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Note about Fixed points of Scott Continuous Self-Mappings

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Journal of Mathematical research and Exposition 2011年第1期31卷 187-190页

作者： xiao Yong xi1,2,Yong Ming LI3 1.College of Mathematics and Information science.Shaanxi normal university,Shaanxi 710062,p.r.china 2.College of Mathematics science.Xuzhou normal university,Jiangsu 221009,p.r.china 3.College of computer science.Shaanxi normal university,Shaanxi 710062,p.r.china College of Mathematics and Info'rmatio'n science Shaanxi Normat University Shaanxi 710062 College of computer science Shaanxi Normal University Shaanxi 710062

It is discussed in this paper that under what conditions, for a continuous domain L, there is a Scott continuous self-mapping f ： L → L such that the set of fixed points fix（f） is not continuous in the ordering induced by L. For any algebraic domain L with a countable base and a smallest element, the problem presented by Huth is partially solved. Also, an example is given and shows that there is a bounded complete domain L such that for any Scott continuous stable self-mapping f, fix（f） is not the retract of L.

关键词： Scott continuous fixed points stable mapping.

The structure of L*-inverse semigroups

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science.china Mathematics 2006年第8期49卷 1065-1081页

作者： rEN Xueming & SHUM Karping department of Mathematics, xi’an university of Architecture and Technology, xi’an 710055, china Faculty of science. The Chinese university of Hong Kong, Hong Kong, china department of Mathematics Xi'an University of Architecture and Technology Xi'an 710055 China Faculty of science The Chinese University of Hong Kong Hong Kong Hong Kong

The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.

关键词： L*-inverse semigroups type A semigroups left regular bands left wreath products.

ASYMpTOTIC normalITY OF MAxiMUM QUASI-LIKELIHOOD ESTIMATOrS IN GENErALIZED LINEAr MODELS WITH FIXED DESIGN

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Journal of Systems science.& Complexity 2008年第3期21卷 463-473页

作者： Qibing GAO Yaohua WU Chunhua ZHU Zhanfeng WANG School of Mathematics and computer science Nanjing Normal University Nanjing 210097 China department of Statistics and Finance University of Science and Technology of China Hefei 230026 China School of Mathematics science Anhui University Hefei 230039 China

In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n xi（yi -μ（xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nxixi′, xi are bounded p × q regressors, and yi are q × 1 responses.

关键词： Asymptotic normality fixed design generalized linear models maximum quasi-likelihood estimator

CToMp: a cycle-task-oriented memory protection scheme for unmanned systems

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science.china(Information science.) 2024年第6期67卷 399-417页

作者： Chengyan MA Ning xi Di LU Yebo FENG Jianfeng MA School of Cyber Engineering Xidian University School of computer science.and Technology Xidian University department of computer and Information science University of Oregon

Memory corruption attacks(MCAs) refer to malicious behaviors of system intruders that modify the contents of a memory location to disrupt the normal operation of computing systems, causing leakage of sensitive data or perturbations to ongoing processes. Unlike general-purpose systems, unmanned systems cannot deploy complete security protection schemes, due to their limitations in size, cost and *** in unmanned systems are particularly difficult to defend against. Furthermore, MCAs have diverse and unpredictable attack interfaces in unmanned systems, severely impacting digital and physical sectors. In this paper, we first generalize, model and taxonomize MCAs found in unmanned systems currently, laying the foundation for designing a portable and general defense approach. According to different attack mechanisms,we found that MCAs are mainly categorized into two types — return2libc and return2shellcode. To tackle return2libc attacks, we model the erratic operation of unmanned systems with cycles and then propose a cycle-task-oriented memory protection(CToMp) approach to protect control flows from tampering. To defend against return2shellcode attacks, we introduce a secure process stack with a randomized memory address by leveraging the memory pool to prevent Shellcode from being executed. Moreover, we discuss the mechanism by which CTo Mp resists the return-oriented programming(rOp) attack, a novel variant of return2libc attacks. Finally, we implement CTo Mp on CUAV V5+ with Ardupilot and Crazyflie. The evaluation and security analysis results demonstrate that the proposed approach CTo Mp is resilient to various MCAs in unmanned systems with low footprints and system overhead.

关键词： unmanned system memory corruption attack memory protection system security randomized memory address

Explicit classes of permutation polynomials of F33m

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science.china Mathematics 2009年第4期52卷 639-647页

作者： DING CunSheng1, xiANG Qing2, YUAN Jin3 & YUAN pingZhi4 1 department of computer science.and Engineering, The Hong Kong university of science.and Technology, Clearwater Bay, Kowloon, Hong Kong, china 2 department of Mathematical science., university of Delaware, Newark, DE 19716, USA 3 department of Computing, Macquarie university, NSW 2109, Australia 4 School of Mathematics, South china normal university, Guangzhou 510631, china department of computer science.and Engineering The Hong Kong University of Science and Technology Hong Kong China department of Mathematical science. University of Delaware Newark USA department of Computing Macquarie University Sydney Australia School of Mathematics South China Normal University Guangzhou China

permutation polynomials have been an interesting subject of study for a long time and have applications in many areas of mathematics and engineering. However, only a small number of specific classes of permutation polynomials are known so far. In this paper, six classes of linearized permutation polynomials and six classes of nonlinearized permutation polynomials over F33m are presented. These polynomials have simple shapes, and they are related to planar functions.

关键词： permutation polynomials planar functions

Asynchronous cooperative communication systems:A survey on signal designs

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science.china(Information science.) 2011年第8期54卷 1547-1561页

作者： WANG HuiMing 1,2 & xiA xiangGen 3 1 School of Electronic and Information Engineering, xi’an Jiaotong university, xi’an 710049,china 2 State Key Laboratory of Integrated Services Networks, xidian university,xi’an 710049, china 3 department of Electrical and computer Engineering,university of Delaware,Newark,DE 19716,USA School of Electronic and Information Engineering Xi’an Jiaotong University Xi’an China State Key Laboratory of Integrated Services Networks Xidian University Xi’an China department of Electrical and computer Engineering University of Delaware Newark USA

Cooperative communications is a promising technique for future high speed wireless *** systems may be formulated as virtual multi-input multi-output (MIMO) systems where spatial/cooperetive diversity is a key advantage. However,different from MIMO systems,one of the major chal- lenges for cooperative communications systems is that the cooperative transmissions in cooperative systems may be neither time nor frequency synchronized,since the transmissions are from multiple cooperative nodes at different *** existing signal designs for co-located MIMO systems may not be able to collect the cooperative diversity in cooperative communications *** paper gives an overview of recent research efforts on combating the time and frequency asynchronism of the cooperative communication *** focus on the signal designs (or space-time codings/modulations) to achieve full cooperative diversity,and summarize some of the resent distributed space-timing coding and space-frequency coding techniques to combat timing errors and frequency offsets,and in the meantime to achieve full cooperative diversity,in both one-way and two-way cooperative networks.

关键词： cooperative communications time and frequency offsets space-time coding space-frequency codes full cooperative diversity linear receiver

DErIVATIONS ON DIFFErENTIAL OpErATOr ALGEBrA AND WEYL ALGEBrA

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Chinese Annals of Mathematics,Series B 1996年第2期17卷 199-212页

作者： CHEN CAOYU department of Mathematics, Shanghai normal university, Shanghai 200234, china. 上海师范大学数学系上海

Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.

关键词： Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra

prE-IMAGE ENTrOpY OF NONAUTONOMOUS DYNAMICAL SYSTEMS

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Journal of Systems science.& Complexity 2008年第3期21卷 441-445页

作者： xianjiu HUANG xi WEN Fanping ZENG department of Mathematics Nanchang University Nanchang 330031 China department of computer Nanchang University Nanchang 330031 China department of Mathematics Liuzhou Theachers College Liuzhou 545004 China

The authors define and study topological pre-image entropy for the non-autonomous discrete dynamical systems given by a sequence {fi}i=1^∞ of continuous self-maps of a compact topological space. The basic properties and the invariant with respect to equiconjugacy of pre-image entropy for the non-autonomous discrete dynamical systems are obtained.

关键词： Equiconjugacy non-autonomous pre-image entropy sequence of continuous self-maps

Exact satisfiability and phase transition analysis of the regular(k,d)-CNF formula

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Frontiers of computer science 2024年第1期18卷 263-265页

作者： Guoxia NIE Daoyun XU xi WANG Zaijun ZHANG College of computer science.and Technology Guizhou UniversityGuiyang 550025China School of Mathematics and Statistics Qiannan Normal University for NationalitiesDuyun 558000China Key Laboratory of Industrial Automation and Machine Vision of Qiannan Duyun 558000China

1Introduction The satisfiability(SAT)problem has been considered the"seed"of other Np-complete *** regular partial exact(k,d)-SAT problem is an important extension of the SAT *** any(k,d)-CNF formula with a variable set V,V'is a proper subset of V,the problem involves determining whether a truth assignment set on V'exists such that only a literal in each clause is *** V'=V,it is a regular exact(k,d)-SAT ***,both experimental verifications and theoretical analyses of k-SAT problem have shown that the ratioα(clause constraint density)of the number of clauses m to the number of variables n is an important parameter affecting the satisfiability of the formula[1].However,the regular(k,d)-SAT problem has the same clause constraint density d/k.

关键词： formula constraint exact