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Although the concept of U-value (or U-factor) is universal, U-values can be expressed in different units. In most countries, U-value is expressed in SI units, as watts per square metre-kelvin: W/(m 2 ⋅K) In the United States, U-value is expressed as British thermal units (Btu) per hour-square feet-degrees Fahrenheit: Btu/(h⋅ft 2 ⋅°F)
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Exponential Utility Function for different risk profiles. In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes referred to as uncertainty) is present, in which case expected utility is maximized. Formally, exponential utility is given by:
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
Law of the unconscious statistician: The expected value of a measurable function of , (), given that has a probability density function (), is given by the inner product of and : [34] [()] = (). This formula also holds in multidimensional case, when g {\displaystyle g} is a function of several random variables, and f {\displaystyle f} is ...
Note that, as per the affine transformation property alluded to above, the utility function gives the same preferences orderings as does ; thus it is irrelevant that the values of and its expected value are always negative: what matters for preference ordering is which of two gambles gives the higher expected utility, not the numerical values ...
An initial value problem is a differential equation ′ = (, ()) with : where is an open set of , together with a point in the domain of (,),called the initial condition.. A solution to an initial value problem is a function that is a solution to the differential equation and satisfies
The expectation value of the total Hamiltonian H (including the term V ee) in the state described by ψ 0 will be an upper bound for its ground state energy. V ee is −5E 1 /2 = 34 eV, so H is 8E 1 − 5E 1 /2 = −75 eV. A tighter upper bound can be found by using a better trial wavefunction with 'tunable' parameters.