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This notation represents (i) the number of vertices, (ii) the number of polygons around each vertex (arranged clockwise) and (iii) the number of sides to each of those polygons. For example: 3 6 ; 3 6 ; 3 4 .6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling.
The converse of the statement above is, however, not always true. For example, the digital root of 12, which is not a triangular number, is 3 and divisible by three. If x is a triangular number, a is an odd square, and b = a − 1 / 8 , then ax + b is also a triangular number.
The constant random variables X = μ. The cumulant generating function is K(t) = μt. The first cumulant is κ 1 = K′(0) = μ and the other cumulants are zero, κ 2 = κ 3 = κ 4 = ⋅⋅⋅ = 0. The Bernoulli distributions, (number of successes in one trial with probability p of success).
There is a straightforward process to convert any linear program into one in standard form, so using this form of linear programs results in no loss of generality. In geometric terms, the feasible region defined by all values of x {\displaystyle \mathbf {x} } such that A x ≤ b {\textstyle A\mathbf {x} \leq \mathbf {b} } and ∀ i , x i ≥ 0 ...
An immutable sequence of numbers commonly used for looping a specific number of times in for loops [120] range (− 1, 10) range (10, − 5, − 2) set: mutable Unordered set, contains no duplicates; can contain mixed types, if hashable {4.0, 'string', True} set str: immutable A character string: sequence of Unicode codepoints 'Wikipedia ...
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a ...
Simplified Chinese Pinyin Notes Buddha's delight: 羅漢齋: 罗汉斋: luóhàn zhāi: a vegetarian dish popular among Buddhists Pickled vegetables: 榨菜: 榨菜: jiàngcài: various vegetables or fruits that have been fermented by pickling with salt and brine, or marinated in mixtures based on soy sauce or savory bean pastes
Here, A stands for the electromagnetic potential 1-form, J is the current 1-form, F is the field strength 2-form and the star denotes the Hodge star operator. This is exactly the same Lagrangian as in the section above, except that the treatment here is coordinate-free; expanding the integrand into a basis yields the identical, lengthy expression.