Numerical integration (Not including applications to differential equations and related topics.)

Thesis (M.A.)--Boston University, 1944. This item was digitized by the Internet Archive

Dimensional expansions for two‐electron atoms

Approximate expansions in inverse powers of the dimensionality of space D are obtained for the ground‐state energies of two‐electron atoms. The method involves fitting polynomials in δ=1/D to accurate eigenvalues of the generalized D‐dimensional Schrödinger equation. To the maximum order obtainable from the data, about δ7, the power series for nuclear charges Z=2, 3, and 6 all diverge at D=3. Asymptotic summation yields an energy for the Z=2 atom 1% in excess of the true value at D=3. However, expansions with a shifted origin, i.e., expansions in (δ−δ0), show improved convergence. Of particular interest is the case δ0=1, because the expansion coefficients can in principle be calculated by perturbation theory applied to the one‐dimensional atom. Series in powers of (δ−1) appear to converge rapidly. Also the series in (δ−1) can be evaluated even for the hydride ion, with Z=1. For helium, this series is quite comparable to the more familiar expansion in powers of λ=1/Z, with errors in the partial sums decreasing by roughly an order of magnitude per term. Thus, for Z=2 the first four terms of the expansion in (δ−1) yield an energy within 0.02% of the true value at D=3. Similar results are found in an analogous treatment of accurate eigenvalues for the Hartree–Fock approximation. This provides a rapidly convergent dimensional expansion for the correlation energy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70931/2/JCPSA6-86-4-2114-1.pd

Analyzing Traffic Problem Model With Graph Theory Algorithms

This paper will contribute to a practical problem, Urban Traffic. We will investigate those features, try to simplify the complexity and formulize this dynamic system. These contents mainly contain how to analyze a decision problem with combinatorial method and graph theory algorithms; how to optimize our strategy to gain a feasible solution through employing other principles of Computer Science.Comment: 7 pages, 5 figures, Science and Information Conference (SAI), 201

Guidance, flight mechanics and trajectory optimization. Volume 6 - The N-body problem and special perturbation techniques

Analytical formulations and numerical integration methods for many body problem and special perturbative technique

Some considerations of strong, electromagnetic and gravitational interactions of Hadrons

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