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The Sun–Earth Lagrangian points L 2 and L 1 are usually given as 1.5 million km from Earth. If the mass of the smaller object (M E) is much smaller than the mass of the larger object (M S), then the quintic equation can be greatly reduced and L 1 and L 2 are at approximately the radius of the Hill sphere, given by:
The following names are assigned to polynomials according to their degree: [2] [3] [4] Special case – zero (see § Degree of the zero polynomial, below) Degree 0 – non-zero constant [5] Degree 1 – linear; Degree 2 – quadratic; Degree 3 – cubic; Degree 4 – quartic (or, if all terms have even degree, biquadratic) Degree 5 – quintic
In binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. Thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. The factor (2 −1) is a right arithmetic shift, a (0) results in no operation (since 2 0 = 1 is the multiplicative identity element), and a (2 1) results in a left arithmetic shift ...
for certain polynomials A n (z) and B n (z) with integer coefficients, A n (z) of degree φ(n)/2, and B n (z) of degree φ(n)/2 − 2. Furthermore, A n (z) is palindromic when its degree is even; if its degree is odd it is antipalindromic. Similarly, B n (z) is palindromic unless n is composite and n ≡ 3 (mod 4), in which case it is ...
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree.
The Hoffman–Singleton theorem states that any Moore graph with girth 5 must have degree 2, 3, 7, or 57. The Moore graphs are: [3] The complete graphs K n on n > 2 nodes (diameter 1, girth 3, degree n − 1, order n) The odd cycles C 2n+1 (diameter n, girth 2n + 1, degree 2, order 2n + 1). This includes C 5 with diameter 2, girth 5, degree 2 ...
It is inspired by the typographic practice of end marks, an element that marks the end of an article. [1] [2] In Unicode, it is represented as character U+220E ∎ END OF PROOF. Its graphic form varies, as it may be a hollow or filled rectangle or square. In AMS-LaTeX, the symbol is automatically appended at the end of a proof environment ...