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Mathematics & Computation
Division members promote the advancement of mathematical and computational methods for solving problems arising in all disciplines encompassed by the Society. They place particular emphasis on numerical techniques for efficient computer applications to aid in the dissemination, integration, and proper use of computer codes, including preparation of computational benchmark and development of standards for computing practices, and to encourage the development on new computer codes and broaden their use.
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ANS Student Conference 2025
April 3–5, 2025
Albuquerque, NM|The University of New Mexico
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Latest News
First astatine-labeled compound shipped in the U.S.
The Department of Energy’s National Isotope Development Center (NIDC) on March 31 announced the successful long-distance shipment in the United States of a biologically active compound labeled with the medical radioisotope astatine-211 (At-211). Because previous shipments have included only the “bare” isotope, the NIDC has described the development as “unleashing medical innovation.”
Risto Vanhanen
Nuclear Science and Engineering | Volume 179 | Number 4 | April 2015 | Pages 411-422
Technical Paper | doi.org/10.13182/NSE14-75
Articles are hosted by Taylor and Francis Online.
We propose a novel application of a method to compute the nearest positive semidefinite matrix. When applied to covariance matrices of multigroup nuclear data, the method removes unphysical components of the covariances while preserving the physical components of the original covariance matrix. The result is a mathematically proper covariance matrix.
We show that the method preserves the so-called zero sum rule of covariances of distributions in exact arithmetic. The results also hold for typical cases of finite precision arithmetic. We identify conditions that might damage the zero sum rule.
Rounding can distort the eigenvalues of a symmetric matrix. We give a known bound on how large distortions can occur due to round-off. Consequently, there is a known upper bound on how large negative eigenvalues can be attributed to round-off error. Current evaluations and processing codes do produce larger negative eigenvalues.
Three practical examples are processed and analyzed. We demonstrate that satisfactory results can be achieved.
We discuss briefly the relevance of the method, its properties, and alternative approaches. The method can be used as a part of a quality assurance program and would be a valuable addition to nuclear data processing codes.