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A quadric is said to be non-degenerate if the matrix is invertible. A non-degenerate quadric is non-singular in the sense that its projective completion has no singular point (a cylinder is non-singular in the affine space, but it is a degenerate quadric that has a singular point at infinity).
Simultaneously generalizing the case of imaginary quadratic fields and cyclotomic fields is the case of a CM field K, i.e. a totally imaginary quadratic extension of a totally real field. In 1974, Harold Stark conjectured that there are finitely many CM fields of class number 1. [12] He showed that there are finitely many of a fixed degree.
In algebraic number theory, a quadratic field is an algebraic number field of degree two over , the rational numbers. Every such quadratic field is some Q ( d ) {\displaystyle \mathbf {Q} ({\sqrt {d}})} where d {\displaystyle d} is a (uniquely defined) square-free integer different from 0 {\displaystyle 0} and 1 {\displaystyle 1} .
Towel volleyball: towel volleyball is a popular form of outdoor entertainment. The game takes place in a volleyball court, and players work in pairs, holding towels in their hands and attempting to throw the ball into the opponent's field. This version can also be played with blankets held by four people. There are several variations. [54]
The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...
Geometrically, the discriminant of a quadratic form in three variables is the equation of a quadratic projective curve. The discriminant is zero if and only if the curve is decomposed in lines (possibly over an algebraically closed extension of the field). A quadratic form in four variables is the equation of a projective surface.
Every month, thousands of Eritreans attempt to flee repression, torture and indefinite forced conscriptions by embarking on a dangerous journey to Europe.
Float serves are only possible with minimal to no spin of the volleyball while it is moving in the air. [1] Unlike a topspin serve, which uses the spin of the ball to create a constant difference in pressure that drives the ball downward at a high speed, the float serve can be affected in any direction by the random forces of the air and pressure (drag, lift, drag crisis, turbulence) because ...