If the concept of proof (including arithmetic proof) is syntactically restricted to closed sentences (or their Godel numbers), then the standard accounts of Godel's Incompleteness Theorems (and Lob's Theorem) ...If the concept of proof (including arithmetic proof) is syntactically restricted to closed sentences (or their Godel numbers), then the standard accounts of Godel's Incompleteness Theorems (and Lob's Theorem) are blocked. In these standard accounts (Godel's own paper and the exposition in Boolos' Computability and Logic are treated as exemplars), it is assumed that certain formulas (notably so called "Godel sentences") containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term "provable" (and indeed "unprovable") favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.展开更多
Increment of mobile cloud video motivates mobile users to utilize cloud storage service to address their demands, cloud storage provider always furnish a location-independent platform for managing user's data. Howeve...Increment of mobile cloud video motivates mobile users to utilize cloud storage service to address their demands, cloud storage provider always furnish a location-independent platform for managing user's data. However, mobile users wonder if their cloud video data leakage or dynamic migration to illegal service providers. In this paper, we design a novel provable data possession protocol based on data geographic location attribute, which allows data owner to auditing the integrity of their video data, which put forward an ideal choice for remote data possession checking in the mobile cloud storage. In our proposed scheme, we check out whether the video data dynamic migrate to an unspecified location (such as: overseas) by adding data geographic location attribute tag into provable data possession protocol. Moreover, we make sure the security of our proposed scheme under the Computational Diffic-Hellman assumption. The analysis and experiment results demonstrate that our proposed scheme is provably secure and efficient.展开更多
This paper deals with an alternative proof of Beurling-Lax theorem by adopting a constructive approach instead of the isomorphism technique which was used in the original proof.
This article is devoted to the study of high order accuracy difference methods tor the Cahn-rnmara equation. A three level linearized compact difference scheme is derived. The u^ique solvability and uaconditional conv...This article is devoted to the study of high order accuracy difference methods tor the Cahn-rnmara equation. A three level linearized compact difference scheme is derived. The u^ique solvability and uaconditional convergence of the difference solution are proved. The convergence order is O(T2+h4) in the maximum norm. The mass conservation and the non-increase of the total energy are also verified. Some numerical examples are given to demonstrate the theoretical results.展开更多
A nonlinear version of Krein Rutman Theorem is established.This paper presents aunified proof of the Krein Rutman Theorem for linear operators and for nonlinear operators,and ofthe Perron-Frobenius theorem for nonnega...A nonlinear version of Krein Rutman Theorem is established.This paper presents aunified proof of the Krein Rutman Theorem for linear operators and for nonlinear operators,and ofthe Perron-Frobenius theorem for nonnegative matrices and for nonnegative tensors.展开更多
In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impul...In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.展开更多
It is well known by the strong multiplicity one thatπis uniquely determined by the Satake parameter c(π,v)for almost all v.Also,it suffices for us to test only finitely many v.We proved some S-effective version of m...It is well known by the strong multiplicity one thatπis uniquely determined by the Satake parameter c(π,v)for almost all v.Also,it suffices for us to test only finitely many v.We proved some S-effective version of multiplicity one theorems.Roughly speaking,ifπandπ′are not equivalent,then there is also a bound N(S)which is some expression in terms of K,d and max(N(π),N(π′)),which are analytic conductor ofπandπ′,respectively(will be defined soon),such that there is a v/∈S withπv~=π′vand N pv<N.We also proved S-effective multiplicity one for the Chebotarev Density Theorem,and for GL(1).展开更多
A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S^(4n-1)→ S^(2n)× S^m as a module and demonstrate that it is not necessarily determined by the map in...A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S^(4n-1)→ S^(2n)× S^m as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality.展开更多
We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the...We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.展开更多
We give a new proof of Wu's theorem on vortex sheets by using WI'p estimate for the elliptic equation of divergence form with partially BMO coitlcients and Lp boundedness of commutators of Calder6n- Zygmund operators.
文摘If the concept of proof (including arithmetic proof) is syntactically restricted to closed sentences (or their Godel numbers), then the standard accounts of Godel's Incompleteness Theorems (and Lob's Theorem) are blocked. In these standard accounts (Godel's own paper and the exposition in Boolos' Computability and Logic are treated as exemplars), it is assumed that certain formulas (notably so called "Godel sentences") containing the Godel number of an open sentence and an arithmetic proof predicate are closed sentences. Ordinary usage of the term "provable" (and indeed "unprovable") favors their restriction to closed sentences which unlike so-called open sentences can be true or false. In this paper the restricted form of provability is called strong provability or unprovability. If this concept of proof is adopted, then there is no obvious alternative path to establishing those theorems.
基金supported in part by National High Tech Research and Development Program(863 Program)of China(No.2015 AA016005)
文摘Increment of mobile cloud video motivates mobile users to utilize cloud storage service to address their demands, cloud storage provider always furnish a location-independent platform for managing user's data. However, mobile users wonder if their cloud video data leakage or dynamic migration to illegal service providers. In this paper, we design a novel provable data possession protocol based on data geographic location attribute, which allows data owner to auditing the integrity of their video data, which put forward an ideal choice for remote data possession checking in the mobile cloud storage. In our proposed scheme, we check out whether the video data dynamic migrate to an unspecified location (such as: overseas) by adding data geographic location attribute tag into provable data possession protocol. Moreover, we make sure the security of our proposed scheme under the Computational Diffic-Hellman assumption. The analysis and experiment results demonstrate that our proposed scheme is provably secure and efficient.
基金supported by the Multi-Year Research Grant(No.MYRG115(Y1-L4)-FST13-QT)the Multi-Year Research Grant(No.MYRG116(Y1-L3)-FST13-QT)+1 种基金Macao Government(No.FDCT098/2012/A3)the Natural Science Foundation of Guangdong Province(No.S2011010004986)
文摘This paper deals with an alternative proof of Beurling-Lax theorem by adopting a constructive approach instead of the isomorphism technique which was used in the original proof.
基金supported by Natural Science Foundation of China (Grant No. 10871044)
文摘This article is devoted to the study of high order accuracy difference methods tor the Cahn-rnmara equation. A three level linearized compact difference scheme is derived. The u^ique solvability and uaconditional convergence of the difference solution are proved. The convergence order is O(T2+h4) in the maximum norm. The mass conservation and the non-increase of the total energy are also verified. Some numerical examples are given to demonstrate the theoretical results.
文摘A nonlinear version of Krein Rutman Theorem is established.This paper presents aunified proof of the Krein Rutman Theorem for linear operators and for nonlinear operators,and ofthe Perron-Frobenius theorem for nonnegative matrices and for nonnegative tensors.
文摘In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.
基金supported by the State Key Development Program for Basic Researchof China(973 project)(Grant No.2013CB834202)National Natural Science Foundation of China(Grant No.11321101)the One Hundred Talent’s Program from Chinese Academy of Science
文摘It is well known by the strong multiplicity one thatπis uniquely determined by the Satake parameter c(π,v)for almost all v.Also,it suffices for us to test only finitely many v.We proved some S-effective version of multiplicity one theorems.Roughly speaking,ifπandπ′are not equivalent,then there is also a bound N(S)which is some expression in terms of K,d and max(N(π),N(π′)),which are analytic conductor ofπandπ′,respectively(will be defined soon),such that there is a v/∈S withπv~=π′vand N pv<N.We also proved S-effective multiplicity one for the Chebotarev Density Theorem,and for GL(1).
基金supported by the National Science and Engineering Research Council of Canada
文摘A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S^(4n-1)→ S^(2n)× S^m as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality.
文摘We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.
基金supported by National Natural Science Foundation of China (Grant Nos.10990013 and 11071007)
文摘We give a new proof of Wu's theorem on vortex sheets by using WI'p estimate for the elliptic equation of divergence form with partially BMO coitlcients and Lp boundedness of commutators of Calder6n- Zygmund operators.