Search results
Results from the WOW.Com Content Network
It may not be obvious why the partition function, as we have defined it above, is an important quantity. First, consider what goes into it. The partition function is a function of the temperature T and the microstate energies E 1, E 2, E 3, etc. The microstate energies are determined by other thermodynamic variables, such as the number of ...
Consider the sum = = where >0 for all N.Since all the terms are positive, the value of S must be greater than the value of the largest term, , and less than the product of the number of terms and the value of the largest term.
In each iteration, select two k-tuples A and B in which the difference between the maximum and minimum sum is largest, and combine them in reverse order of sizes, i.e.: smallest subset in A with largest subset in B, second-smallest in A with second-largest in B, etc. Proceed in this way until a single partition remains. Examples:
A Riemann sum of over [,] with partition is defined as = = (), where = and [,]. [1] One might produce different Riemann sums depending on which x i ∗ {\displaystyle x_{i}^{*}} 's are chosen. In the end this will not matter, if the function is Riemann integrable , when the difference or width of the summands Δ x i {\displaystyle \Delta x_{i ...
The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...
Such is the case for the partition function in quantum field theory. A common, useful modification to the partition function is to introduce auxiliary functions. This allows, for example, the partition function to be used as a generating function for correlation functions. This is discussed in greater detail below.
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
Let C i (for i between 1 and k) be the sum of subset i in a given partition. Instead of minimizing the objective function max(C i), one can minimize the objective function max(f(C i)), where f is any fixed function. Similarly, one can minimize the objective function sum(f(C i)), or maximize min(f(C i)), or maximize sum(f(C i)).