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The rotation operator gates (), and () are the analog rotation matrices in three Cartesian axes of SO(3), [c] along the x, y or z-axes of the Bloch sphere projection. As Pauli matrices are related to the generator of rotations, these rotation operators can be written as matrix exponentials with Pauli matrices in the argument.
The minus–plus sign, ∓, is generally used in conjunction with the ± sign, in such expressions as x ± y ∓ z, which can be interpreted as meaning x + y − z or x − y + z (but not x + y + z or x − y − z). The ∓ always has the opposite sign to ±.
I := λx.x S := λx.λy.λz.x z (y z) K := λx.λy.x B := λx.λy.λz.x (y z) C := λx.λy.λz.x z y W := λx.λy.x y y ω or Δ or U := λx.x x Ω := ω ω. I is the identity function. SK and BCKW form complete combinator calculus systems that can express any lambda term - see the next section. Ω is UU, the smallest term that has no normal form.
The paraboloid y = x z is shown in blue and orange. The paraboloid x = y z is shown in cyan and purple. In the image the paraboloids are seen to intersect along the z = 0 axis. If the paraboloids are extended, they should also be seen to intersect along the lines z = 1, y = x; z = −1, y = −x. The two paraboloids together look like a pair of ...
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
Spectrogram of [ʏ]. The near-close front rounded vowel, or near-high front rounded vowel, [1] is a type of vowel sound, used in some spoken languages.. The symbol in the International Phonetic Alphabet that represents this sound is ʏ , a small capital version of the Latin letter y, and the equivalent X-SAMPA symbol is Y.
The evolution of the universe and its horizons in proper distances. The x-axis is distance, in billions of light years; the y-axis is time, in billions of years since the Big Bang. This is the same model as in the earlier figure, with dark energy and an event horizon.
Turned v (majuscule: Ʌ, minuscule: ʌ) is a letter of the Latin alphabet, based on a turned form of the letter V. It is used in the orthographies of Dan , Ch’ol , Nankina , Northern Tepehuán , Temne , Oneida , and Wounaan and also some orthographies of Ibibio .