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A Triangular Decomposition Algorithm for Differential Polynomial Systems with Elementary Computation Complexity

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Journal of Systems Science & Complexity 2017年第2期30卷 464-483页

作者： ZHU Wei gao Xiao-shan Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.

关键词： Differential polynomial system regular triangular set saturated triangular set triangular decomposition.

Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems

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Journal of Systems Science & Complexity 2019年第1期32卷 62-77页

作者： HU Youren gao Xiao-shan KLMM Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematics University of Chinese Academy of Sciences Chinese Academy of Sciences

In this paper, a Ritt-Wu characteristic set method for Laurent partial differential polynomial systems is presented. The concept of Laurent regular differential chain is de?ned and its basic properties are proved. The authors give a partial method to decide whether a Laurent differential chain A is Laurent regular. The decision for whether A is Laurent regular is reduced to the decision of whether a univariate differential chain A1 is Laurent regular. For a univariate differential chain A1,the authors ?rst give a criterion for whether A1 is Laurent regular in terms of its generic zeros and then give partial results on deciding whether A1 is Laurent regular.

关键词： Newton polygon Laurent partial differential polynomial system Laurent regular triangular set Ritt-Wu characteristic set

Quantum Algorithm for Boolean Equation Solving and Quantum Algebraic Attack on Cryptosystems

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Journal of Systems Science & Complexity 2022年第1期35卷 373-412页

作者： CHEN Yu-Ao gao Xiao-shan Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

This paper presents a quantum algorithm to decide whether a Boolean equation system F has a solution and to compute one if F does have solutions with any given success *** runtime complexity of the algorithm is polynomial in the size of F and the condition number of certain Macaulay matrix associated with *** a consequence,the authors give a polynomial-time quantum algorithm for solving Boolean equation systems if their condition numbers are polynomial in the size of *** authors apply the proposed quantum algorithm to the cryptanalysis of several important cryptosystems:The stream cipher Trivum,the block cipher AES,the hash function SHA-3/Keccak,the multivariate public key cryptosystems,and show that they are secure under quantum algebraic attack only if the corresponding condition numbers are *** leads to a new criterion for designing such cryptosystems which are safe against the attack of quantum computers:The corresponding condition number.

关键词： Block cipher AES Boolean equation solving condition number hash function SHA3/Keccak HHL algorithm MPKC polynomial system solving quantum algorithm stream cipher Trivum

Cognition-Based Interactive Phases and Strategies in Teaching Academic Reading

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Journal of Electronic Science and Technology 2017年第1期15卷 33-40页

作者： Zhao gao shan gao Qi Yang School of Foreign Languages University of Electronic Science and TechnologyChengdu 610054China

Academic English reading requires deeper cognitive involvement in addition to language proficiency and plays a vital role in moulding a critical mindset. However, cognitive progress is seldom targeted in classroom teaching. This study proposed a teaching method of three reading phases in terms of cognitive mechanism and communicative teaching *** university freshmen of non-English major participated in the study, who were taking the course of Academic English Reading in the 2nd semester. The data were collected from self-report Research Skills Assessment twice and semi-structured interview, and analyzed with paired sample t test and Pearson correlation. The results showed that 1） “critical thinking”, “organizing ideas”, and “finding information” were believed to improve significantly at the end of the course; 2） reading skill was associated with writing skill and the sense of “big picture” in self perception; 3） the cognition-based interactive reading instruction was acknowledged to be conducive to academic reading. It complements Academic English reading pedagogy by juxtaposing the need for both individual cognition and group interaction in classroom teaching.

关键词： Reading classroom skill proficiency interview thinking acknowledged instruction comprehension cognition

MULTIPLICITY-PRESERVING TRIANGULAR SET DECOMPOSITION OF TWO POLYNOMIALS

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Journal of Systems Science & Complexity 2014年第6期27卷 1320-1344页

作者： CHENG Jin-San gao Xiao-shan Key Laboratory of Mathematics Mechanization Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence of two polynomials once and certain GCD computations. The algorithm decomposes the unmixed variety defined by two polynomials into square free and disjoint （for non-vertical components, see Definition 4） algebraic cycles represented by triangular sets which may have negative multiplicities. Thus, the authors can count the multiplicities of the non-vertical components. In the bivariate case, the amthors give a complete algorithm to decompose tile system into zeros represented by triangular sets with multiplicities. The authors also analyze the complexity of the algorithm in the bivariate ease. The authors implement the algorithm and show the effectiveness of the method with extensive experiments.

关键词： Algebraic cycle multiplicity-preserving primitive polynomial remainder sequence trian-gular set decomposition.

Language as Context Modulates Social Judgments

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Journal of Electronic Science and Technology 2017年第1期15卷 48-51页

作者： shan gao Zhao gao Ting Gou School of Foreign Languages University of Electronic Science and Technology of China Key Laboratory for Neurolnformation of Ministry of Education Centre for Information in MedicineUniversity of Electronic Science and Technology of ChinaChengdu 611731China

Social judgments are usually made in the context of complex information including verbal *** we investigated the impact of verbal statements on social judgments by biasing male and female neutral faces with descriptives of differentially-valenced behaviour（criticizing or praising） targeting others or objects. Results showed significant main effects of valence and target, such that critical individuals were rated lower in likeability than praising ones and those targeting others relative to objects were valued less. In particular, those who criticized others were the most unlikeable. Among critical individuals, men were less likeable than women. Similarly, men became less valued while targeting others. Overall these findings suggest that the negative impact of critical attributes may trigger avoidance in social interaction while the positive impact of praise may trigger approach.

关键词： Context verbal praise targeting statements behaviour valued avoidance likely neutral

A RepairableGeoX/G/1 Retrial Queue with Bernoulli Feedback and Impatient Customers

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 205-222页

作者： shan gao Zai-ming LIU Department of Mathematics Fuyang Normal College School of Mathematics and Statistics Central South University

Abstract This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting *** from standard batch arrival retrial queues with starting failures,we assume that each customer after service either immediately returns to the orbit for another service with probabilityθor leaves the system forever with probability 1θ（0≤θ〈1）.On the other hand,if the server is started unsuccessfully by a customer（external or repeated）,the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 q（0≤q〈1）.Firstly,we introduce an embedded Markov chain and obtain the necessary and sufcient condition for ergodicity of this embedded Markov ***,we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary *** also derive a stochastic decomposition *** the special case of individual arrivals,we develop recursive formulae for calculating the steady-state distribution of the orbit ***,we investigate the relation between our discrete-time system and its continuous ***,some numerical examples show the influence of the parameters on the mean orbit size.

关键词： discrete-time queue retrial queue starting failure steady state Bernoulli feedback

Deviation of the Lagrangian particle tracing method in the evaluation of the Southern Hemisphere annual subduction rate

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Journal of Oceanology and Limnology 2022年第3期40卷 891-906页

作者： Kai LIU shan gao Fan WANG Institute of Oceanology Chinese Academy of SciencesQingdao 266071China Center for Ocean Mega-Science Chinese Academy of SciencesQingdao 266071China University of Chinese Academy of Sciences Beijing 100049China China Laboratory for Ocean Dynamics and Climate Pilot National Laboratory for Marine Science and Technology(Qingdao)Qingdao 266237China

The classical Lagrangian particle tracing method is widely used in the evaluation of the ocean annual subduction ***,our analysis indicates that in addition to neglecting the effect of mixing,there are two possible deviations in the method:one is an overestimation due to not considering that the amount of subducted water at the source location may be inadequate during the late winter of the first year when the mixed layer becomes shallow;the other one is an underestimation due to the neglect of the effective subduction caused by strong vertical *** analysis shows that these two deviations mainly exist in the low-latitude subduction areas of the South Pacific and South *** two deviations have very similar distribution areas and can partially off set each ***,the overall deviation is still large,and the maximum relative deviation ratio can reach 50%;therefore,it cannot be ignored.

关键词： subduction rate Lagrangian particle tracing method mixed layer tropical water eastern subtropical mode water

ON FUNCTIONAL DECOMPOSITION OF MULTIVARIATE POLYNOMIALS WITH DIFFERENTIATION AND HOMOGENIZATION

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Journal of Systems Science & Complexity 2012年第2期25卷 329-347页

作者： shangwei ZHAO Ruyong FENG Xiao-shan gao Beijing Electronic Science and Technology Institute KLMM Academy of Mathematics and Systems ScienceChinese Academy of Sciences

This paper gives a theoretical analysis for the algorithms to compute functional decomposition for multivariate polynomials based on differentiation and homogenization which were proposed by Ye, Dai, and Lam （1999） and were developed by Faugere, Perret （2006, 2008, 2009）. The authors show that a degree proper functional decomposition for a set of randomly decomposable quartic homoge- nous polynomials can be computed using the algorithm with high probability. This solves a conjecture proposed by Ye, Dal, and Lam （1999）. The authors also propose a conjecture which asserts that the decomposition for a set of polynomials can be computed from that of its homogenization and show that the conjecture is valid with high probability for quartic polynomials. Finally, the authors prove that the right decomposition factors for a set of polynomials can be computed from its right decomposition factor space.

关键词： Cryptosystem analysis functional decomposition homogeneous polynomials multivariatepolynomial right factor space.