This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained b...This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.展开更多
在模糊推理中,基于贴近度的方法(简称SAR)是一种运算简便、且计算结果符合实际的推理方法。该方法的两种最基本的形式是扩展形式和还原形式。然而这两种形式都距离规则结论B太远,而扩展形式中最小的结果与还原形式中最大的结果也都过于...在模糊推理中,基于贴近度的方法(简称SAR)是一种运算简便、且计算结果符合实际的推理方法。该方法的两种最基本的形式是扩展形式和还原形式。然而这两种形式都距离规则结论B太远,而扩展形式中最小的结果与还原形式中最大的结果也都过于绝对。在已有的SAR方法中,采用的都是某个特殊的贴近度公式。在文献[Y.F.Li,K.Y.Qin,X.X.He.Some new approaches to constructing similarity measures.Fuzzy Sets and Systems,2014,234:46-60]中,我们给出了统一的贴近度的计算公式,证明了已有了多数贴近度公式都可以由所给出的统一贴近度公式得到。文章基于前期关于贴近度的工作,将统一的贴近度公式应用到SAR方法中,将扩展形式中最小的结果与还原形式中最大的结果求算数平均得到SAR方法的一种新的计算形式,并证明利用这种形式计算出的模糊推理的结果满足三条重要的推理原则:假言推理、近似性与逼近性。展开更多
The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks...The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (<em>ε</em>-PQC) on <em>fermionic</em> Gaussian systems (<em>i.e.</em>, <em>ε</em>-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for <em>ε</em>-FPQC on the fermionic Gaussian systems with respect to the Schatten <em>p</em>-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the <em>ε</em>-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.展开更多
The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields ar...The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = (?)u ·Ln + X2 u is proved, where u ∈ BVx(?) and (Ω)u denotes the approximate differential of u.展开更多
In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of...In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.展开更多
We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronge...We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.展开更多
基金supported by Ministry of Human Resource and Development(MHR-02-23-200-429/304)
文摘This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.
文摘在模糊推理中,基于贴近度的方法(简称SAR)是一种运算简便、且计算结果符合实际的推理方法。该方法的两种最基本的形式是扩展形式和还原形式。然而这两种形式都距离规则结论B太远,而扩展形式中最小的结果与还原形式中最大的结果也都过于绝对。在已有的SAR方法中,采用的都是某个特殊的贴近度公式。在文献[Y.F.Li,K.Y.Qin,X.X.He.Some new approaches to constructing similarity measures.Fuzzy Sets and Systems,2014,234:46-60]中,我们给出了统一的贴近度的计算公式,证明了已有了多数贴近度公式都可以由所给出的统一贴近度公式得到。文章基于前期关于贴近度的工作,将统一的贴近度公式应用到SAR方法中,将扩展形式中最小的结果与还原形式中最大的结果求算数平均得到SAR方法的一种新的计算形式,并证明利用这种形式计算出的模糊推理的结果满足三条重要的推理原则:假言推理、近似性与逼近性。
文摘The private quantum channel (PQC) maps any quantum state to the maximally mixed state for the discrete as well as the bosonic Gaussian quantum systems, and it has fundamental meaning on the quantum cryptographic tasks and the quantum channel capacity problems. In this paper, we primally introduce a notion of approximate private quantum channel (<em>ε</em>-PQC) on <em>fermionic</em> Gaussian systems (<em>i.e.</em>, <em>ε</em>-FPQC), and construct its explicit form of the fermionic (Gaussian) private quantum channel. First of all, we suggest a general structure for <em>ε</em>-FPQC on the fermionic Gaussian systems with respect to the Schatten <em>p</em>-norm class, and then we give an explicit proof of the statement in the trace norm case. In addition, we study that the cardinality of a set of fermionic unitary operators agrees on the <em>ε</em>-FPQC condition in the trace norm case. This result may give birth to intuition on the construction of emerging fermionic Gaussian quantum communication or computing systems.
文摘The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = (?)u ·Ln + X2 u is proved, where u ∈ BVx(?) and (Ω)u denotes the approximate differential of u.
基金support from the Key R&D Program of Shandong Province(Grant No.2019JZZY010431)the National Natural Science Foundation of China(Grant No.52175130)+1 种基金the Sichuan Science and Technology Program(Grant No.2022YFQ0087)the Sichuan Science and Technology Innovation Seedling Project Funding Projeet(Grant No.2021112)are gratefully acknowledged.
文摘In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.
基金The National Natural Science Foundation of China(11961069)Outstanding Young Science and Technology Training Program of Xinjiang(2019Q022)+1 种基金Natural Science Foundation of Xinjiang(2019D01A71)Scientific Research Programs of Colleges in Xinjiang(XJEDU2018Y033)。
基金Supported by National Natural Science Foundation of China(Grant No.11571387)CUFE Young Elite Teacher Project(Grant No.QYP1902)。
文摘We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.
