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In the Ruy Lopez, Exchange Variation pieces (White's bishop and Black's knight) rather than pawns are traded. In the Exchange Variation of the Grunfeld Defense, both a pair of pawns and a pair of knights are traded. The diagram at right shows a position in the Exchange Variation of the French Defense, after the moves: 1. e4 e6 2. d4 d5 3. exd5 exd5
The variation's most devoted practitioner has been its eponym, Ashot Nadanian.Various famous players such as Viktor Korchnoi, Maxime Vachier-Lagrave, Bu Xiangzhi, Alexander Riazantsev, Igor Lysyj, Walter Browne, Smbat Lputian, Timur Gareyev, Jonathan Rowson, Andrei Kharlov, Bogdan Lalić have employed it at some time or another, though few have made it their main line against the Grünfeld ...
After 6.cxd5 Nxg5 7.Nxg5 e6, White has 8.Qd2 exd5 9.Qe3+, with attacking chances (though the interpolation 8...h6 9.Nf3 exd5 is a significant alternative), or the more usual 8.Nf3 exd5 after which play generally proceeds on lines analogous to the Queen's Gambit Declined, Exchange Variation, with a queenside minority attack by White (b2–b4 ...
The Exchange Variation can be a powerful psychological weapon. Black is forced to play actively, which is psychologically difficult if all one needs is a draw. Lasker's famous win against Jose Raul Capablanca in the St. Petersburg 1914 chess tournament is an example of this. With a lead in the tournament, Capablanca was intent on simplifying ...
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]
The Marshall Defense is a chess opening that begins with the moves: . 1. d4 d5 2. c4 Nf6?!. The Marshall Defense is a fairly dubious variation of the Queen's Gambit Declined.It was played by Frank Marshall in the 1920s, but he gave it up after losing with it to Alekhine at Baden-Baden in 1925. [1]
The volatilities in the market for 90 days are 18% and for 180 days 16.6%. In our notation we have , = 18% and , = 16.6% (treating a year as 360 days). We want to find the forward volatility for the period starting with day 91 and ending with day 180.
The hyperexponential distribution is an example of a mixture density. An example of a hyperexponential random variable can be seen in the context of telephony , where, if someone has a modem and a phone, their phone line usage could be modeled as a hyperexponential distribution where there is probability p of them talking on the phone with rate ...