Number-theoretic degeneracy of the energy levels of a perturbed N-dimensional isotropic harmonic oscillator - ScienceDirect
Export JavaScript is disabled on your browser. Please enable JavaScript to use all the features on this page., June 1981, Pages 138-171Author links open overlay panelShow moreopen archiveAbstractThe problem of constructing all integer solutions n1 ≥ n2 ≥ … ≥ nN to the pair of Diophantine equations n = n1 + … + nN, m = n12 + … + nN2 arises in the determination of the degeneracy of a given energy level of an N-dimensional isotropic quantum oscillator that is perturbed by an isotropic quartic potential energy term. This problem is solved recursively (in N) using the concept of a multiplet, which is a finite set of points in a lattice space LN whose points are N-tuples of integers that sum to zero. The basic definition and properties of multiplets are given and then used to obtain the solutions to the Diophantine equations described above. The classification of multiplets into two types, fundamental and nonfundamental, is shown to have an important role in elucidating the structure of multiplets. The concept of a fundamental multiplet is demonstrated to be an important characterization of the solutions to a pair of Diophantine equations that are closely related to those of the original problem.Recommended articlesCiting articles (0)louu5，行车中老是出现这个字母闪现，是什么问题？请教良师。谢谢。_百度知道
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louu5，行车中老是出现这个字母闪现，是什么问题？请教良师。谢谢。
louu5，行车中老是出现这个字母闪现，是什么问题？请教良师。谢谢。
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回答问题，赢新手礼包Truncated gag products encoded by Gv-1-responsive endogenous retrovirus loci. - Abstract - Europe PMC
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(PMID:2789292 PMCID:PMC251027)
P F Policastro
Merete Fredholm
University of Copenhagen
M C Wilson
Department of Molecular Biology, Research Institute of Scripps Clinic, La Jolla, California 92037.
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[01 Oct ):]
Research Support, U.S. Gov't, P.H.S., Research Support, Non-U.S. Gov't, research-article, Journal Article
The conversion of endogenous or exogenous murine retroviruses to a leukemogenic phenotype involves recombination with retroviral sequences present in host genomic DNA. In the 129 Gix+ inbred strain, these endogenous sequences are replication defective but still express retroviral proteins under the apparent transcriptional control of the Gv-1 regulatory locus. To study the protein-coding potential of Gv-1-regulated endogenous retroviral loci, we used oligonucleotide probes directed to env deletion breakpoints identified in previously characterized cDNA clones. Four endogenous retroviral loci were isolated from a library of 129 Gix+ genomic DNA with these probes. Three loci cloned with the env deletion probe del env-1 had virtually identical proviral inserts by restriction analysis. A unique locus was identified and cloned with the del env-2 probe, which must therefore represent a Gv-1-responsive element. Restriction enzyme and nucleotide sequence analyses indicated that the del env-1 and del env-2 loci represented members of the polytropic and modified polytropic classes of endogenous retrovirus, respectively. Despite this divergence, members of both classes contained identical deletions of 19 nucleotides within p30gag and of 1,474 nucleotides from p10gag into the reverse transcriptase-coding region of pol, suggesting that a recombination event had occurred between these proviral sequences prior to insertion within the genome. The del env-1 and del env-2 loci retained coding capacity for truncated gag polyproteins, confirmed by in vitro translation and immunoprecipitation of the protein products. Nucleotide sequence comparison of the untranslated leader (L) regions of the del env-1 and del env-2 loci to a replication-competent ecotropic virus indicated regions that might be important to dispersion of these endogenous retroviral elements throughout the host genome.
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