High accuracy for atomic calculations involving logarithmic sums

High accuracy for atomic calculations involving logarithmic sums

A hybrid mean value involving a new Gauss sums and Dedekind sums

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

Quantum Monte Carlo for High Accuracy ab initio Calculations

Quantum Monte Carlo (QMC) is among the most accurate ab initio Quantum Chemistry methods available. Furthermore, in stark contrast with comparable methods, it is trivially parallelizable, it requires only a negligible amount of memory, and it’s computational cost scales as only O(N^3). Unfortunately, as a stochastic method, it requires a sizeable number of state space evaluations. We have been ...

Maintaining Partial Sums in Logarithmic Time

We present a data structure that allows to maintain in logarithmic time all partial sums of elements of a linear array during incremental changes of element’s values.

Logarithmic Representability of Integers as K-sums

A set A = Ak,n ⇢ [n] [ {0} is said to be an additive k-basis if each element in {0, 1, . . . , kn} can be written as a k-sum of elements of A in at least one way. Seeking multiple representations as k-sums, and given any function (n) ! 1, we say that A is said to be a truncated (n)-representative k-basis for [n] if for each j 2 [↵n, (k ↵)n] the number of ways that j can be represented as a k-su...