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The discrete fractional random cosine and sine transforms

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Zhengjun Liu, Qing Guo, Shutian Liu

Mathematical Physics · Submitted 22 May 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT.

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arXiv IDmath-ph/0605063 (version 1)
Pith IDLHUNBCWJ, Pith's permanent record of this paper and its review
CitationQing Guo, Shutian Liu, Zhengjun Liu. "The discrete fractional random cosine and sine transforms." arXiv:math-ph/0605063 (2006). https://pith.science/paper/LHUNBCWJ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,918 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.13 · mentions code or data availability 0.03.

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arXiv listing abstract v1. Results and the main claim are underlined; .

Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. Numeral results of DFRNCT and DFRNST for one and two dimensional functions have been given.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). contribution 1.00 0.92 0.27 asserted 1.00
s1 We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. interpretation 0.46 0.90 0.47 asserted 1.00
s2 Numeral results of DFRNCT and DFRNST for one and two dimensional functions have been given. result 0.96 0.91 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.77.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Based on the discrete fractional random transform (DFRNT), we present the discrete fractional random cosine and sine transforms (DFRNCT and DFRNST). We demonstrate that the DFRNCT and DFRNST can be regarded as special kinds of DFRNT and thus their mathematical properties are inherited from the DFRNT. Numeral results of DFRNCT and DFRNST for one and two dimensional functions have been given.

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