the poles is the maximum of the degrees of the numerator and the denominator. (wikipedia.org)
  • South Pole
  • The Amundsen-Scott South Pole Station is a United States scientific research station at the South Pole , the southernmost place on the Earth . (wikipedia.org)
  • Before November 1956, there was no permanent human structure at the South Pole, and very little human presence in the interior of Antarctica at all. (wikipedia.org)
  • Since the Amundsen-Scott Station is located at the South Pole, it is at the only place on the land surface of the Earth where the Sun is continuously up for six months and then continuously down for six months. (wikipedia.org)
  • During the six-month "night", it gets extremely cold at the South Pole, with air temperatures sometimes dropping below −73 °C (−99 °F). This is also the time of the year when blizzards, sometimes with gale -force winds, strike the Amundsen-Scott Station. (wikipedia.org)
  • Ceremonial South Pole. (wikipedia.org)
  • The Amundsen-Scott South Pole Station during the 2007-2008 summer season. (wikipedia.org)
  • lands
  • In the lands vital to German expansion, hundreds of thousands of Poles were deported, replaced by ethnic Germans. (ushmm.org)
  • Live
  • In the 1950s, a study of the city noted that "nearly all the Poles live in this area [South Omaha]", and that the neighborhoods were "the most segregated and congested of all the districts in Omaha. (wikipedia.org)
  • especially
  • Discusses the organization and structure of concentration camps, prisoner categories, and daily life and activities of Poles, especially members of the intelligentsia. (ushmm.org)
  • During the late 19th century rapid industrialisation in the Ruhr region attracted about 300,000 Poles, especially from East Prussia, West Prussia, Poznań, and Silesia. (wikipedia.org)
  • high
  • Given that only 30% of first year ice survives the summer, the chances that there will be significant open water at the pole itself is high. (realclimate.org)
  • Share
  • Increase of Poles number and share was caused by the reduction of so-called "not indicated" ethnicity in the Residents' Register. (wikipedia.org)
  • results
  • Peter Poles (born February 6, 1978 in Slovenj Gradec) is a Slovenian television personality, responsible for presenting the Slovenian televote results in various editions of Eurovision Song Contest. (wikipedia.org)
  • majority
  • Only since 18th century there were several waves of political and economic emigration of Poles to Bessarabia, the land which constitutes the majority of modern Moldova. (wikipedia.org)
  • Close
  • This new ice formed quite close to the Pole, and with the prevailing winds and currents (which push ice from Siberia towards Greenland) is now over the Pole itself. (realclimate.org)
  • length
  • The fetal pole may be seen at 2-4 mm crown-rump length (CRL). (wikipedia.org)
  • Personal preference, skiing technique, and differing body types play a big part in pole length. (backcountry.com)
  • The shortest length of the pole when all sections have been compacted. (mec.ca)
  • The Poles River flows to the bottom of the northeast bay of Evans Lake, facing an island with a length of 1.1 kilometres (0.68 mi). (wikipedia.org)
  • Union
  • After a brief period of liberal attitude towards Poles in the Soviet Union, the nationality had undergone repressions, dispersal, and assimilation, and its history remained largely a blank spot for a long time. (wikipedia.org)
  • half
  • You'll hit half the line of rails and then wildly traverse over to the last set of jumps that the ski resort has set up for the season, and Line's Pin Ski Pole follows all your spins and jibs. (backcountry.com)
  • members
  • Around the turn of the century, members of the Hanscom Park Methodist Episcopal Church became concerned with the "lawlessness and destitute behavior" of Poles living in Sheelytown. (wikipedia.org)
  • Order
  • In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0. (wikipedia.org)
  • The Riemann zeta function is also meromorphic in the whole complex plane, with a single pole of order 1 at z = 1. (wikipedia.org)
  • It has a pole of order 1 or simple pole at z = 0 , {\displaystyle z=0,} and a simple zero at infinity. (wikipedia.org)
  • presence
  • In that case, the report was of the presence of some open water at the pole - which as the correction stated, is not that uncommon as ice floes and leads interact. (realclimate.org)
  • Poles have had a presence in Omaha since the late 1870s, when they started arriving to work in the meatpacking, stockyards, smelting and railroad industries. (wikipedia.org)
  • good
  • We can think of an almost endless number of obscure reasons why carrying poles is a good idea (Chris once managed to stretcher an injured Labrador off a mountain with a set! (upandunder.co.uk)
  • Point
  • pole of rotation ( Euler pole ) A point on the Earth 's surface which defines a line through the centre of the Earth about which the relative motion of two plates may be described. (encyclopedia.com)
  • renewed questions
  • Nevertheless, a few recent scholarly works have renewed questions concerning active participation by some Poles in pogroms and atrocities committed against Jews. (ushmm.org)
  • among
  • Poles then spent the next few seasons jumping among the New York Lincoln Stars, Brooklyn Royal Giants, and the Hilldale Daisies. (wikipedia.org)
  • area
  • The Poles River is a tributary of Evans Lake in Regional County Municipality (RCM) of Eeyou Istchee Baie-James (municipality) in the area of the Nord-du-Québec, Canadian province of Quebec, in Canada. (wikipedia.org)
  • A statue was placed in honor of Poles from the Omaha area who fought with the Blue Army during World War I at St. John's Cemetery in the suburb of Bellevue. (wikipedia.org)
  • The Concord Spirit Poles were a controversial public art project installed in the Bay Area city of Concord, California in 1989, at the direction of artist Gary Rieveschl, at a cost of approximately $100,000. (wikipedia.org)
  • dance
  • Join us for a multi-level atlanta-style funky pole tricks class catered to ladies that want to pole dance ATL-style! (ustream.tv)