A novel nonlinear adaptive control method is presented for a near-space hypersonic vehicle (NHV) in the presence of strong uncertainties and disturbances. The control law consists of the optimal generalized predicti...A novel nonlinear adaptive control method is presented for a near-space hypersonic vehicle (NHV) in the presence of strong uncertainties and disturbances. The control law consists of the optimal generalized predictive controller (OGPC) and the functional link network (FLN) direct adaptive law. OGPC is a continuous-time nonlinear predictive control law. The FLN adaptive law is used to offset the unknown uncertainties and disturbances in a flight through the online learning. The learning process does not need any offline training phase. The stability analyses of the NHV close-loop system are provided and it is proved that the system error and the weight learning error are uniformly ultimately hounded. Simulation results show the satisfactory performance of the con- troller for the attitude tracking.展开更多
Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.
The feasibility study of the AlCl(g) generated by Al_2O-AlCl_2-C system under vacuum was carried out by thermodynamic analysis and CASTEP package of the Material Studio program which was based on density functional th...The feasibility study of the AlCl(g) generated by Al_2O-AlCl_2-C system under vacuum was carried out by thermodynamic analysis and CASTEP package of the Material Studio program which was based on density functional theory(DFT) formalism. Thermodynamic calculations indicate that Al Cl and CO molecules can be formed under conditions of temperature 1760 K and the pressure of 60 Pa. The interaction of Al_2O and AlCl_2 with C shows that the chemical adsorption of Al_2O and AlCl_2 does take place on C(001) crystal plane, and at the same time, new chemical bond is formed between Al atom in Al_2O and Cl atoms from one of the Al—Cl bonds in AlCl_2. The results, after 1.25 ps dynamics simulation, indicate that adsorbed Al Cl molecules are generated and CO molecule will be formed in this system, and they will escape from C(001) surface after a longer period of dynamic simulation time. It means that the reaction of Al_2O and AlCl_2 with C can be carried out under given constraint condition.展开更多
Electrochemical N_(2) reduction provides a green and sustainable alternative to the Haber-Bosch technology for NH_(3 )synthesis.However,the extreme inertness of N_(2) molecules is a formidable challenge,which requires...Electrochemical N_(2) reduction provides a green and sustainable alternative to the Haber-Bosch technology for NH_(3 )synthesis.However,the extreme inertness of N_(2) molecules is a formidable challenge,which requires the development of an active electrocatalyst to drive the N_(2) reduction reaction(NRR)for NH_(3) production at ambient conditions.Herein,we demonstrate the development of La-doped TiO_(2) nanorods as an efficient NRR electrocatalyst for ambient NH3 synthesis.The optimized La-TiO_(2) catalyst offers a large NH_(3) yield of 23.06 pg h1 mgcat 1 and a high Faradaic efficiency of 14.54%at-0.70 V versus reversible hydrogen electrode in 0.1 M L1CIO_(4),outperforming most La-and Ti-based catalysts reported before.Significantly,it also demonstrates high electrochemical stability and its activity decay is negligible after 48 h test.The mechanism is further revealed by density functional theory calculations.展开更多
This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are ...This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.展开更多
In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality. From one example the article indicates that the fundamentality of the locally solid Riesz spa...In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality. From one example the article indicates that the fundamentality of the locally solid Riesz space is independent from the Lebesgue property.展开更多
In this paper, the author gives a new section theorem in L-convex spaces. And as its applications, the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.
For heterogeneous catalysts,the build-up of interface contacts can influence markedly their activities.Being different from the conventional supported metal/oxide catalysts,the reverse type of oxide/metal structures,e...For heterogeneous catalysts,the build-up of interface contacts can influence markedly their activities.Being different from the conventional supported metal/oxide catalysts,the reverse type of oxide/metal structures,e.g.the ceria/Pt composite,have emerged as novel catalytic materials in many fields.However,it remains challenging to determine the optimal interface structure and/or the metal-oxide synergistic effect that can boost catalytic activities.In this work,we conducted density functional theory calculations with on-site Coulomb interaction correction to determine the optimal structures and investigate the physical as well as catalytic properties of various Ce O2/Pt(111)composites containing Ce O2(111)monolayer,bilayer,and trilayer at Pt(111).We found that the interaction strength between Ce O2(111)and Pt(111)substrate first reduces as the ceria slab grows from monolayer to bilayer,and then largely gets converged when the trilayer occurs.Such trend was well rationalized by analyzing the number and distances of O–Pt bonds at the interface.Calculated Bader charges uncovered the significant charge redistribution occurring around the interface,whereas the net electron transfer across the interface is non-significant and decreases as ceria thickness increases.Moreover,comparative calculations on oxygen vacancy formation energies clarified that oxygen removal can be promoted on the Ce O2/Pt(111)composites,especially at the interface.We finally employed CO oxidation as a model reaction to probe the surface reactivity,and determined an intrinsic activity order of monolayer Ce O2(111)>monolayer Ce O2(111)/Pt(111)>regular Ce O2(111).More importantly,we emphasized the significant role of the moderate ceria-Pt interaction at the interface that endows the Ce O2/Pt reverse catalyst both good thermostability and high catalytic activity.The monolayer Ce O2(111)/Pt(111)composite was theoretically predicted highly efficient for catalyzing CO oxidation.展开更多
Density functional theory calculations were carried out to investigate the influence of doping transition metal(TM) ions into the ceria surface on the activation of surface lattice oxygen atoms. For this purpose, the ...Density functional theory calculations were carried out to investigate the influence of doping transition metal(TM) ions into the ceria surface on the activation of surface lattice oxygen atoms. For this purpose, the structure and stability of the most stable(111) surface termination of CeO2 modified by TM ions was determined. Except for Zr and Pt dopants that preserve octahedral oxygen coordination, the TM dopants prefer a square-planar coordination when substituting the surface Ce ions. The surface construction from octahedral to square-planar is facile for all TM dopants, except for Pt(1.14 e V) and Zr(square-planar coordination unstable). Typically, the ionic radius of tetravalent TM cations is much smaller than that of Ce4+, resulting a significant tensile-strained lattice and explaining the lowered oxygen vacancy formation energy. Except for Zr, the square-planar structure is the preferred one when one oxygen vacancy is created. Thermodynamic analysis shows that TM-doped CeO2 surfaces contain oxygen defects under typical conditions of environmental catalysis. A case of practical importance is the facile lattice oxygen activation in Zr-doped CeO2(111), which benefits CO oxidation. The findings emphasize the origin of lattice oxygen activation and the preferred location of TM dopants in TM-ceria solid solution catalysts.展开更多
In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation (K-functional) we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation (K-functional) we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
The lattice parameters, elastic constants, cohesive energy, structural energy differences, as well as the properties of point defects and planar defects of hexagonal closepacked yttrium (hcpY) have been studied with...The lattice parameters, elastic constants, cohesive energy, structural energy differences, as well as the properties of point defects and planar defects of hexagonal closepacked yttrium (hcpY) have been studied with ab initio density functional theory for constructing an ex tensive database. Based on an analytical bondorder poial scheme, empirical manybody interatomic potential for hcpY has been developed. The model is fitted to some properties of Y, e.g., the lattice parameters, elastic constants, bulk modulus, cohesive energy, vacancy formation energy, and the structural energy differences. The present potential has ability to reproduce defect properties including the selfinterstitial atoms formation energies, vacancy formation energy, divacancy binding energy, as well as the bulk properties and the thermal dynamic properties.展开更多
We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variationa...We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.展开更多
In this paper,a new GLKKM type theorem is established for noncompact complete L-convex metric spaces.As applications,the properties of the solution set of variational in-equalities,intersection point sets,Ky Fan secti...In this paper,a new GLKKM type theorem is established for noncompact complete L-convex metric spaces.As applications,the properties of the solution set of variational in-equalities,intersection point sets,Ky Fan sections and maximal element sets are shown,and a Fan-Browder fixed point theorem is obtained.展开更多
In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^...In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.展开更多
This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional com...This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators,the Hermitian adjoint, classification of antilinear normal operators,(skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.展开更多
The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces...The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane.展开更多
The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive ...The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others.展开更多
基金Supported by the National Nature Science Foundation of China (90716028)~~
文摘A novel nonlinear adaptive control method is presented for a near-space hypersonic vehicle (NHV) in the presence of strong uncertainties and disturbances. The control law consists of the optimal generalized predictive controller (OGPC) and the functional link network (FLN) direct adaptive law. OGPC is a continuous-time nonlinear predictive control law. The FLN adaptive law is used to offset the unknown uncertainties and disturbances in a flight through the online learning. The learning process does not need any offline training phase. The stability analyses of the NHV close-loop system are provided and it is proved that the system error and the weight learning error are uniformly ultimately hounded. Simulation results show the satisfactory performance of the con- troller for the attitude tracking.
文摘Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.
基金Projects(51104078,51264023)supported by the National Natural Science Foundation of ChinaProject(2010CD022)supported by Yunnan Province Applied Basic Research Fund,China+2 种基金Project(IRT1250)supported by the Program for Innovative Research Team in University of Ministry of Education of ChinaProject(U1202271)supported by the National Natural Science Foundation of China-Yunnan United FundProject(KKZ3201252020)supported by Kunming University of Science and Technology for Talent Training,China
文摘The feasibility study of the AlCl(g) generated by Al_2O-AlCl_2-C system under vacuum was carried out by thermodynamic analysis and CASTEP package of the Material Studio program which was based on density functional theory(DFT) formalism. Thermodynamic calculations indicate that Al Cl and CO molecules can be formed under conditions of temperature 1760 K and the pressure of 60 Pa. The interaction of Al_2O and AlCl_2 with C shows that the chemical adsorption of Al_2O and AlCl_2 does take place on C(001) crystal plane, and at the same time, new chemical bond is formed between Al atom in Al_2O and Cl atoms from one of the Al—Cl bonds in AlCl_2. The results, after 1.25 ps dynamics simulation, indicate that adsorbed Al Cl molecules are generated and CO molecule will be formed in this system, and they will escape from C(001) surface after a longer period of dynamic simulation time. It means that the reaction of Al_2O and AlCl_2 with C can be carried out under given constraint condition.
文摘Electrochemical N_(2) reduction provides a green and sustainable alternative to the Haber-Bosch technology for NH_(3 )synthesis.However,the extreme inertness of N_(2) molecules is a formidable challenge,which requires the development of an active electrocatalyst to drive the N_(2) reduction reaction(NRR)for NH_(3) production at ambient conditions.Herein,we demonstrate the development of La-doped TiO_(2) nanorods as an efficient NRR electrocatalyst for ambient NH3 synthesis.The optimized La-TiO_(2) catalyst offers a large NH_(3) yield of 23.06 pg h1 mgcat 1 and a high Faradaic efficiency of 14.54%at-0.70 V versus reversible hydrogen electrode in 0.1 M L1CIO_(4),outperforming most La-and Ti-based catalysts reported before.Significantly,it also demonstrates high electrochemical stability and its activity decay is negligible after 48 h test.The mechanism is further revealed by density functional theory calculations.
文摘This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.
基金the Research Fund for the Doctoral Program of Higher Education(20010055013)
文摘In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality. From one example the article indicates that the fundamentality of the locally solid Riesz space is independent from the Lebesgue property.
基金the Scientific Research Common Program of Beijing Municipal Commission of Education(KM200610005014)
文摘In this paper, the author gives a new section theorem in L-convex spaces. And as its applications, the author proves a coincident theorem and a two-functional minimax theorem established in L-convex spaces.
文摘For heterogeneous catalysts,the build-up of interface contacts can influence markedly their activities.Being different from the conventional supported metal/oxide catalysts,the reverse type of oxide/metal structures,e.g.the ceria/Pt composite,have emerged as novel catalytic materials in many fields.However,it remains challenging to determine the optimal interface structure and/or the metal-oxide synergistic effect that can boost catalytic activities.In this work,we conducted density functional theory calculations with on-site Coulomb interaction correction to determine the optimal structures and investigate the physical as well as catalytic properties of various Ce O2/Pt(111)composites containing Ce O2(111)monolayer,bilayer,and trilayer at Pt(111).We found that the interaction strength between Ce O2(111)and Pt(111)substrate first reduces as the ceria slab grows from monolayer to bilayer,and then largely gets converged when the trilayer occurs.Such trend was well rationalized by analyzing the number and distances of O–Pt bonds at the interface.Calculated Bader charges uncovered the significant charge redistribution occurring around the interface,whereas the net electron transfer across the interface is non-significant and decreases as ceria thickness increases.Moreover,comparative calculations on oxygen vacancy formation energies clarified that oxygen removal can be promoted on the Ce O2/Pt(111)composites,especially at the interface.We finally employed CO oxidation as a model reaction to probe the surface reactivity,and determined an intrinsic activity order of monolayer Ce O2(111)>monolayer Ce O2(111)/Pt(111)>regular Ce O2(111).More importantly,we emphasized the significant role of the moderate ceria-Pt interaction at the interface that endows the Ce O2/Pt reverse catalyst both good thermostability and high catalytic activity.The monolayer Ce O2(111)/Pt(111)composite was theoretically predicted highly efficient for catalyzing CO oxidation.
基金supported by The Netherlands Organization for Scientific Research(NWO)through a Vici grant and Nuffic fundingfunding from the European Union’s Horizon 2020 research and innovation programme under grant No.686086(Partial-PGMs)。
文摘Density functional theory calculations were carried out to investigate the influence of doping transition metal(TM) ions into the ceria surface on the activation of surface lattice oxygen atoms. For this purpose, the structure and stability of the most stable(111) surface termination of CeO2 modified by TM ions was determined. Except for Zr and Pt dopants that preserve octahedral oxygen coordination, the TM dopants prefer a square-planar coordination when substituting the surface Ce ions. The surface construction from octahedral to square-planar is facile for all TM dopants, except for Pt(1.14 e V) and Zr(square-planar coordination unstable). Typically, the ionic radius of tetravalent TM cations is much smaller than that of Ce4+, resulting a significant tensile-strained lattice and explaining the lowered oxygen vacancy formation energy. Except for Zr, the square-planar structure is the preferred one when one oxygen vacancy is created. Thermodynamic analysis shows that TM-doped CeO2 surfaces contain oxygen defects under typical conditions of environmental catalysis. A case of practical importance is the facile lattice oxygen activation in Zr-doped CeO2(111), which benefits CO oxidation. The findings emphasize the origin of lattice oxygen activation and the preferred location of TM dopants in TM-ceria solid solution catalysts.
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation (K-functional) we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
文摘The lattice parameters, elastic constants, cohesive energy, structural energy differences, as well as the properties of point defects and planar defects of hexagonal closepacked yttrium (hcpY) have been studied with ab initio density functional theory for constructing an ex tensive database. Based on an analytical bondorder poial scheme, empirical manybody interatomic potential for hcpY has been developed. The model is fitted to some properties of Y, e.g., the lattice parameters, elastic constants, bulk modulus, cohesive energy, vacancy formation energy, and the structural energy differences. The present potential has ability to reproduce defect properties including the selfinterstitial atoms formation energies, vacancy formation energy, divacancy binding energy, as well as the bulk properties and the thermal dynamic properties.
基金supported by National Natural Science Foundation of China (Grant No.10871061)
文摘We formulate a class of functionals in space forms such that its critical points include the r-minimal hyper-surface and the minimal hyper-surface as special cases. We obtain the algebraic, differential and variational characteristics of the critical surfaces determined by the critical points. We prove the Simons' type nonexistence theorem which indicates that in the unit sphere, there exists no stable critical surfaces, and the Alexandrov's type existence theorem which indicates that in Euclidean space, the sphere is the only stable critical surfaces.
基金Foundation item: the Natural Science Research Foundation of Guizhou Provincial Education Department (No. 2008072) the Natural Science Foundation of Science and Technologe Bureau of Bijie Area (No. 2008-06).
文摘In this paper,a new GLKKM type theorem is established for noncompact complete L-convex metric spaces.As applications,the properties of the solution set of variational in-equalities,intersection point sets,Ky Fan sections and maximal element sets are shown,and a Fan-Browder fixed point theorem is obtained.
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2017JQ1022)the Fundamental Research Funds for the Central Universities (Grant No. GK201802015)
文摘In this paper, we investigate the positive solutions to the following integral system with a polyharmonic extension operator on R^+_n:{u(x)=c_n,a∫_?R_+~n(x_n^(1-a_v)(y)/|x-y|^(n-a))dy,x∈R_+~n,v(y)=c_n,a∫_R_+~n(x_n^(1-a_uθ)(x)/|x-y|^(n-a))dx,y∈ ?R_+~n,where n 2, 2-n < a < 1, κ, θ > 0. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Chen(2014). The explicit formulations of positive solutions are obtained by the method of moving spheres for the critical case κ =n-2+a/n-a,θ =n+2-a/ n-2+a. Moreover,we also give the nonexistence of positive solutions in the subcritical case for the above system.
文摘This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics.Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators,the Hermitian adjoint, classification of antilinear normal operators,(skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.
基金supported by the National Natural Science Foundation of China(Nos.11201199,11671361)
文摘The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane.
基金Research Foundation of Henan University (No.06YBZR034)
文摘The Mann iterations have no strong convergence even for nonexpansive mappings in Hilbert spaces. The aim of this paper is to propose a modification of the Mann iterations for strictly asymptotically pseudocontractive maps in Hilbert spaces to have strong convergence. Our results extend those of Kim, Xu, Nakajo, Takahashi and many others.