This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ...This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,展开更多
The automatic loading systems of artillery are critical for the accurate,efficient,and reliable delivery of pro-jectiles and propellants into the gun chamber.In modern artillery,the ammunition conveyor serves as the e...The automatic loading systems of artillery are critical for the accurate,efficient,and reliable delivery of pro-jectiles and propellants into the gun chamber.In modern artillery,the ammunition conveyor serves as the end effector of the automatic loading system,and its motion state significantly impacts the accuracy of projectiles.Therefore,it is of immense importance to precisely and effectively evaluate the reliability of the motion accuracy of the ammunition conveyor.This paper aims to propose a practical and efficient analysis method for evaluating the reliability of the motion accuracy of the ammunition conveyor.The proposed approach involves the use of a deep learning network to approximate the physical model and the extremum method to obtain a single cycle sequence decoupling strategy for solving the time-varying reliability issue of complex systems.Employing this strategy,the time-varying reliability of the ammunition conveyor is transformed into a static reliability problem.The proposed method includes the use of a deep feedforward neural network,second-order saddle point ap-proximation(SPA)method,extremum method,and efficient global optimization(EGO)technology.The results reveal that the reliability of the motion accuracy of the ammunition conveyor is 93.42%,with the maximum failure probability occurring at 0.21 s.These results serve as an important reference for the structural optimi-zation design of the ammunition conveyor based on reliability and the maintenance of the operational process.展开更多
In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde...In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.展开更多
Dear Editor,This letter focuses on the remaining useful life(RUL)prediction task under limited labeled samples.Existing machine-learning-based RUL prediction methods for this task usually pay attention to mining degra...Dear Editor,This letter focuses on the remaining useful life(RUL)prediction task under limited labeled samples.Existing machine-learning-based RUL prediction methods for this task usually pay attention to mining degradation information to improve the prediction accuracy of degradation value or health indicator for the next epoch.However,they ignore the cumulative prediction error caused by iterations before reaching the failure point.展开更多
In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal...In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.展开更多
The study of operators satisfying σja（T ） = σa（T ） is of significant interest. Does σja（T ） = σa（T ） for n-perinormal operator T ∈ B（H）？ This question was raised by Mecheri and Braha [Oper. Matrices 6 ...The study of operators satisfying σja（T ） = σa（T ） is of significant interest. Does σja（T ） = σa（T ） for n-perinormal operator T ∈ B（H）？ This question was raised by Mecheri and Braha [Oper. Matrices 6 （2012）, 725-734]. In the note we construct a counterexample to this question and obtain the following result： if T is a n-perinormal operator in B（H）, then σja（T ）／{0} = σa（T ）／{0}. We also consider tensor product of n-perinormal operators.展开更多
Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of clos...In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.展开更多
The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian ...The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method.展开更多
An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(...An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.展开更多
The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectr...The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.展开更多
Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the i...Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.展开更多
Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and as...Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.展开更多
文摘This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,
基金Supported by National Natural Science Foundation of China(Grant No.U2141246)Key Laboratory of Artillery Launch and Control Technology of China(Grant No.2021-001)Basic Research of State Administration of Science Technology and Industry for National Defense of China(Grant No.JXJL202208A001).
文摘The automatic loading systems of artillery are critical for the accurate,efficient,and reliable delivery of pro-jectiles and propellants into the gun chamber.In modern artillery,the ammunition conveyor serves as the end effector of the automatic loading system,and its motion state significantly impacts the accuracy of projectiles.Therefore,it is of immense importance to precisely and effectively evaluate the reliability of the motion accuracy of the ammunition conveyor.This paper aims to propose a practical and efficient analysis method for evaluating the reliability of the motion accuracy of the ammunition conveyor.The proposed approach involves the use of a deep learning network to approximate the physical model and the extremum method to obtain a single cycle sequence decoupling strategy for solving the time-varying reliability issue of complex systems.Employing this strategy,the time-varying reliability of the ammunition conveyor is transformed into a static reliability problem.The proposed method includes the use of a deep feedforward neural network,second-order saddle point ap-proximation(SPA)method,extremum method,and efficient global optimization(EGO)technology.The results reveal that the reliability of the motion accuracy of the ammunition conveyor is 93.42%,with the maximum failure probability occurring at 0.21 s.These results serve as an important reference for the structural optimi-zation design of the ammunition conveyor based on reliability and the maintenance of the operational process.
基金Supported both by the Teaching and Research Award Fund for Outstanding Young Teachers inHigher Educational Institutions of MOEChinaand by the Dawn Program Fund in Shanghai
文摘In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.
基金supported in part by the National Natural Science Foundation of China(U2034209)the Postdoctoral Science Foundation of Chongqing(cstc2021jcyj-bsh X0047)+1 种基金the Fundamental Research Funds for the Central Universities(2022CDJJMRH-008)the National Natural Science Foundation of China(62203075)
文摘Dear Editor,This letter focuses on the remaining useful life(RUL)prediction task under limited labeled samples.Existing machine-learning-based RUL prediction methods for this task usually pay attention to mining degradation information to improve the prediction accuracy of degradation value or health indicator for the next epoch.However,they ignore the cumulative prediction error caused by iterations before reaching the failure point.
基金Supported by the Education Foundation of Henan Province(2003110006)
文摘In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.
基金supported by NNSF(1122618511201126)the Basic Science and Technological Frontier Project of Henan Province(132300410261)
文摘The study of operators satisfying σja（T ） = σa（T ） is of significant interest. Does σja（T ） = σa（T ） for n-perinormal operator T ∈ B（H）？ This question was raised by Mecheri and Braha [Oper. Matrices 6 （2012）, 725-734]. In the note we construct a counterexample to this question and obtain the following result： if T is a n-perinormal operator in B（H）, then σja（T ）／{0} = σa（T ）／{0}. We also consider tensor product of n-perinormal operators.
文摘Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
文摘In this article, we study characterization, stability, and spectral mapping the- orem for Browder＇s essential spectrum, Browder＇s essential defect spectrum and Browder＇s essential approximate point spectrum of closed densely defined linear operators on Banach spaces.
文摘The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method.
基金Supported by the Natural Science Foundation of the Department of Education of Henan Province（12B110025, 102300410012）
文摘An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.
文摘The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal.
文摘Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.
文摘Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
基金Foundation item： the National Natural Science Foundation of China （No. 10771141） the Natural Science Foundation of Zhejiang Province （Y605191） the Natural Science Foundation of Heilongjiang Province （No. A0211） and the Scientific Research Foundation from Zhejiang Province Education Committee （No. 20051897）.
文摘Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.
