Space is a common entity in any static or dynamic system of objects whether the system is a bound system or an open system. Space is described by either measured or abstract dimensions. All motions, momentum and energ...Space is a common entity in any static or dynamic system of objects whether the system is a bound system or an open system. Space is described by either measured or abstract dimensions. All motions, momentum and energy transfers take place in space in any given system of objects. By understanding space we understand many physical phenomena happening in space. One method is to observe similarities among phenomena, deduce possible relations and validate the relations through known results. De Broglie wavelength for matter waves is a typical theorized abstract dimension existence of which is established through experiments later. In this paper, the author studies two bound spaces in two bound systems, namely, atomic bound systems and gravitationally bound systems. Both these bound systems have similar characteristics;they have inertial masses in motion with constant kinetic energies for a given orbital distance around the respective central object. In atomic bound space, the central object is the central positive charge which plays the role of creating the bound space around it. In gravitationally bound space, it is the central mass that plays the same role. Thus for these two bound systems a common constitutive relation between the energies of inertial masses in kinetic state, their distance from central object could be present. By noticing the similarities of the two systems, the author proposes such a relation through introduction of an additional space dimension. The existence of the proposed additional dimension is proved in this paper by considering hydrogen atom for atomic bound space and by considering any gravitational system for gravitationally bound space. Though the magnitude of the additional space dimension is different in both the situations, the additional space dimension exists. It is observed that in hydrogen atom the additional space dimension is a constant for the given positive charge of hydrogen atom when electron is in any energy state having principal quantum number of any value from 1 to 5 and with the orbital quantum number zero. For other quantum numbers additional space dimension exists. In the case of gravitational bound space, the additional space dimension is constant for a given mass of the central object for any energy of orbiting inertial mass. The author concludes that total mass energy of an inertial mass having a constant kinetic energy in any bound space is related to an additional space dimension defined by the constitutional property of the central object creating that bound space. As the relation is generic, it throws opportunity to examine other known similar macro, micro or quantum bound spaces created by central objects with different constitutive properties.展开更多
Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper pr...Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper presents a novel control strategy for stabilization of a space robot in postcapture considering actuator failures and bounded torques. In the control strategy, the motion of the manipulator is not regarded as a disturbance to the base; in contrast, it is utilized to compensate for the limitation of the control torques by means of an inverse dynamical model of the system. Different scenarios where actuators are external mechanisms or momentum exchange devices have been carried out, and for actuator failures, both single-and two-actuator failures have been considered. Regarding to the performance of actuators, control torques are bounded. In cases that either single or two actuators have failed, the base can be stabilized kinematically when actuators are external mechanisms, but can only be stabilized dynamically when only momentum exchange devices are used. Finally, a space robot with a seven-degree-of-freedom manipulator in postcapture is studied to verify the validity and feasibility of the proposed control scheme. Simulation results show that the whole system can be stabilized rapidly.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of consi...LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn...Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.展开更多
Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used....Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used. In this paper a set of approximation algorithms is presented for cases in which the ability to preview at most k（〉=2） arriving bins is given. With the essential assumption that all bin sizes are not less than the largest item size, analytical results show the asymptotic worst case ratios of all k-bounded space and offiine algorithms are 2. Based on experiments by applying algorithms to instances in which item sizes and bin sizes are drawn independently from the continuous uniform distribution respectively in the interval [0,u] and [u,l ], averagecase experimental results show that, with fixed k, algorithms with the Best Fit packing（closing） rule are statistically better than those with the First Fit packing（closing） rule.展开更多
In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operat...In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.展开更多
In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa...In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.展开更多
Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new pr...Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.展开更多
In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space...In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.展开更多
For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in additi...For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .展开更多
In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bou...In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.展开更多
Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is co...Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is contained and bounded in some (En,ξn）. Theovem 1.(DS) holds provided that (i) for each n∈N,there is a neighborhood Un of o in (En,ξn） and m(n)∈ such that -↑Un^E包含于Em(n),and (ii) for any neighborhood V n of o in (En,ξn）,∞↑Un=1 Vn absorbs every bounded set in (E,ξ）. theorem 2 Let all (En,ξn） be metrizable and (DS) hold,then for each bounded set B IN (E,ξ）and each n ∈N thcrc is a neighborhood U k of o in (Ek,ξk）, 1≤k≤n ,and m(n)∈N such that ——↑(B+U1+U2+…+Un)^E包含于 Em(n). theorem 3. Let all (En,ξn） be Frechet spaces.Then (DST) holds if and only if (i) for each n ∈N,there is u neighborhood U n of in (En,ξn） and m(n)∈N such that 0↑Un^E包含于Em(n),and (ii) for each each closed ,absosed,absolutely conuex,bounded set B in (E,ξ）,∞↑Un=1(（εnB)∩Un）absorbs B,where U n is any neighborhood of o in (En,ξn） and εn is any positive number for every n ∈N。展开更多
In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log ...In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log h) of the running time for the general sequential B&B algorithm and the lower bound Ω(m/p+h log p) for the general parallel best-first B&B algorithm in PRAM-CREW are proposed, where p is the number of processors available. Moreover, the lower bound Ω(M/p+H+(H/p) log (H/p)) is presented for the parallel algorithms on distributed memory system, where M and H represent total number of the active nodes and that of the expanded nodes processed by p processors, respectively. In addition, a nearly fastest general parallel best-first B&B algorithm is put forward. The parallel algorithm is the fastest one as p = max{hε, r}, where ε = 1/ rootlogh, and r is the largest branch number of the nodes in the state-space tree.展开更多
It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially norm...It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.展开更多
In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we ...In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-norm...Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
We obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case o...We obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case of the classical LP（1 〈 p 〈 ∞） theory for second order elliptic equations. Our approach is based on a standard technique of perturbation rather than that of integral representation formula.展开更多
文摘Space is a common entity in any static or dynamic system of objects whether the system is a bound system or an open system. Space is described by either measured or abstract dimensions. All motions, momentum and energy transfers take place in space in any given system of objects. By understanding space we understand many physical phenomena happening in space. One method is to observe similarities among phenomena, deduce possible relations and validate the relations through known results. De Broglie wavelength for matter waves is a typical theorized abstract dimension existence of which is established through experiments later. In this paper, the author studies two bound spaces in two bound systems, namely, atomic bound systems and gravitationally bound systems. Both these bound systems have similar characteristics;they have inertial masses in motion with constant kinetic energies for a given orbital distance around the respective central object. In atomic bound space, the central object is the central positive charge which plays the role of creating the bound space around it. In gravitationally bound space, it is the central mass that plays the same role. Thus for these two bound systems a common constitutive relation between the energies of inertial masses in kinetic state, their distance from central object could be present. By noticing the similarities of the two systems, the author proposes such a relation through introduction of an additional space dimension. The existence of the proposed additional dimension is proved in this paper by considering hydrogen atom for atomic bound space and by considering any gravitational system for gravitationally bound space. Though the magnitude of the additional space dimension is different in both the situations, the additional space dimension exists. It is observed that in hydrogen atom the additional space dimension is a constant for the given positive charge of hydrogen atom when electron is in any energy state having principal quantum number of any value from 1 to 5 and with the orbital quantum number zero. For other quantum numbers additional space dimension exists. In the case of gravitational bound space, the additional space dimension is constant for a given mass of the central object for any energy of orbiting inertial mass. The author concludes that total mass energy of an inertial mass having a constant kinetic energy in any bound space is related to an additional space dimension defined by the constitutional property of the central object creating that bound space. As the relation is generic, it throws opportunity to examine other known similar macro, micro or quantum bound spaces created by central objects with different constitutive properties.
基金co-supported by the National Natural Science Foundation of China (Nos. 11402200 and 11502203)the China Scholarship Council (CSC)
文摘Space robotics is regarded as one of the most impressing approaches for space debris removal missions. Due to the residual momentum of debris, it is essential to stabilize the base rapidly after capture. This paper presents a novel control strategy for stabilization of a space robot in postcapture considering actuator failures and bounded torques. In the control strategy, the motion of the manipulator is not regarded as a disturbance to the base; in contrast, it is utilized to compensate for the limitation of the control torques by means of an inverse dynamical model of the system. Different scenarios where actuators are external mechanisms or momentum exchange devices have been carried out, and for actuator failures, both single-and two-actuator failures have been considered. Regarding to the performance of actuators, control torques are bounded. In cases that either single or two actuators have failed, the base can be stabilized kinematically when actuators are external mechanisms, but can only be stabilized dynamically when only momentum exchange devices are used. Finally, a space robot with a seven-degree-of-freedom manipulator in postcapture is studied to verify the validity and feasibility of the proposed control scheme. Simulation results show that the whole system can be stabilized rapidly.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F（p, q, s） on Ω. Characterizing functions in the F（p, q, s） space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F（p, q, s） space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F（p, q, s） space and Bloch type space on Ω too.
文摘Let L be the infinitesimal generator of an analytic semigroup on L^2 （R^n） with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k（w） when the symbol b belongs to BMO（Rn） or the homogeneous Lipschitz space.
文摘Given a list of items and a sequence of variable-sized bins arriving one by one, it is NP-hard to pack the items into the bin list with a goal to minimize the total size of bins from the earliest one to the last used. In this paper a set of approximation algorithms is presented for cases in which the ability to preview at most k（〉=2） arriving bins is given. With the essential assumption that all bin sizes are not less than the largest item size, analytical results show the asymptotic worst case ratios of all k-bounded space and offiine algorithms are 2. Based on experiments by applying algorithms to instances in which item sizes and bin sizes are drawn independently from the continuous uniform distribution respectively in the interval [0,u] and [u,l ], averagecase experimental results show that, with fixed k, algorithms with the Best Fit packing（closing） rule are statistically better than those with the First Fit packing（closing） rule.
文摘In this paper, we introduce the weighted Bloch spaces on the first type of classical bounded symmetric domains , and prove the equivalence of the norms and . Furthermore, we study the compactness of composition operator from to , and obtain a sufficient and necessary condition for to be compact.
基金Supported by the National Natural Science Foundation of China (10771064)Natural Science Foundation of Zhejiang Province (Y7080197, Y6090036, Y6100219)+1 种基金Foundation of Creative Group in Colleges and Universities of Zhejiang Province (T200924)Foundation of Department of Education of Zhejiang province (20070482)
文摘In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.
文摘Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.
文摘In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.
文摘For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .
文摘In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.
文摘Let (E,ξ）=indlim (En,ξn） be an inductive limit of a sequence of locally convex spaces,For brevity,denote by (DS) each set Bbounded in (E,ξ） is contained in some En； and (DST) each set B bounded in (E,ξ） is contained and bounded in some (En,ξn）. Theovem 1.(DS) holds provided that (i) for each n∈N,there is a neighborhood Un of o in (En,ξn） and m(n)∈ such that -↑Un^E包含于Em(n),and (ii) for any neighborhood V n of o in (En,ξn）,∞↑Un=1 Vn absorbs every bounded set in (E,ξ）. theorem 2 Let all (En,ξn） be metrizable and (DS) hold,then for each bounded set B IN (E,ξ）and each n ∈N thcrc is a neighborhood U k of o in (Ek,ξk）, 1≤k≤n ,and m(n)∈N such that ——↑(B+U1+U2+…+Un)^E包含于 Em(n). theorem 3. Let all (En,ξn） be Frechet spaces.Then (DST) holds if and only if (i) for each n ∈N,there is u neighborhood U n of in (En,ξn） and m(n)∈N such that 0↑Un^E包含于Em(n),and (ii) for each each closed ,absosed,absolutely conuex,bounded set B in (E,ξ）,∞↑Un=1(（εnB)∩Un）absorbs B,where U n is any neighborhood of o in (En,ξn） and εn is any positive number for every n ∈N。
基金This paper was supported by Ph. D. Foundation of State Education Commission of China.
文摘In this paper, it is supposed that the B&B algorithm finds the first optimal solution after h nodes have been expanded and m active nodes have been created in the state-space tree. Then the lower bound Ω(m+h log h) of the running time for the general sequential B&B algorithm and the lower bound Ω(m/p+h log p) for the general parallel best-first B&B algorithm in PRAM-CREW are proposed, where p is the number of processors available. Moreover, the lower bound Ω(M/p+H+(H/p) log (H/p)) is presented for the parallel algorithms on distributed memory system, where M and H represent total number of the active nodes and that of the expanded nodes processed by p processors, respectively. In addition, a nearly fastest general parallel best-first B&B algorithm is put forward. The parallel algorithm is the fastest one as p = max{hε, r}, where ε = 1/ rootlogh, and r is the largest branch number of the nodes in the state-space tree.
文摘It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.
基金Supported by the National Natural Science Foundation of China(Grant No.11471236)
文摘In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
基金Supported by NSF of China (10371087)NSF of Anhui Province(07021019)Education Committee of Anhui Province(KJ2007A009)
文摘Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
基金Supported by the National Natural Science Foundation of China(11471236)
文摘Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
基金Supported by NNSF of China Grant No.10571084NNSF of China Grant No.10771097
文摘We obtain a priori estimates and solvability in Hardy type space in a bounded domain of Rn for second order elliptic equations with coefficients of limited smoothness. Such a result can be served as an endpoint case of the classical LP（1 〈 p 〈 ∞） theory for second order elliptic equations. Our approach is based on a standard technique of perturbation rather than that of integral representation formula.
