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Hace 1 día · A fundamental result in analytical mechanics is D'Alembert's principle, introduced in 1708 by Jacques Bernoulli to understand static equilibrium, and developed by D'Alembert in 1743 to solve dynamical problems. The principle asserts for N particles the virtual work, i.e. the work along a virtual displacement, δr k, is zero:
Hace 2 días · The Bernoulli numbers OEIS: A164555 (n)/ OEIS: A027642 (n) were introduced by Jakob Bernoulli in the book Ars Conjectandi published posthumously in 1713 page 97. The main formula can be seen in the second half of the corresponding facsimile.
Hace 3 días · What is Bernoulli’s Principle? What is Lift? What other Factors Influence Lift? Conclusion. What is Bernoulli’s Principle? Bernoulli’s Principle applied to aerodynamics tells us that: “In a streamlined flow of an ideal fluid, the sum of the static pressure and the dynamic pressure remains constant” Let’s unpack this.
Hace 3 días · When k is 2 and n is 1, the multinomial distribution is the Bernoulli distribution. When k is 2 and n is bigger than 1, it is the binomial distribution. When k is bigger than 2 and n is 1, it is the categorical distribution.
Hace 4 días · A Bessel equation is a special case of a confluent hypergeometric equation. The Bessel function of the first kind of order ν: where Γ(z) = ∫∞0xz − 1e − xdx is the gamma function. There are two Bessel functions of the second kind of order ν: one is called the Weber function: Yν(x) = cosνπJν(x) − J − ν(x) sinνπ.
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Hace 2 días · In 1961 Daniel Ellsberg published an article titled “Risk, Ambiguity, and the Savage Axioms” in the Quarterly Journal of Economics, which became a seminal contribution to the theory of decision-making under uncertainty. This paper analyzes Ellsberg’s 1961 classic, situates it within the context of decision-making theory in the 1950s and early 1960s and within the development of Ellsberg ...
