The apparent paradox of the divergent partition function can be resolved, and it does not mean that either quantum theory or statistical mechanics are wrong. You may have access to this article ...

👉 Learn how to graph exponential functions involving horizontal shift. An exponential function is a function that increases rapidly as the value of x increases. To graph an exponential function, it ...

👉 Learn how to evaluate a piecewise function. A piecewise function is a function which uses different rules for different intervals. When evaluating a piecewise function, pay attention to the ...

Abstract: Partition functions and graph polynomials have found many applications in combinatorics, physics, biology and even the mathematics of finance. Studying their complexity poses some problems.

Abstract: Recent work has related the belief propagation algorithm for probabilistic inference problem to some approximations to the free energy function in statistical physics. In this paper we ...