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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 ...
A tricky move order by Black, trying to transpose into the Grünfeld Defence if White plays natural developing moves, e.g., 4.Nc3 Nxd5 is the Grünfeld Exchange Variation. But if White plays 4.Qa4+, Black cannot regain the pawn on d5 and will not have enough compensation for the pawn.
In finance, an option on realized variance (or variance option) is a type of variance derivatives which is the derivative securities on which the payoff depends on the annualized realized variance of the return of a specified underlying asset, such as stock index, bond, exchange rate, etc.
The Exchange Variation of the Ruy Lopez is a chess opening that begins with the moves: 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Bxc6. Black may recapture on c6 with either pawn; although 4...bxc6 is playable, 4...dxc6 is almost always chosen at master level. Black has gained the bishop pair at the cost of a weakened pawn structure, having doubled pawns ...
This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line.. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to be much less than the inherent precision of the floating-point arithmetic used to perform the computation.
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]