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The depth of supercritical flow, y 1, ‘jumps’ up to its subcritical conjugate depth, y 2, and the result of this abrupt change in flow conditions is considerable turbulence and Energy Loss, E L. [4] Figure 1 shows a schematic of typical jump characteristics where E 1 is the energy of the upstream flow, E 2 is the energy of the downstream ...
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]
The Harris–Benedict equation (also called the Harris-Benedict principle) is a method used to estimate an individual's basal metabolic rate (BMR).. The estimated BMR value may be multiplied by a number that corresponds to the individual's activity level; the resulting number is the approximate daily kilocalorie intake to maintain current body weight.
The Holliday-Segar formula is a formula to help approximate water and caloric loss (and therefore the water requirements) using a patient's body weight. [1] Primarily aimed at pediatric patients, the Holliday-Segar formula is the most commonly used estimate of daily caloric requirements. [ 2 ]
The formula is still valid if x is a complex number, and is also called Euler's formula in this more general case. [1] Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2]
In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A. [ 1 ] If A is a differentiable map from the real numbers to n × n matrices, then
The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages.
Exponential utility implies constant absolute risk aversion (CARA), with coefficient of absolute risk aversion equal to a constant: ″ ′ =. In the standard model of one risky asset and one risk-free asset, [1] [2] for example, this feature implies that the optimal holding of the risky asset is independent of the level of initial wealth; thus on the margin any additional wealth would be ...