We adopt the following symbols and notations. Let C;be the class of all real continuous functions in [0,1] which have N continuousderivatives, L;0,1];be the space of real pth power integrable functions on [0,1], and ...We adopt the following symbols and notations. Let C;be the class of all real continuous functions in [0,1] which have N continuousderivatives, L;0,1];be the space of real pth power integrable functions on [0,1], and Δ;, asusual, be the class of kth monotone functions.展开更多
In this paper, we give a counterexample to the article 'Globally asymptotic stability of a recurrence sequence', Ann. of Diff. Eqs., 17:1(2001), 82-85.
If K ∩ AlgL is weak. dense in AlgL, where K is the set of all compactoperators in B(H), is completely distributive? In this note, we prove that there is a reflexivesubspace lattice L on some Hilbert space, which sati...If K ∩ AlgL is weak. dense in AlgL, where K is the set of all compactoperators in B(H), is completely distributive? In this note, we prove that there is a reflexivesubspace lattice L on some Hilbert space, which satisfies the following conditions: (a) F(AlgL) isdense in AlgL in the ultrastrong operator topology, where F(AlgL) is the set of all finite rankoperators in AlgL; (b) L isnt a completely distributive lattice. The subspace lattices that satisfythe above conditions form a large class of lattices. As a special case of the result, it easy to seethat the answer to Problem 7 is negative.展开更多
Entropy is important in philosophy of science,but some fallacies originate from the misunderstanding entropy increases.The basis of thermodynamics is the statistics and its basic principle of statistical independence....Entropy is important in philosophy of science,but some fallacies originate from the misunderstanding entropy increases.The basis of thermodynamics is the statistics and its basic principle of statistical independence.We proposed possible entropy decrease due to fluctuation magnified and internal interactions in isolated systems,and discuss this possibility of various aspects on science and nature.Further,we derive quantitatively a total formula of entropy change for universal evolution of any natural and social systems,and discuss entropy decrease in economics and social sciences.Entropy change is a testable science.As long as we break through the bondage of the second law of thermodynamics,the rich and complex world is full of examples of entropy decrease.We believe world is not pessimistic always.展开更多
This paper adopts counterexample guided abstraction refinement scheme to alleviate the state explosion problem of deadlock detection. We extend the classical labeled transition system models by qualifying transitions ...This paper adopts counterexample guided abstraction refinement scheme to alleviate the state explosion problem of deadlock detection. We extend the classical labeled transition system models by qualifying transitions as certain and uncertain to make deadlock-freedom conservative, i.e. if the abstraction of a system is deadlock-free, then the system is deadlock-free. An abstraction refinement approach to deadlock detection is proposed, and the correctness of the approach is proved.展开更多
CEGAR （Counterexample-guided abstraction refinement）-based slicing is one of the most important techniques in reducing the state space in model checking. However, CEGAR-based slicing repeatedly explores the state sp...CEGAR （Counterexample-guided abstraction refinement）-based slicing is one of the most important techniques in reducing the state space in model checking. However, CEGAR-based slicing repeatedly explores the state space handled previously in case a spurious counterexample is found. Inspired by lazy abstraction, we introduce the concept of lazy slicing which eliminates this repeated computation. Lazy slicing is done on-the-fly, and only up to the precision necessary to rule out spurious counterexamples. It identifies a spurious counterexample by concretizing a path fragment other than the full path, which reduces the cost of spurious counterexample decision significantly. Besides, we present an improved over-approximate slicing method to build a more precise slice model. We also provide the proof of the correctness and the termination of lazy slicing, and implement a prototype model checker to verify safety property. Experimental results show that lazy slicing scales to larger systems than CEGAR-based slicing methods.展开更多
In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, ...In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validating it with a numerical example.展开更多
In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works(Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is...In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works(Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is presented to illustrate how a monotone non-convex optimization problem can be transformed into an equivalent convex minimization problem.展开更多
In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators....In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.展开更多
基金Supported in part by Zhejiang Provincial Natural Science Foundation of Chinaa Special Research Fund ot" State Council of Education of China
文摘We adopt the following symbols and notations. Let C;be the class of all real continuous functions in [0,1] which have N continuousderivatives, L;0,1];be the space of real pth power integrable functions on [0,1], and Δ;, asusual, be the class of kth monotone functions.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘In this paper, we give a counterexample to the article 'Globally asymptotic stability of a recurrence sequence', Ann. of Diff. Eqs., 17:1(2001), 82-85.
文摘If K ∩ AlgL is weak. dense in AlgL, where K is the set of all compactoperators in B(H), is completely distributive? In this note, we prove that there is a reflexivesubspace lattice L on some Hilbert space, which satisfies the following conditions: (a) F(AlgL) isdense in AlgL in the ultrastrong operator topology, where F(AlgL) is the set of all finite rankoperators in AlgL; (b) L isnt a completely distributive lattice. The subspace lattices that satisfythe above conditions form a large class of lattices. As a special case of the result, it easy to seethat the answer to Problem 7 is negative.
文摘Entropy is important in philosophy of science,but some fallacies originate from the misunderstanding entropy increases.The basis of thermodynamics is the statistics and its basic principle of statistical independence.We proposed possible entropy decrease due to fluctuation magnified and internal interactions in isolated systems,and discuss this possibility of various aspects on science and nature.Further,we derive quantitatively a total formula of entropy change for universal evolution of any natural and social systems,and discuss entropy decrease in economics and social sciences.Entropy change is a testable science.As long as we break through the bondage of the second law of thermodynamics,the rich and complex world is full of examples of entropy decrease.We believe world is not pessimistic always.
基金supported by the Natural Science Foundation of Shanghai (Grant No.09ZR1412100)the National Natural Science Foundation of China (Grant No.60673115)the Shanghai Leading Academic Discipline Project (Grant No.J50103)
文摘This paper adopts counterexample guided abstraction refinement scheme to alleviate the state explosion problem of deadlock detection. We extend the classical labeled transition system models by qualifying transitions as certain and uncertain to make deadlock-freedom conservative, i.e. if the abstraction of a system is deadlock-free, then the system is deadlock-free. An abstraction refinement approach to deadlock detection is proposed, and the correctness of the approach is proved.
基金Supported by the National Natural Science Foundation of China under Grant No. 60873038the National Key Technology Research and Development Program of the Ministry of Science and Technology of China under Grant Nos. 2009BAH42B02 and 2012BAH08B02
文摘CEGAR （Counterexample-guided abstraction refinement）-based slicing is one of the most important techniques in reducing the state space in model checking. However, CEGAR-based slicing repeatedly explores the state space handled previously in case a spurious counterexample is found. Inspired by lazy abstraction, we introduce the concept of lazy slicing which eliminates this repeated computation. Lazy slicing is done on-the-fly, and only up to the precision necessary to rule out spurious counterexamples. It identifies a spurious counterexample by concretizing a path fragment other than the full path, which reduces the cost of spurious counterexample decision significantly. Besides, we present an improved over-approximate slicing method to build a more precise slice model. We also provide the proof of the correctness and the termination of lazy slicing, and implement a prototype model checker to verify safety property. Experimental results show that lazy slicing scales to larger systems than CEGAR-based slicing methods.
文摘In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validating it with a numerical example.
基金founded by the National Natural Science Foundation of China(Nos.11991024,11871128,and 11771064).
文摘In this paper,firstly,we give a counterexample to point out there exist deficiencies in our previous works(Wu et al.in J Glob Optim 31:45-60,2005).In addition,we improve the corresponding results.Finally,an example is presented to illustrate how a monotone non-convex optimization problem can be transformed into an equivalent convex minimization problem.
基金This work is supported by Visiting Scholar Foundation of Key Lab in Peking UniversityThe project supported by the Science and Technical Development Foundation of Fuzhou UniversityThe projcect supported by the Science and Technical Foundation to the E
文摘In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.
