In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some result...In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some results on the partial ordering of the range symmetric matrices with respect to the Minkowski adjoint. Further, we establish some results regarding the partial ordering of m-projectors with respect to the Minkowski adjoint and manipulate them to characterize some sets of range symmetric elements in the Minkowski Space M. All the results obtained in this paper are an extension to the Minkowski space of those given by A. Hernandez, et al. in [The star partial order and the eigenprojection at 0 on EP matrices, Applied Mathematics and Computation, 218: 10669-10678, 2012].展开更多
Rational planning of spares configuration project is an effective approach to improve equipment availability as well as reduce life cycle cost （LCC）. With an analysis of various impacts on support system, the spares...Rational planning of spares configuration project is an effective approach to improve equipment availability as well as reduce life cycle cost （LCC）. With an analysis of various impacts on support system, the spares demand rate forecast model is constructed. According to systemic analysis method, spares support effectiveness evaluation indicators system is built, and then, initial spares configuration and optimization method is researched. To the issue of discarding and con-sumption for incomplete repairable items, its expected backorders function is approximated by Laplace demand distribution. Combining the （s-1, s） and （R, Q） inventory policy, the spares resup-ply model is established under the batch ordering policy based on inventory state, and the optimi-zation analysis flow for spares configuration is proposed. Through application on shipborne equipment spares configuration, the given scenarios are analyzed under two constraint targets：one is the support effectiveness, and the other is the spares cost. Analysis reveals that the result is consistent with practical regulation;therefore, the model＇s correctness, method＇s validity as well as optimization project＇s rationality are proved to a certain extent.展开更多
In this paper,we introduce the D-star order,T-star order,and P-star order on the class of dual matrices.By applying the matrix decomposition and dual generalized inverses,we discuss properties,characterizations,and re...In this paper,we introduce the D-star order,T-star order,and P-star order on the class of dual matrices.By applying the matrix decomposition and dual generalized inverses,we discuss properties,characterizations,and relations among these orders,and illustrate their relations with examples.展开更多
Ⅰ. INTRODUCTION Computer-assisted molecular design and synthetic planning is an important aspect in modern chemical research. To give assistance to chemical design, a computer should acquire the ability to recognize ...Ⅰ. INTRODUCTION Computer-assisted molecular design and synthetic planning is an important aspect in modern chemical research. To give assistance to chemical design, a computer should acquire the ability to recognize chemical structures, namely, the internal representation (adjacent matrix) and external representation (linear notation, 2-D or 3-D molecular graphics and struc-展开更多
Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain...Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.展开更多
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.展开更多
We consider the following quasiconvex functional I(u)=∫ Gf(x,δu,D mu) d x where u is a vector valued function in W m,p (G),m>1 and p>2. The partial C m,a —regularity is proved fo...We consider the following quasiconvex functional I(u)=∫ Gf(x,δu,D mu) d x where u is a vector valued function in W m,p (G),m>1 and p>2. The partial C m,a —regularity is proved for minimizers of I(u) under weaker conditions.展开更多
We investigate relationships between the Moore-Penrose inverse （ABA^＊）＋ and the product [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） through some rank and inertia formulas for the difference of （ABA^＊）^＋ - [（AB）^...We investigate relationships between the Moore-Penrose inverse （ABA^＊）＋ and the product [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） through some rank and inertia formulas for the difference of （ABA^＊）^＋ - [（AB）^（1,2,3）]^＊B（AB）^（1,2,3）, where B is Hermitian matrix and （AB）^（1,2,3） is a {1, 2, 3}-inverse of AB. We show that there always exists an （AB）^（1,2,3） such that （ABA^＊）^＋ = [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） holds. In addition, we also establish necessary and sufficient conditions for the two inequalities （ABA^＊）^＋ 〉 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） and （ABA^＊）^＋〈4 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） to hold in the LSwner partial ordering. Some variations of the equalities and inequalities are also presented. In particular, some equalities and inequalities for the Moore-Penrose inverse of the sum A ＋ B of two Hermitian matrices A and B are established.展开更多
In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a...In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.展开更多
This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operato...This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.展开更多
Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only i...Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.展开更多
In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially orde...In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially ordered metric spaces.A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction,and a coupled common fixed point theorem is obtained.Some examples are given to support our results.展开更多
All intermetallic phases have a tendency to atomic long-range ordering, according to the ordering energy, they may be permanently ordered (up to the melting-point) or reversibly ordered (up to a critical temperature)....All intermetallic phases have a tendency to atomic long-range ordering, according to the ordering energy, they may be permanently ordered (up to the melting-point) or reversibly ordered (up to a critical temperature). The paper considers ways of disordering intermetallic phases, in relation to the ordering energy and diffusivities, and some properties of partially ordered intermetallic phases (including mechanical properties) The kinetics of re-ordering of disordered starting material will be examined,including sluggishly ordering phases (which can be aided by concurrent irradiation). The circumstances under which a partially disordered intermetallic phase may transform into an amorphous form will be outlined.展开更多
In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich ...In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.展开更多
In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric...In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.展开更多
We experimentally study the generation of a partially coherent non-diffractive beam by focusing a partially coherent vortex beam with an axieon. The investigation results show that when the partially coherent vortex b...We experimentally study the generation of a partially coherent non-diffractive beam by focusing a partially coherent vortex beam with an axieon. The investigation results show that when the partially coherent vortex beam is focused by the axicon, the beam is transferred into a partially coherent higher-order non-diffractive beam. In the non-diffractive zone, the transverse intensity distribution of the partially coherent higher-order non-diffractive beam is invariant during propagation. In addition, the range of the non-diffractive zone is related to the coherence of the partially coherent vortex beam. The poorer the coherence of the partially coherent vortex beam, the shorter the range of the non-diffractive zone.展开更多
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing t...The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.展开更多
In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a com...In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.展开更多
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish...In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.展开更多
文摘In this paper, we obtain some new characterizations of the range symmetric matrices in the Minkowski Space M by using the Block representation of the matrices. These characterizations are used to establish some results on the partial ordering of the range symmetric matrices with respect to the Minkowski adjoint. Further, we establish some results regarding the partial ordering of m-projectors with respect to the Minkowski adjoint and manipulate them to characterize some sets of range symmetric elements in the Minkowski Space M. All the results obtained in this paper are an extension to the Minkowski space of those given by A. Hernandez, et al. in [The star partial order and the eigenprojection at 0 on EP matrices, Applied Mathematics and Computation, 218: 10669-10678, 2012].
基金co-supported by the General Armament Department Pre-research Foundation of China (Nos. 51304010206, 51327 020105)
文摘Rational planning of spares configuration project is an effective approach to improve equipment availability as well as reduce life cycle cost （LCC）. With an analysis of various impacts on support system, the spares demand rate forecast model is constructed. According to systemic analysis method, spares support effectiveness evaluation indicators system is built, and then, initial spares configuration and optimization method is researched. To the issue of discarding and con-sumption for incomplete repairable items, its expected backorders function is approximated by Laplace demand distribution. Combining the （s-1, s） and （R, Q） inventory policy, the spares resup-ply model is established under the batch ordering policy based on inventory state, and the optimi-zation analysis flow for spares configuration is proposed. Through application on shipborne equipment spares configuration, the given scenarios are analyzed under two constraint targets：one is the support effectiveness, and the other is the spares cost. Analysis reveals that the result is consistent with practical regulation;therefore, the model＇s correctness, method＇s validity as well as optimization project＇s rationality are proved to a certain extent.
基金supported partially by the Guangxi Natural Science Foundation of China(Grant Number 2018GXNSFDA281023)the National Natural Science Foundation of China(Grant Number 12061015)+1 种基金Xiangsihu Young Scholars Innovative Research Team of Guangxi Minzu University(Grant Number 2019RSCXSHQN03)Thousands of Young and Middle-Aged Key Teachers Training Pro-gramme in Guangxi Colleges and Universities(Grant Number GUIJIAOSHIFAN2019-81HAO).
文摘In this paper,we introduce the D-star order,T-star order,and P-star order on the class of dual matrices.By applying the matrix decomposition and dual generalized inverses,we discuss properties,characterizations,and relations among these orders,and illustrate their relations with examples.
基金Project supported by the Structure Research Laboratory, University of Science and Technology of China, Academia Sinica
文摘Ⅰ. INTRODUCTION Computer-assisted molecular design and synthetic planning is an important aspect in modern chemical research. To give assistance to chemical design, a computer should acquire the ability to recognize chemical structures, namely, the internal representation (adjacent matrix) and external representation (linear notation, 2-D or 3-D molecular graphics and struc-
基金supported by the National Basic Research Program of China (2006CB705400)Science & Technology Commission of Shanghai Municipality (071111008)Research & Development Program of China (2006AA4z334)
文摘Motion type (or motion pattern) of a mechanism is defined as the set of all rigid motions achievable by the mechanism’s end-effector;the motion type of a parallel mechanism equals the intersection set of all subchain motion types.The motion type of a non-instantaneous parallel mechanism locally agrees with a regular submanifold (or a Lie subgroup in particular) of the special Euclidean group SE(3).Based on submanifold germs of SE(3), we can define an equivalence relation and a partial order relation for both motion types and parallel mechanisms: two motion types are equivalent if and only if they agree on an open neighbor-hood around the identity element of SE(3);two motion types are comparable if and only if one is a submanifold of the other on an open neighborhood around the identity of SE(3).It is also possible to define equivalence relation and partial ordering on the col-lection of parallel mechanisms.In this paper, we first study properties of the equivalence and partial order relation of both motion types and parallel mechanisms, then we discuss their application in type synthesis, mobility analysis and non-overconstrained ness realization of parallel mechanisms.
基金supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
文摘Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.
文摘We consider the following quasiconvex functional I(u)=∫ Gf(x,δu,D mu) d x where u is a vector valued function in W m,p (G),m>1 and p>2. The partial C m,a —regularity is proved for minimizers of I(u) under weaker conditions.
基金Supported by the National Natural Science Foundation of China(Grant No.11271384)
文摘We investigate relationships between the Moore-Penrose inverse （ABA^＊）＋ and the product [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） through some rank and inertia formulas for the difference of （ABA^＊）^＋ - [（AB）^（1,2,3）]^＊B（AB）^（1,2,3）, where B is Hermitian matrix and （AB）^（1,2,3） is a {1, 2, 3}-inverse of AB. We show that there always exists an （AB）^（1,2,3） such that （ABA^＊）^＋ = [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） holds. In addition, we also establish necessary and sufficient conditions for the two inequalities （ABA^＊）^＋ 〉 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） and （ABA^＊）^＋〈4 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） to hold in the LSwner partial ordering. Some variations of the equalities and inequalities are also presented. In particular, some equalities and inequalities for the Moore-Penrose inverse of the sum A ＋ B of two Hermitian matrices A and B are established.
文摘In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.
文摘This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.
基金The NSF(11371233)of Chinathe Fundamental Research Funds(GK201301007)for the Central Universities
文摘Let B（H） be the C^＊-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B（H） preserving the star partial order in both directions if and only if one of the following assertions holds. （1） There exist a nonzero complex number a and two unitary operators U and V on H such that φ（X） = a UXV or φ（X） = α UX^＊ V for all X ∈B（H）. （2） There exist a nonzero a and two anti-unitary operators U and V on H such that φ（X） = αUXV or φ（X） = aUX^＊ Vfor all X∈ B（H）.
基金Supported by the National Natural Science Foundation of China(11701245)the Scientific Research Fund of Sichuan Provincial Education Department(18ZB0272)
文摘In this article,some coupled coincidence point results for two mappings g:X→X and G:X×X→X satisfying F-contractive type conditions are obtained,and some coupled fixed point results are derived in partially ordered metric spaces.A sufficient condition for uniqueness of coupled point of coincidence are established for F type contraction,and a coupled common fixed point theorem is obtained.Some examples are given to support our results.
文摘All intermetallic phases have a tendency to atomic long-range ordering, according to the ordering energy, they may be permanently ordered (up to the melting-point) or reversibly ordered (up to a critical temperature). The paper considers ways of disordering intermetallic phases, in relation to the ordering energy and diffusivities, and some properties of partially ordered intermetallic phases (including mechanical properties) The kinetics of re-ordering of disordered starting material will be examined,including sluggishly ordering phases (which can be aided by concurrent irradiation). The circumstances under which a partially disordered intermetallic phase may transform into an amorphous form will be outlined.
基金Supported by the NNSF of China(10961014)Supported by the NSF of Jiangxi Province(2008GZ048)Supported by the SF of Education Department of Jiangxi Province(GJJZ[2007]134)
文摘In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.
文摘In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.
基金Project supported by the National Natural Science Foundation of China (Grant No.60977068)the Foundations of the State Key Laboratory for Transient Optical and Photonic Technology of Chinese Academy of Sciences (Grant No.SKL ST200912)
文摘We experimentally study the generation of a partially coherent non-diffractive beam by focusing a partially coherent vortex beam with an axieon. The investigation results show that when the partially coherent vortex beam is focused by the axicon, the beam is transferred into a partially coherent higher-order non-diffractive beam. In the non-diffractive zone, the transverse intensity distribution of the partially coherent higher-order non-diffractive beam is invariant during propagation. In addition, the range of the non-diffractive zone is related to the coherence of the partially coherent vortex beam. The poorer the coherence of the partially coherent vortex beam, the shorter the range of the non-diffractive zone.
基金The Innovation Foundation for College Research Team of Shanxi University of Finance and Economics
文摘The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method. Some new existence results are obtained.
基金Supported by the National Natural Science Foundation of China(12161056,11701259,11771198)Natural Science Foundation of Jiangxi Province of China(20202BAB201001).
文摘In this paper,we introduce the concept of comparable T-completeness of a partially ordered Menger PM-space and discuss the existence of fixed points for mappings satisfying certain conditions in the framework of a comparable T-complete partially ordered Menger PM-space.We obtain some new results which generalize many known ones in the literature.Moreover,we derive some consequent results and give an example to illustrate our main result.
文摘In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequallities.
