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Receptors 2
Published in James E. Ferrell, Systems Biology of Cell Signaling, 2021
where the coefficients in the denominator of the form (ni) represent the combinations of n things taken i at a time, as given by (ni)=n!i!(n−i)!, and are the binomial coefficients from the nth row of Pascal’s triangle.
Combinatorics
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Binomial coefficients are usually presented in a triangular array, called Pascal’s Triangle (although it certainly predates Pascal; see [2] or [4], which specify earlier Chinese, Indian, and European sources). In the figure below, the entry in row n and column k is (nk).
Mathematical Background
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
2.17 Definition Let n and k be non-negative integers. The binomial coefficient(nk) is the number of different ways of choosing k distinct objects from a set of n distinct objects, where the order of choice is not important.
An extended gained and lost dominance score method based risk prioritization for Fine-Kinney model with interval type-2 fuzzy information
Published in Human and Ecological Risk Assessment: An International Journal, 2022
Weizhong Wang, Wenjun Jiang, Xiao Han, Shuli Liu
(Maclaurin 1729; Qin and Liu 2015a). Assume that the set is a collection of non-negative real numbers, then the following aggregation operator for the non-negative real numbers is defined as the MSM operator. in which, is the binomial coefficient, is any a tuple combination of
Comments on “Effect of the finite width of the temperature transition in diffusive condensation particle counters” by J. Fernandez de la Mora
Published in Aerosol Science and Technology, 2020
The first recursion formula can be put into non-recursive form as where is the binomial coefficient and is the triple factorial or 3rd order multifactorial. Note that at such that The non-recursive form for the coefficients is rather more challenging to deduce.
Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations
Published in Inverse Problems in Science and Engineering, 2018
Assume , then using the binomial theorem for both and (which for converges as ) and using that the negative binomial coefficient can be written as follows: