In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new...In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.展开更多
Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the ...Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.展开更多
The concept of Fan-Browder mappings was first introduced in topological spaces without any convex structure. Then a new continuous selection theorem was obtained for the Fan-Browder mapping with range in a topological...The concept of Fan-Browder mappings was first introduced in topological spaces without any convex structure. Then a new continuous selection theorem was obtained for the Fan-Browder mapping with range in a topological space without any convex structure and noncompact domain. As applications, some fixed point theorems, coincidence theorems and a nonempty intersection theorem were given. Both the new concepts and results unify and extend many known results in recent literature.展开更多
The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonli...The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.展开更多
The neutrality’s origin,character,and extent are studied in the Neutrosophic set.The neutrosophic set is an essential issue to research since it opens the door to a wide range of scientific and technological applicat...The neutrality’s origin,character,and extent are studied in the Neutrosophic set.The neutrosophic set is an essential issue to research since it opens the door to a wide range of scientific and technological applications.The neutrosophic set can find its spot to research because the universe is filled with indeterminacy.Neutrosophic set is currently being developed to express uncertain,imprecise,partial,and inconsistent data.Truth membership function,indeterminacymembership function,and falsitymembership function are used to express a neutrosophic set in order to address uncertainty.The neutrosophic set producesmore rational conclusions in a variety of practical problems.The neutrosophic set displays inconsistencies in data and can solve real-world problems.We are directed to do our work in semi-continuous and almost continuous mapping on the basis of the neutrosophic set by observing these.Since we are going to study the properties of semi continuous and almost continuous mapping,we present the meaning of N-semi-open set,N-semi-closed set,N-regularly open set,N-regularly closed set,N-continuous mapping,N-open mapping,N-closed mapping,Nsemi-continuous mapping,N-semi-open mapping,N-semi-closed mapping.Additionally,we attempt to demonstrate a portion of their properties and furthermore referred to some examples.展开更多
Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by man...Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler＇s topological entropy is also presented.展开更多
Planning and implementation as well as increased control over the Business Continuity Management （BCM） is a complex task in the company requiring adequate resources. BCM aims to reduce risks and develops plans for r...Planning and implementation as well as increased control over the Business Continuity Management （BCM） is a complex task in the company requiring adequate resources. BCM aims to reduce risks and develops plans for restoring business activities if they are interrupted by a disaster. The purpose of the paper is to analyze and describe two standards, Information Technology Infrastructure Library （ITIL） and Control Objectives for Information and Related Technology （COBIT）, especially their mapping for the improved planning and implementation of the BCM as well as the increased control over the BCM activities. COBIT is used more as a management framework, providing management tools, such as control objectives, metrics and maturity models in order to complement the control framework. ITIL includes process steps and tasks because it is more oriented towards IT processes （process framework）, defining the best practice for IT service management. Within this mapping, ITIL processes may be used to achieve and demonstrate compliance with COBIT control objectives for BCM process.展开更多
The concept of finitely continuous topological space is introduced and the basic properties of the space are given. Several continuous selection theorems and fixed point theorems for Ф-maps are established, and as ap...The concept of finitely continuous topological space is introduced and the basic properties of the space are given. Several continuous selection theorems and fixed point theorems for Ф-maps are established, and as applications of the above fixed point theorems, some section problems are discussed. The results generalize and improve many corresponding conclusions.展开更多
A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to...A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.展开更多
It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved...It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved effectively in the ficld of statics.In this paper,the fail-safe topology optimization problem is extended to the field of frequency topology optimization.Based on the independent continuous mapping(ICM)method,the model of fail-safe topology optimization is established with the objective of minimal weight integrating with the discrete condition of topological variables and the constraint of the fundamental frequency.The fail-safe optimization model established above is substituted by a sequence of subproblems in the form of the quadratic program with exact second-order information and solved efficiently by the dual sequence quadratic programming(DSQP)algorithm.The numerical result reveals that the optimized fail-safe structure has more complex configuration and preserved materials than the structure obtained from the traditional frequency topology optimization,which means that the optimized fail-safe structure has higher redundancy.Moreover,the optimized fail-safe structure guarantees that the natural frequency meets the constraint of fundamental frequency when the local failure ocurs,which can avoid the structural frequency to be sensitive to local failure.The fail-safe optimirzation topology model is proved effective and feasible by four numerical examples.展开更多
A finite element model for coupled thermo-meehanical analysis has been developed in hot continuous rolling process for Inconel 718 alloy round rod with diameter of 45 mm. The stability of this alloy is discussed by in...A finite element model for coupled thermo-meehanical analysis has been developed in hot continuous rolling process for Inconel 718 alloy round rod with diameter of 45 mm. The stability of this alloy is discussed by integration of FEM and processing map reported in literatures. The result shows that the stability of Inconel 718 alloy is analyzed effectively during that process and good stability appears as the initial temperature is 960 ℃ and the initial velocity is from 0. 15 to 0.45 m · s^-1 or the initial temperature is 980 ℃ and the initial velocity is from 0. 15 to 0. 25 m · s^-1.展开更多
Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K ...Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.展开更多
Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach...The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.展开更多
In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigro...In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup.展开更多
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.展开更多
Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax i...Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.展开更多
In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration ...In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.展开更多
This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combi...This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.展开更多
文摘In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.
基金This work was supported by the National Natural Science Foundation of China(11872080)Beijing Natural Science Foundation(3192005).
文摘Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.
基金Project supported by the Natural Science Foundation of Chongqing (CSTC)(No.2005BB2097)
文摘The concept of Fan-Browder mappings was first introduced in topological spaces without any convex structure. Then a new continuous selection theorem was obtained for the Fan-Browder mapping with range in a topological space without any convex structure and noncompact domain. As applications, some fixed point theorems, coincidence theorems and a nonempty intersection theorem were given. Both the new concepts and results unify and extend many known results in recent literature.
基金The project was supported by the National Natural Science Foundation of China (60375014) and the Postdoctoral Sci-ence Foundation of China
文摘The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.
文摘The neutrality’s origin,character,and extent are studied in the Neutrosophic set.The neutrosophic set is an essential issue to research since it opens the door to a wide range of scientific and technological applications.The neutrosophic set can find its spot to research because the universe is filled with indeterminacy.Neutrosophic set is currently being developed to express uncertain,imprecise,partial,and inconsistent data.Truth membership function,indeterminacymembership function,and falsitymembership function are used to express a neutrosophic set in order to address uncertainty.The neutrosophic set producesmore rational conclusions in a variety of practical problems.The neutrosophic set displays inconsistencies in data and can solve real-world problems.We are directed to do our work in semi-continuous and almost continuous mapping on the basis of the neutrosophic set by observing these.Since we are going to study the properties of semi continuous and almost continuous mapping,we present the meaning of N-semi-open set,N-semi-closed set,N-regularly open set,N-regularly closed set,N-continuous mapping,N-open mapping,N-closed mapping,Nsemi-continuous mapping,N-semi-open mapping,N-semi-closed mapping.Additionally,we attempt to demonstrate a portion of their properties and furthermore referred to some examples.
文摘Topological entropy can be an indicator of complicated behavior in dynamical systems. It is first introduce by Adler, Konheim and McAndrew by using open covers in 1965. After that it is still an active research by many researchers to produce more properties and applications up to nowadays. The purpose of this paper is to review and explain most important concepts and results of topological entropies of continuous self-maps for dynamical systems on compact and non-compact topological and metric spaces. We give proofs for some of its elementary properties of the topological entropy. Slight modification on Adler＇s topological entropy is also presented.
文摘Planning and implementation as well as increased control over the Business Continuity Management （BCM） is a complex task in the company requiring adequate resources. BCM aims to reduce risks and develops plans for restoring business activities if they are interrupted by a disaster. The purpose of the paper is to analyze and describe two standards, Information Technology Infrastructure Library （ITIL） and Control Objectives for Information and Related Technology （COBIT）, especially their mapping for the improved planning and implementation of the BCM as well as the increased control over the BCM activities. COBIT is used more as a management framework, providing management tools, such as control objectives, metrics and maturity models in order to complement the control framework. ITIL includes process steps and tasks because it is more oriented towards IT processes （process framework）, defining the best practice for IT service management. Within this mapping, ITIL processes may be used to achieve and demonstrate compliance with COBIT control objectives for BCM process.
文摘The concept of finitely continuous topological space is introduced and the basic properties of the space are given. Several continuous selection theorems and fixed point theorems for Ф-maps are established, and as applications of the above fixed point theorems, some section problems are discussed. The results generalize and improve many corresponding conclusions.
基金This work is partially supported by D.G.E.S. PB 96-1338-CO2-01 and the Junta de Andalucla.
文摘A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.
基金the National Natural Science Foundation of China(Grant 11872080).
文摘It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures.Such a fail-safe topology optimization problem has been solved effectively in the ficld of statics.In this paper,the fail-safe topology optimization problem is extended to the field of frequency topology optimization.Based on the independent continuous mapping(ICM)method,the model of fail-safe topology optimization is established with the objective of minimal weight integrating with the discrete condition of topological variables and the constraint of the fundamental frequency.The fail-safe optimization model established above is substituted by a sequence of subproblems in the form of the quadratic program with exact second-order information and solved efficiently by the dual sequence quadratic programming(DSQP)algorithm.The numerical result reveals that the optimized fail-safe structure has more complex configuration and preserved materials than the structure obtained from the traditional frequency topology optimization,which means that the optimized fail-safe structure has higher redundancy.Moreover,the optimized fail-safe structure guarantees that the natural frequency meets the constraint of fundamental frequency when the local failure ocurs,which can avoid the structural frequency to be sensitive to local failure.The fail-safe optimirzation topology model is proved effective and feasible by four numerical examples.
基金Sponsored by National Natural Science Foundation of China(50634030)the Program of Education Ministry for New Century Excellent Talents in University(NECT-06-0285)
文摘A finite element model for coupled thermo-meehanical analysis has been developed in hot continuous rolling process for Inconel 718 alloy round rod with diameter of 45 mm. The stability of this alloy is discussed by integration of FEM and processing map reported in literatures. The result shows that the stability of Inconel 718 alloy is analyzed effectively during that process and good stability appears as the initial temperature is 960 ℃ and the initial velocity is from 0. 15 to 0.45 m · s^-1 or the initial temperature is 980 ℃ and the initial velocity is from 0. 15 to 0. 25 m · s^-1.
文摘Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.
文摘Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
基金the Natural Science Foundation of Yibin University （No.2005Z3）
文摘The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.
文摘In this paper, we get a sufficient condition to estimate the essential type of a strongly continuous sendgroup in a Banach space, using oh condition we prove that the essential type of the strongly continuous semigroup don't increase under the A-smoothing perturbation and establish the spectral mapping theorem for the asymptotic parts of the spectrum of generator and semgroup.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
基金Project supported by the National Natural Science Foundation of China(No.11126346)
文摘Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.
文摘In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.
文摘This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.
