M-estimator based Chinese Remainder Theorem with few remainders using a Kroenecker product based mapping vector

The Chinese Remainder Theorem (CRT) explains how to estimate an integer-valued number from the knowledge of the remainders obtained by dividing such unknown integer by co-prime integers. As an algebraic theorem, CRT is the basis for several techniques concerning data processing. For instance, considering a single-tone signal whose frequency value is above the sampling rate, the respective peak in the DFT informs the impinging frequency value modulo the sampling rate. CRT is nevertheless sensitive to errors in the remainders, and many efforts have been developed in order to improve its robustness. In this paper, we propose a technique to estimate real-valued numbers by means of CRT, employing for this goal a Kroenecker based M-Estimation (ME), specially suitable for CRT systems with low number of remainders. Since ME schemes are in general computationally expensive, we propose a mapping vector obtained via Kroenecker products which considerably reduces the computational complexity. Furthermore, our proposed technique enhances the probability of estimating an unknown number accurately even when the errors in the remainders surpass 1/4 of the greatest common divisor of all moduli. We also provide a version of the mapping vectors based on tensorial n-mode products, delivering in the end the same information of the original method. Our approach outperforms the state-of-the-art CRT methods not only in terms of percentage of successful estimations but also in terms of smaller average error.     

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结合儿童OTC(非处方药)药品的包装设计，分析了我国OTC药品包装设计的现状，讨论了OTC药品包装的设计思想及设计步骤。文章指出，在OTC药品包装设计时需要着重研究其设计理念、消费群体及消费定位问题。     

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新世纪我国建陶企业在整个国民经济的带动下将进一步发展，入世后经济全球化的市场竞争格局，建陶企业只有走新产口研发之路，严格企业管理，才会在日趋激烈的市场竞争中得以生存和可持续发展。     

Preparation and properties of nano-sized SnO2 powder

1　INTRODUCTIONSnO2isoneofthemainmaterialsusedingassensor.Becauseofthehumidityandgassensingfunction,itattractsmoreandmoreattentions.Butthepresentproblemishowtoimprovethestabilityandsensibilityofgassensor.Researchershavetakenmanymeasurestoresolvethisproble…     

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