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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
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 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 ...
The Modern Variation is the most common variation of the Alekhine Defence. As in the Exchange Variation, White accepts a more modest spatial advantage, and hopes to be able to hang on to it. There are a number of possible Black responses: 4...Bg4, pinning the knight is the most common response, which White usually parries with 5.Be2.
The Semi-Slav Defense is a variation of the Queen's Gambit Declined chess opening defined by the position reached after the moves: 1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. Nc3 e6. The position may readily be reached by a number of different move orders. Black's supporting pawns resemble a mixture of the Orthodox Queen's Gambit Declined, e6, and the Slav ...
The Bogo-Indian Defence is a chess opening characterised by the moves: . 1. d4 Nf6 2. c4 e6 3. Nf3 Bb4+. The position after 1.d4 Nf6 2.c4 e6 is common. The traditional move for White here is 3.Nc3, threatening to set up a big pawn centre with 4.e4.
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]