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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

Land Use/Land Cover Change(LUCC) and Eco-Environment response to LUCC in Farming-pastoral Zone,china

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Agricultural sciences in china 2009年第1期8卷 91-97页

作者： HAO Hui-mei and rEN Zhi-yuan college of Tourism and Environmental science,shaanxi normal university,Xi’an 710062,p.r.china college of Tourism and Environmental science Shaanxi Normal University Xi'an 710062 P. R. China

In order to understand land use/land cover changes （LUCC） and the eco-environment response to LUCC in farming- pastoral zone of the northern china during the recent twenty years, Baotou prefecture was selected as a case study area for investigation and quantitative evaluation. Technologies of remote sensing （rS）, global positioning system （GpS）, geographic information system （GIS）, and other statistical methods were employed to implement. results showed that：（1） During the recent twenty years, the areas of forest lands, grasslands and water were reduced, whereas the areas of other types were enlarged. parts of forest lands, grasslands, and waters had become farmlands, and about 31.5% of the changed grasslands transferred into unused lands. The newly increased farmlands mainly came from grasslands and unused lands. And the newly increased construction lands mainly came from grasslands and farmlands. （2） regional eco- environmental quality decreased by 12.6%, for which the land degradation （especially the meadow degeneration） and the developing of the cultivated land were mainly responsible, and their contributions to the regional eco-environment changes were 51.84 and 23.63% respectively. （3） The tendency of LUCC and the eco-environment response to LUCC displayed spatial heterogeneity. It can be concluded that the present agricultural production mode was not sustainable in farming-pastoral zone of northern china. Land degradation, especially meadow degradation induced by over-trampling and overgrazing, and developing of cultivated land were mainly responsible for regional eco-environment deterioration. Changing the cultivated land to forest or grass, however, can relieve deterioration of local eco-environment to some extents. And in the farming-pastoral zone in the northern china, evaluating regional eco-environment responses to LUCC was very necessary due to its fragile eco-environments.

关键词： farming-pastoral zone LUCC eco-environment responses to LUCC

Effects of ABA Content on the Development of Abscission Zone and Berry Falling After Harvesting of Grapes

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Agricultural sciences in china 2009年第1期8卷 59-67页

作者： ZHANG You-lin and ZHANG run-guang college of Food Engineering and Nutritional science,shaanxi normal university,Xi’an 710062,p.r.china college of Food Engineering and Nutritional science Shaanxi Normal University Xi'an 710062 P. R. China

The commodity price of grape reduces as berry falling after harvest. It is crucial to prevent grape from berry falling during storage. In this article, the structure change of grape cells in the abscission zone was observed, the ABA content and the activities of cellulase and polygalacturonase （pG） were measured, and the relationship of ABA and berry falling was investigated. The results suggest that cells in the abscission zone grow into a separation layer soon after the grapes are cut off. According to the level of development, we designed 6 grades to sort the different development stages. The grade 3 plays an important role in berry falling. ABA enhances the activities of cellulase and polygalacturonase, and accelerates the decomposition of cellulose and pectin, which determines the level of development of abscission zone and berry falling. If ABA ratio is less than 20 ng g-i flesh weight （FW）, the abscission zone is not developed to the grade 3, and the berry falling is effectively stopped. We treated grape bunches with nine plant growth regulators and two chemicals. The results indicated that 2,3,5-triiodobenzoic acid （TIBA） can （a） inhibit the generation of ABA significantly, （b） inactivate the activities of cellulase and pG, （c） delay the development of the grade 3 of abscission zone, and （d） stop berry falling. Indole acetic acid （IAA）, gibberellic acid （GA3）, naphthalene acetic acid （NAA）, 6-benzylaminopurine （6-BA）, calcium chloride （CaCl2）, and potassium permanganate （KMnO4） caused similar results as TIBA. Chlorocholine chloride （CCC）, dimethyl amino succinamic acid （B9）, chloroethylphosphonic acid （CEpA） and exogenous ABA showed opposite effects.

关键词： grape phytohormone enzyme berry falling

Duality properties between spectra and tilings

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science china Mathematics 2010年第5期53卷 270-280页

作者： LI JianLin college of Mathematics and Information science,shaanxi normal university,Xi’an 710062,china college of Mathematics and Information science Shaanxi Normal University Xi’an China

Spectra and tilings play an important role in analysis and geometry *** relations between spectra and tilings have bafied the mathematicians for a long *** conjectures,such as the Fuglede conjecture,are placed on the establishment of relations between spectra and tilings,although there are no desired *** the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.

关键词： spectral pair periodic set packing and covering tiling pair

property(ω) and Its perturbations

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Journal of Mathematical research with Applications 2012年第4期32卷 450-458页

作者： Qiaoling XIN,Xiaohong CAO college of Mathematics and Information science,shaanxi normal university,shaanxi 710062,p.r.china college of Mathematics and Information science Shaanxi Normal University Shaanxi 710062

In the note,we establish for a bounded linear operator defined on a Hilbert space the necessary and sufficient conditions for the stability of property(ω) by means of the variant of the essential approximate point spectrum and the induced spectrum of consistency in Fredholm and *** addition,the stability of property(ω) for H(p) operators is considered.

关键词： property(ω) perturbation consistency in Fredholm and index.

Borel probabilistic and quantitative logic

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science china(Information sciences) 2011年第9期54卷 1843-1854页

作者： ZHOU HongJun & WANG GuoJun college of Mathematics and Information science,shaanxi normal university,Xi’an 710062,china college of Mathematics and Information science Shaanxi Normal University Xi’an China

The present paper introduces the notion of the probabilistic truth degree of a formula by means of Borel probability measures on the set of all valuations,endowed with the usual product topology,in classical two-valued propositional *** approach not only overcomes the limitations of quantitative logic,which require the probability measures on the set of all valuations to be the countably infinite product of uniform probability measures,but also remedies the drawback that probability logic behaves only *** is proved that the notions of truth degree,random truth degree in quantitative logic and the probability of formulas in probability logic can all be brought as special cases into the unified framework of the probabilistic truth *** quantitative logic and probability logic are *** also proves a one-to-one correspondence between deductively closed theories and topologically closed subsets of the space of all valuations,and a one-to-one correspondence between probabilistic truth degree functions and Borel probability measures on the space of all *** second part of the present paper proposes an axiomatic definition of the probabilistic truth degree,and it is finally proved that each probabilistic truth degree function is represented by a unique Borel probability measure on the space of all valuations in the way given in the first *** a theory which we call probabilistic and quantitative logic in the framework of classical propositional logic is established.

关键词： probabilistic truth degree finite separation property probability logic quantitative logic probabilistic and quantitative logic

Linear Maps preserving projections of Jordan products on the Space of Self-Adjoint Operators

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Journal of Mathematical research with Applications 2012年第2期32卷 235-240页

作者： Meifeng WANG,Guoxing JI college of Mathematics and Information science,shaanxi normal university,shaanxi 710062,china college of Mathematics and Information science Shaanxi Normal University Shaanxi 710062

Let Bs(H) be the real linear space of all self-adjoint operators on a complex Hilbert space H with dim H ≥ *** is proved that a linear surjective map on Bs (H) preserves the nonzero projections of Jordan products of two operators if and only if there is a unitary or an anti-unitary operator U on H such that (X)=λU XU,X∈Bs(H) for some constant λ with λ∈{1,1}.

关键词： self-adjoint operator Jordan product projection linear map.

randomization of classical inference patterns and its application

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science in china(Series F) 2007年第6期50卷 867-877页

作者： WANG GuoJun1,2 & HUI XiaoJing1,31 Institute of Mathematics, shaanxi normal university, Xi’an 710062, china 2 research Center for science, Xi’an Jiaotong university, Xi’an 710049, china 3.college of Mathematics and computer science, Yan’an university, 716000, china Institute of Mathematics Shaanxi Normal University Xi’an China research Center for science Xi’an Jiaotong University Xi’an China college of Mathematics and computer science Yan’an University China

By means of randomization, the concept of D-randomized truth degree of formulas in two-valued propositional logic is introduced, and it is proved that the set of values of D-randomized truth degree of formulas has no isolated point in [0,1]. The concepts of D-logic pseudo-metric and D-logic metric space are also introduced and it is proved that there is no isolated point in the space. The new built D-randomized concepts are extensions of the corresponding concepts in quantified logic. Moreover, it is proved that the basic logic connectives are continuous operators in D-logic metric space. Lastly, three different types of approximate reasoning patterns are proposed.

关键词： D-randomized mapping D-randomized truth degree D-similarity D-logic metric space approximate reasoning

(2,n)secret sharing scheme for gray and color images based on Boolean operation

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science china(Information sciences) 2012年第5期55卷 1151-1161页

作者： DONG Lin 1,WANG DaoShun 1,LI ShunDong 2 & DAI YiQi 1 1 Department of computer science and Technology,Tsinghua university,Beijing 100084,china 2 School of computer science,shaanxi normal university,Xi'an 710062,china Department of computer science and Technology Tsinghua University Beijing China School of computer science Shaanxi Normal University Xi’an China

Traditional secret sharing (SS) schemes can reconstruct the secret precisely,but have high com-putation *** secret sharing (VSS) schemes use human visual system to reconstruct the secret without cryptographic computation,but have pixel expansion and loss of *** et *** a (2,n)-SS scheme for binary images based on Boolean operation,which has low computation complexity,no pixel expansion and the contrast is 1/*** this paper,we first construct an r runs (2,n)-SS scheme to improve the contrast of Wang et al.'s binary (2,n)-SS *** we present two approaches to construct r runs (2,n)-SS schemes for grayscale image and color *** two approaches are both based on Boolean operation,while one approach uses halftone technology and the other uses bit level *** proposed schemes have low computation complexity and almost ideal contrast.

关键词： secret sharing scheme Boolean operation halftone contrast