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Finite automata based on quantum logic and monadic second-order quantum logic

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science china(information sciences) 2010年第1期53卷 101-114页

作者： li YongMing college of Computer science, shaanxi normal university, xi’an 710062, china college of Computer science Shaanxi Normal University Xi’an China

We introduce monadic second-order quantum logic and prove that the behaviors of finite automata based on quantum logic are precisely the quantum languages definable with sentences of our monadic secondorder quantum logic. This generalizes Büchi’s and Elgot’s fundamental theorems to quantum logic setting. We also consider first-order quantum logic and show that star-free quantum languages and aperiodic quantum languages introduced here coincide with the first-order quantum definable ones. This generalizes Schützenberger’s fundamental theorems to quantum logic setting. The determinazation of finite automata based on quantum logic is studied by introducing the generalized subset construction method. Then the Kleene theorem in the frame of quantum logic is presented here.

关键词： quantum logic finite automaton monadic second quantum logic quantum language quantum computation Kleene theorem

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.

Preparation of Cu-SiO_2 composite aerogel by ambient drying and the influence of synthesizing conditions on the structure of the aerogel

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Chinese science Bulletin 2011年第7期56卷 685-690页

作者： li GuiAn, ZHU Tingliang, DENG ZhongXun, ZHANG YaJuan, JIAO Fei & ZHENG HaiRong college of Physics and information Technology, shaanxi normal university, xi’an 710062, china college of Physics and information Technology Shaanxi Normal University Xi’an China

A copper-doped silica composite aerogel with high specific surface area was prepared using a sol-gel method at ambient pressure. A drying control chemical additive (DCCA) N,N-dimethylformamide (DMF) was introduced to the composite sol of tetraethyl orthosilicate (TEOS) and copper nitrate (Cu(NO3)2·3H2O) during the synthesizing process. The influence of the preparation conditions including Cu loading, catalyst concentration and heat treatment on the structure of copper-doped silica was investigated. The results showed that the obtained aerogel particles were uniformly distributed. The pore diameter was in a range of 2 to 15 nm. Heavier Cu loading benefited the formation of CuO crystalline, and reduced the specific surface area and pore diameter. When the catalyst concentration was high, the aggregation of Si-O network was reduced with the increase of it. The composite aerogel exhibited a good thermal stability after the heat treatment at high temperature.

关键词：复合气凝胶铜掺杂凝胶结构合成条件 Si02 常压正硅酸乙酯溶胶凝胶法

Phase-Dislocation-Mediated High-Dimensional Fractional Acoustic-Vortex Communication

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Research 2024年第3期2023卷 575-584页

作者： Ruijie Cao Gepu Guo Wei Yue Yang Huang xinpeng li Chengzhi Kai Yuzhi li Juan Tu Dong Zhang Peng xi Qingyu Ma School of Computer and Electronic information Nanjing Normal UniversityNanjing 210023China Department of Biomedical Engineering College of Future TechnologyPeking UniversityBeijing 100871China nstitute of Acoustics Nanjing UniversityNanjng 210093China National Biomedical Imaging Center Peking UniversityBeijing 100871China

With unlimited topological modes in mathematics,the fractional orbital angular momentum(FOAM)demonstrates the potential to infinitely increase the channel capacity in acoustic-vortex(AV)***,the accuracy and stability of FOAM recognition are still limited by the nonorthogonality and poor anti-interference of fractional AV *** popular machine learning,widely used in optics based on large datasets of images,does not work in acoustics because of the huge engineering of the 2-dimensional point-by-point ***,we report a strategy of phase-dislocation-mediated high-dimensional fractional AV communication based on pair-FOAM multiplexing,circular sparse sampling,and machine *** unique phase dislocation corresponding to the topological charge provides important physical guidance to recognize FOAMs and reduce sampling points from theory to practice.A straightforward convolutional neural network considering turbulence and misalignment is further constructed to achieve the stable and accurate communication without involving experimental *** experimentally present that the 32-point dual-ring sampling can realize the 10-bit information transmission in a limited topological charge scope from±0.6 to±2.4 with the FOAM resolution of 0.2,which greatly reduce the divergence in AV *** infinitely expanded channel capacity is further verified by the improved FOAM resolution of *** with other milestone works,our strategy reaches 3-fold OAM utilization,4-fold information level,and 5-fold OAM *** of the extra advantages of high dimension,high speed,and low divergence,this technology may shed light on the next-generation AV communication.

关键词： infinitely topological fractional

一类高次自催化反应扩散系统平衡态的稳定性及分歧

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陕西师范大学学报（自然科学版） 2003年第2期31卷 20-24页

作者：张丽李艳玲陕西师范大学数学与信息科学学院陕西西安710062

研究了一类发生在密闭容器内且扩散系数不同的高次自催化反应,用线性化理论讨论了平衡态(u,v)=(μ ,μ)的稳定性,并且证明了由稳定态产生的分歧是稳定空间非一致解的必要条件是参数D(=λb/λa)<(n-1)2/(n-1)(其中λa,λb分别是化学物种A... 详细信息

研究了一类发生在密闭容器内且扩散系数不同的高次自催化反应,用线性化理论讨论了平衡态(u,v)=(μ ,μ)的稳定性,并且证明了由稳定态产生的分歧是稳定空间非一致解的必要条件是参数D(=λb/λa)<(n-1)2/(n-1)(其中λa,λb分别是化学物种A和B的扩散系数).进一步用弱非线性理论分析了接近分歧点的空间非一致解的性质.

关键词：高次自催化反应扩散系统平衡态稳定性分歧非一致解弱非线性理论

弱L-fuzzy Hausdorff空间及其性质

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陕西师范大学学报（自然科学版） 2003年第2期31卷 16-19页

作者：李尧龙赵彬陕西师范大学数学与信息科学学院陕西西安710062

研究了弱L fuzzyHausdorff空间的性质,包括L 好的推广、遗传性、可乘性、弱同胚不变性及其与其他分离性的关系.讨论了弱L fuzzyHaudorff空间范畴的性质,证明了弱L fuzzyHausdorff空间范畴是次T0拓扑空间范畴的满子范畴及弱L fuzzyHausdo... 详细信息

研究了弱L fuzzyHausdorff空间的性质,包括L 好的推广、遗传性、可乘性、弱同胚不变性及其与其他分离性的关系.讨论了弱L fuzzyHaudorff空间范畴的性质,证明了弱L fuzzyHausdorff空间范畴是次T0拓扑空间范畴的满子范畴及弱L fuzzyHausdorff空间范畴是完备范畴.

关键词：拓扑空间弱L-fuzzy Hausdorff空间范畴遗传性可乘性弱同胚不变性分离性

Approximation Property of Fuzzy Context-free Grammars

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Approximation Property of Fuzzy Context-free Grammars

第一届中国智能计算大会

作者： Yongbing Wang~1 Yongming li~(1,2) 1.college of Mathematic and information science,shaanxi normal university,xi''an,710062,china 2.college of Computer science,shaanxi normal university,xi''an,710062,china

＜正＞Fuzzy context-free max-★ grammar（or FCMTG,for short）as a generalization of（crisp）context-free grammar has been introduced in order that it is possible to effec- tively represent uncertainty,imprecision,and vagueness in natural languages *** recently proposed approximation of fuzzy finite automata,which may ef- fectively cope with the real-world problems of fuzziness, impreciseness and *** this paper,we further develop the approximation of fuzzy context-free gram- *** particular,we show that a fuzzy context-free grammar under max-★ compositional inference can be approximated by some fuzzy context-free grammar un- der max-rain compositional inference with any given ac- *** addition,some related properties of fuzzy context-free grammar and fuzzy languages generated by them are studied.

关键词： Fuzzy context-free grammar Fuzzy context-free language Approximation Equivalence Sensitivity.

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具有分离性的预拓扑空间的范畴性质

山东大学学报（理学版） 2009年第4期44卷 15-20页

作者：于茸茸李生刚陕西师范大学数学与信息科学学院陕西西安710062

刻画了Ti预拓扑空间及连续映射的范畴PTopi中的满态射、单态射、极端单态射和极端满态射(i=0,1,2,3,3(1/2),4)。证明完全正则预拓扑空间及连续映射的范畴Tych和PTopi是预拓扑空间及连续映射的范畴PTop的满反射子范畴(i=0,1,2,3)。

关键词：预拓扑空间分离公理单态射满态射极端单态射极端满态射满反射子范畴

因子von Neumann代数上的多项式零点保持线性映射

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山东大学学报（理学版） 2009年第10期44卷 48-50,53页

作者：崔云丽张建华陕西师范大学数学与信息科学学院陕西西安710062

设M是作用在维数大于2的复可分Hilbert空间上的因子von Neumann代数,并且Φ是从M到自身的线性双射。证明了映射Φ满足对任意A,B∈M,AB=BA*蕴含Φ(A)Φ(B)=Φ(B)Φ(A)*当且仅当存在非零实数λ和M上的*-自同构Ψ使得对任意A∈M,有Φ(A)=λ... 详细信息

设M是作用在维数大于2的复可分Hilbert空间上的因子von Neumann代数,并且Φ是从M到自身的线性双射。证明了映射Φ满足对任意A,B∈M,AB=BA*蕴含Φ(A)Φ(B)=Φ(B)Φ(A)*当且仅当存在非零实数λ和M上的*-自同构Ψ使得对任意A∈M,有Φ(A)=λΨ(A)。

关键词：线性保持映射多项式零点 von Neumann代数