• East Asian mathematical journal
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• 제24권1호
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• pp.67-79
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• 2008

In this paper, we characterize the chaotic operator order $A\;{\gg}\;C\;{\gg}\;B$. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing $A\;{\gg}\;C\;{\gg}\;B$, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order $A\;{\gg}\;B$ in terms of operator equalities.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.33-44
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• 2017

We review weighted power means of positive real numbers and see their properties including the convexity and concavity for weights. We study the mixed power means of positive real numbers related to majorization of weights, which gives us an extension of Muirhead's inequality. Furthermore, we generalize Holland's conjecture to the power means.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제16권11호
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• pp.3761-3779
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• 2022

The performance of existing recognition algorithms for binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals degrade under conditions of low signal-to-noise ratios (SNR). Hence, a novel recognition algorithm based on features in the graph domain is proposed in this study. First, the power spectrum of the squared candidate signal is truncated by a rectangular window. Thereafter, the graph representation of the truncated spectrum is obtained via normalization, quantization, and edge construction. Based on the analysis of the connectivity difference of the graphs under different hypotheses, the sum of degree (SD) of the graphs is utilized as a discriminate feature to classify BPSK and QPSK signals. Moreover, we prove that the SD is a Schur-concave function with respect to the probability vector of the vertices (PVV). Extensive simulations confirm the effectiveness of the proposed algorithm, and its superiority to the listed model-driven-based (MDB) algorithms in terms of recognition performance under low SNRs and computational complexity. As it is confirmed that the proposed method reduces the computational complexity of existing graph-based algorithms, it can be applied in modulation recognition of radar or communication signals in real-time processing, and does not require any prior knowledge about the training sets, channel coefficients, or noise power.