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Implicational lattices and generalization of Stone's representation theorem

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Chinese Science Bulletin 1998年第12期43卷 997-1000页

作者： wang guojun institute of mathematics, shaanxi normal university, xi’an 710062, china institute of mathematics Shaanxi Normal University Xi’an China

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone’s representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.

关键词： Stone’s representation theorem R 0_semantic Lindenbaum algebra implicational lattice fuzzy implicational space representation theorem of regular implicational lattices.

Maximal contractions in Boolean algebras

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Science china(Information Sciences) 2012年第9期55卷 2044-2055页

作者： SHI Huixian & wang guojun institute of mathematics,shaanxi normal university,xi’an 710062,china institute of mathematics Shaanxi Normal University Xi’an China

In the present paper,the concepts of deductive element and maximal contraction are introduced in Boolean algebras,and corresponding theories of consistency and maximal contractions are *** algorithm principle is proposed to compute all maximal contractions for a consistent set with respect to its refutation in Boolean *** is pointed out that the quotient algebra of the first-order language with respect to its provable equivalence relation constitutes a Boolean algebra,and hence the computation of R-contractions for closed formulas in first-order languages can be converted into the one in Boolean algebras proposed in this ***,the concept of basic element is introduced in Boolean algebras,which contributes to the definitions of clause and Horn clause transplanted from logic to a special type of Boolean algebras generated by basic *** is also pointed out that the computation of R-contractions for clauses in the classical propositional logic can be converted into the one in Boolean algebras generated by basic elements proposed in this paper.

关键词： deductive element consistency maximal contraction minimal subtraction basic element clause

Lattice-valued modal propositional logic and its completeness

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Science china(Information Sciences) 2010年第11期53卷 2230-2239页

作者： SHI Huixian & wang guojun1 institute of mathematics, shaanxi normal university, xi’an 710062, china institute of mathematics Shaanxi Normal University Xi’an China

Based on the concept of the complete lattice satisfying the first and second infinite distributive laws, the present paper introduces the semantics of the lattice-valued modal propositional logic. It is pointed out that this semantics generalizes the semantics of both classical modal propositional logic and [0,1]-valued modal propositional logic. The definition of the QMR0-algebra is proposed, and both the Boole-typed latticevalued modal propositional logic system B and the QMR0-typed lattice-valued modal propositional logic system QML* are constructed by use of Boole-algebras and QMR0-algebras, respectively. The main results of the paper are the completeness theorems of both the system B and QML*.

关键词： latticed-valued modal propositional logic modal model QMR0-algebra validity completeness

Quasi-formal deductive system for fuzzy propositional calculus

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Chinese Science Bulletin 1997年第14期42卷 1154-1157页

作者： wang guojuninstitute of mathematics, shaanxi normal university, xi’an 710062, china institute of mathematics Shaanxi Normal University Xi’ an China

ELKAN’s report 'The paradoxical success of fuzzy logic' at the 11th IA Annual Conferenceof America in July, 1993 caused quite a great stir in the research field of IA as well as fuzzysystems, fifteen scholars published papers thereupon to refute it and finally Elkan answeredthem with his paper 'The paradoxical controversy over fuzzy logic'. An exclusive analysiscan be found in Prof. Wu wangming’s paper. It seems from this event that fuzzy proposi-

关键词： ΣR-tautology α-mod us ponens α-hypothetical syllogism quasi-formal deductive system.

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

Physiological Response Mechanism and Drought Resistance Evaluation of Passiflora edulis Sims under Drought Stress

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Phyton-International Journal of Experimental Botany 2024年第6期93卷 1345-1363页

作者： Binyang Zhao Fengchan Wu guojun Cai Peiyu xi Yulin Guo Anding Li College of Forestry Guizhou UniversityGuiyang550025China Guizhou institute of Biology Guizhou Academy of SciencesGuiyang550009China College of Resources and Environment Hunan Agricultural UniversityChangsha410128China

In order to explore the response mechanism of Passiﬂora edulis Sims to drought stress,the changes in morpho-logical and physiological traits of Passiﬂora edulis Sims under different drought conditions were studied.A total of 7 germplasm resources of Passiﬂora edulis Sims were selected and tested under drought stress by the pot culture method under 4 treatment levels:75%–80%(Control,CK)of maximumﬁeld water capacity,55%–60%(Light Drought,LD)of maximumﬁeld water capacity,i.e.,mild drought,40%–45%(Moderate Drought,MD)of max-imumﬁeld water capacity,i.e.,moderate drought and 30%–35%(Severe Drought,SD)of maximumﬁeld water capacity,i.e.,severe *** the 40th day of drought treatment,13 indices,including seedling growth mor-phology,physiology,and biochemistry,were *** results showed that under drought stress,the height and ground diameter of *** Sims gradually decreased with increasing drought stress,and there were signiﬁ-cant differences in seedling height and ground diameter among the *** stress signiﬁcantly inhib-ited the growth of seven *** Sims *** contents of soluble sugar(SS),soluble protein(SP),proline(Pro),and other substances in *** Sims basically increased with increasing drought *** the aggrava-tion of drought stress,the malondialdehyde(MDA)content of *** Sims tended to increase to different degrees,the superoxide dismutase(SOD)activity and peroxidase(POD)activity both tended to increase atﬁrst and then decrease,and the change in catalase(CAT)activity mostly showed a gradual increasing *** con-tents of endogenous hormones in *** Sims signiﬁcantly differed under different degrees of drought *** the aggravation of drought stress,the abscisic acid(ABA)content of *** Sims tended to increase,whereas the contents of gibberellin(GA),indoleacetic acid(IAA),and zeatin nucleoside(ZR)exhibited a down-ward trend.A comprehensive evaluation of the drought resistance of seven *** Sim

关键词： Drought resistance water stress phytohormone morphological trait physiological traits

The nonlinear standing wave inside the space of liquid

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Science china(Physics,Mechanics & Astronomy) 2010年第3期53卷 496-503页

作者： wang ChengHui & LIN ShuYu institute of Applied Acoustics, shaanxi normal university, xi’an 710062, china institute of Applied Acoustics Shaanxi Normal University Xi’an China

Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.

关键词： nonlinear acoustic wave equation nonlinear standing wave perturbation method fundamental wave second harmonic

Relations among the category of topological molecular lattices and certain related categories

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Chinese Science Bulletin 1997年第8期42卷 636-640页

作者： wang guojun and LI Yongming1. institute of mathematics, shaanxi normal university, xi’an 710062, china 2. Department of Basic Science, Northwestern institute of Architecture Engineering, xi’an 710061, china institute of mathematics Shaanxi Normal University Xi’an China Department of Basic Science Northwestern Institute of Architecture Engineering Xi’an China

TAKING the theory of fuzzy topology and point set topology as background,the theory of topo-logical molecular lattices was first advanced in 1979,and after several generalizationsrefs.[4,5] are its general *** topology and point set topology are both special casesof topological molecular lattices as pointed out in ref.[4],whereas it seems not clear whetherone can develop the theory of topological molecular lattices by means of methods in

关键词： category pick-up-one principle.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

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IEEE/CAA Journal of Automatica Sinica 2024年第7期11卷 1557-1565页

作者： Jin-xi Zhang Kai-Di Xu Qing-Guo wang IEEE the State Key Laboratory of Synthetical Automation for Process Industries Northeastern UniversityShenyang 110819China institute of Artificial Intelligence and Future Networks Beijing Normal UniversityZhuhai 519087 Guangdong Key Laboratory of Artificial Intelligence and Multi-Modal Data Processing Beijing Normal University-Hong Kong Baptist University United International CollegeZhuhai 519087

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this ***, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

关键词： Nonlinear systems output constraints prescribed performance reference tracking time delays