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The law of iterated logarithms operates "in between" the law of large numbers and the central limit theorem.There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums S n, scaled by n −1, converge to zero, respectively in probability and almost surely:
Teichmüller's theorem [18] states that between two marked Riemann surfaces (,) and (,) there is always a unique quasiconformal mapping in the isotopy class of which has minimal dilatation. This map is called a Teichmüller mapping.
This standard defines property classes, the metric equivalent of a screw grade, that are almost identical to those defined by ISO 898-1, [2] except for the addition of the 8.8.3 and 10.9.3 classes. These two additional standards are fasteners that have the same mechanical properties as their base property class (i.e. 8.8 and 10.9), but are made ...
By Landau's theorem and the observation about the range of H in the proof of the Little Picard Theorem, there is a constant C > 0 such that |H′(w)| ≤ C / Re(w). Thus, for all real numbers x ≥ 2 and 0 ≤ y ≤ 2π,
The split form, EVIII (or E 8(8)), which has maximal compact subgroup Spin(16)/(Z/2Z), fundamental group of order 2 (implying that it has a double cover, which is a simply connected Lie real group but is not algebraic, see below) and has trivial outer automorphism group.
The theory of Verma modules contains the highest weight theorem. This is the approach taken in many standard textbooks (e.g., Humphreys and Part II of Hall). The Borel–Weil–Bott theorem constructs an irreducible representation as the space of global sections of an ample line bundle; the highest weight theorem results as a consequence. (The ...
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The nth coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the nth region is n times n x n.
The Laplace transform is analytic in the region of absolute convergence: this is a consequence of Fubini's theorem and Morera's theorem. Similarly, the set of values for which F ( s ) converges (conditionally or absolutely) is known as the region of conditional convergence, or simply the region of convergence (ROC).