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A Construction of Authentication Codes with Arbitration from vector spaces over Finite Fields

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Journal of Mathematical Research and Exposition 2011年第2期31卷 269-278页

作者： Wei Jia LI Ji Zhu NAN School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China

This paper is devoted to constructing an authentication code with arbitration using subspaces of vector spaces over finite ***,if we choose the encoding rules of the transmitter and the decoding rules of the receiver according to a uniform probability distribution,then some parameters and the probabilities of successful attacks are computed.

关键词： authentication code with arbitration vector space finite field

AN APPROACH TOWARDS HOLISM IN SCIENCE AND ENGINEERING

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Journal of Systems Science and Systems Engineering 2010年第3期19卷 285-305页

作者： Jason SHERWIN Department of Aerospace Engineering Georgia Institute of Technology

This paper posits the desirability of a shift towards a holistic approach over reductionist approaches in the understanding of complex phenomena encountered in science and engineering. An argument based on set theory is used to analyze three examples that illustrate the shortcomings of the reductionist approach. Using these cases as motivational points, a holistic approach to understand complex phenomena is proposed, whereby the human brain acts as a template to do so. Recognizing the need to maintain the transparency of the analysis provided by reductionism, a promising computational approach is offered by which the brain is used as a template for understanding complex phenomena. Some of the details of implementing this approach are also addressed.

关键词： Reductionism holism agent-based modeling linearizations multi-disciplinary optimization complex phenomena understanding Markov-chain vector space hierarchical temporal memories neuroscience-influenced computing

Design and application of single-antenna GPS/accelerometers attitude determination system

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Journal of Systems Engineering and Electronics 2008年第2期19卷 220-227页

作者： He Jie Huang Xianlin Wang Guofeng Center for Control Theory and Guidance Technique Harbin Inst. of Technology Harbin 150001 P. R. China The Third Research Academy China Aerospace Science &~ Industry Corporation Beijing 100072 P. R. China

In view of the problem that the current single-antenna GPS attitude determination system can only determine the body attitude when the sideslip angle is zero and the multiantenna GPS/SINS integrated navigation system is of large volume, high cost, and complex structure, this approach is presented to determine the attitude based on vector space with single-antenna GPS and accelerometers in the micro inertial measurement unit （MIMU）. It can provide real-time and accurate attitude information. Subsequently, the single-antenna GPS/SINS integrated navigation system is designed based on the combination of position, velocity, and attitude. Finally the semi- physical simulations of single-antenna GPS attitude determination system and single-antenna GPS/SINS integrated navigation system are carried out. The simulation results, based on measured data, show that the single-antenna GPS/SINS system can provide more accurate navigation information compared to the GPS/SINS system, based on the combination of position and velocity. Furthermore, the single-antenna GPS/SINS system is characteristic of lower cost and simpler structure. It provides the basis for the application of a single-antenna GPS/SINS integrated navigation system in a micro aerial vehicle （MAV）.

关键词： single-antenna GPS attitude determination vector space accelerometer integrated navigation MAV.

The Existence of Even Cycles with Specific Lengths in Wenger's Graph

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Acta Mathematicae Applicatae Sinica 2008年第2期24卷 281-288页

作者： Jia-yu Shao Chang-xiang He Hai-ying Shan Department of Mathematics Tongji University Shanghai 200092 China College of Science University of Shanghai for Science and Technology Shanghai 200093 China

Wenger＇s graph Hm（q） is a q-regular bipartite graph of order 2qm constructed by using the mdimensional vector space Fq^m over the finite field Fq. The existence of the cycles of certain even length plays an important role in the study of the accurate order of the Turan number ex（n; C2m） in extremal graph theory. In this paper, we use the algebraic methods of linear system of equations over the finite field and the “critical zero-sum sequences” to show that： if m ≥ 3, then for any integer l with l ≠ 5, 4 ≤ l ≤ 2ch（Fq）（where ch（Fq） is the character of the finite field Fq） and any vertex v in the Wenger＇s graph Hm（q）, there is a cycle of length 21 in Hm（q） passing through the vertex v.

关键词： Graph cycle finite field vector space linear system of equations

Cluster Representation of the Structural Description of Images for Effective Classification

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Computers, Materials & Continua 2022年第12期73卷 6069-6084页

作者： Yousef Ibrahim Daradkeh Volodymyr Gorokhovatskyi Iryna Tvoroshenko Medien Zeghid Department of Computer Engineering and Networks College of Engineering at Wadi AddawasirPrince Sattam Bin Abdulaziz UniversityWadi Addawasir11991Saudi Arabia Department of Informatics Kharkiv National University of Radio ElectronicsKharkiv61166Ukraine Electrical Engineering Department College of Engineering at Wadi AddawasirPrince Sattam Bin Abdulaziz UniversityWadi Addawasir11991Saudi Arabia Electronics and Micro-Electronics Laboratory Faculty of SciencesUniversity of MonastirMonastir5000Tunisia

The problem of image recognition in the computer vision systems is being *** results of the development of efficient classification methods,given the figure of processing speed,based on the analysis of the segment representation of the structural description in the form of a set of descriptors are *** propose three versions of the classifier according to the following principles:“object-etalon”,“object descriptor-etalon”and“vector description of the object-etalon”,which are not similar in level of integration of researched data *** options for constructing clusters over the whole set of descriptions of the etalon database,separately for each of the etalons,as well as the optimal method to compare sets of segment centers for the etalons and object,are *** experimental rating of the efficiency of the created classifiers in terms of productivity,processing time,and classification quality has been realized of the *** proposed methods classify the set of etalons without *** have formed the inference about the efficiency of classification approaches based on segment *** time of image processing according to the developedmethods is hundreds of times less than according to the traditional one,without reducing the accuracy.

关键词： Cluster representation computer vision description relevance descriptor image classification keypoint processing speed vector space

Analysis method and algorithm design of biological sequence problem based on generalized k-mer vector

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Applied Mathematics(A Journal of Chinese Universities) 2021年第1期36卷 114-127页

作者： LIU Wen-li WU Qing-biao Department of Mathematics Zhejiang UniversityHangzhou 310027China Zhejiang Provincial Key Laboratory of Horticultural Plant Integrative Biology Zhejiang UniversityZijingang CampusHangzhou 310012China

K-mer can be used for the description of biological sequences and k-mer distribution is a tool for solving sequences analysis problems in *** can use k-mer vector as a representation method of the k-mer distribution of the biological ***,such as similarity calculations or sequence assembly,can be described in the k-mer vector *** helps us to identify new features of an old sequence-based problem in bioinformatics and develop new algorithms using the concepts and methods from linear space *** this study,we defined the k-mer vector space for the generalized biological *** meaning of corresponding vector operations is explained in the biological *** presented the vector/matrix form of several widely seen sequence-based problems,including read quantification,sequence assembly,and pattern detection *** advantages and disadvantages are ***,we implement a tool for the sequence assembly problem based on the concepts of k-mer vector *** shows the practicability and convenience of this algorithm design strategy.

关键词： vector space biological sequence k-mer algorithm design analysis method.

Structure of Quasi-Invariant vector spaces

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Journal of Mathematical Research and Exposition 2000年第2期20卷 197-200页

作者：冯红大队连理工大学应用数学系

Let V be a vector space over a field F and G a group of linear transformations in V. It is proved in this note that for any subspace U (V, if dimU/(U∩ g(U))≤ 1, for any g∈G, then there is a g∈ G such that U∩g(U) is a G-invariant subspace, or there is an x∈ V\U such that U + is a G-invariant subspace. So a vector-space analog of Brailovsky's results on quasi-invariant sets is given.

关键词： vector space quasi-invariant.

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Science in China(Series F) 2008年第9期51卷 1215-1230页

作者： PENG Jing YANG DongQing TANG ShiWei WANG TengJiao GAO Jun School of Electronics Engineering and Computer Science Peking University Beijing 100871 China Department of Science and Technology Chengdu Municipal Public Security Bureau Chengdu 610017 China

The paper proposes a new text similarity computing method based on concept similarity in Chinese text processing. The new method converts text to words vector space model at first, and then splits words into a set of concepts. Through computing the inner products between concepts, it obtains the similarity between words. The new method computes the similarity of text based on the similarity of words at last. The contributions of the paper include： 1） propose a new computing formula between words; 2） propose a new text similarity computing method based on words similarity; 3） successfully use the method in the application of similarity computing of WEB news; and 4） prove the validity of the method through extensive experiments.

关键词： concept similarity similarity computing vector space inner product space

The C-topology on lattice-ordered groups

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Science China Mathematics 2009年第11期52卷 2397-2403页

作者： YANG YiChuan Department of Mathematics,Key Laboratory of Ministry of Education for Information Mathematics and Behavior,Beihang University,Beijing,100191 China Department of Mathematics Key Laboratory of Ministry of Education for Information Mathematics and Behavior Beihang University Beijing China

Let A be a lattice-ordered group. Gusi? showed that A can be equipped with a C-topology which makes A into a topological group. We give a generalization of Gusi?’s theorem, and reveal the very nature of a “C-group” of Gusi? in this paper. Moreover, we show that the C-topological groups are topological lattice-ordered groups, and prove that every archimedean lattice-ordered vector space is a T 2 topological lattice-ordered vector space under the C-topology. An easy example shows that a C-group need not be T 2. A further example demonstrates that a T 2 topological archimedean lattice-ordered group need not be C-archimedean, either.

关键词： C-topology lattice-ordered group archimedean lattice-ordered group Hausdorff topology vector space 06F30 22A99