In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out...In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.展开更多
Optical bound states in the continuum(BICs)have recently stimulated a research boom,accompanied by demonstrations of abundant exotic phenomena and applications.With ultrahigh quality(Q)factors,optical BICs have powerf...Optical bound states in the continuum(BICs)have recently stimulated a research boom,accompanied by demonstrations of abundant exotic phenomena and applications.With ultrahigh quality(Q)factors,optical BICs have powerful abilities to trap light in optical structures from the continuum of propagation waves in free space.Besides the high Q factors enabled by the confined properties,many hidden topological characteristics were discovered in optical BICs.Especially in periodic structures with well-defined wave vectors,optical BICs were discovered to carry topological charges in momentum space,underlying many unique physical properties.Both high Q factors and topological vortex configurations in momentum space enabled by BICs bring new degrees of freedom to modulate light.BICs have enabled many novel discoveries in light-matter interactions and spin-orbit interactions of light,and BIC applications in lasing and sensing have also been well explored with many advantages.In this paper,we review recent developments of optical BICs in periodic structures,including the physical mechanisms of BICs,explored effects enabled by BICs,and applications of BICs.In the outlook part,we provide a perspective on future developments for BICs.展开更多
The space time spreading, superimposed training sequences, and space-time coding are used to present a multiple input and multiple output （MIMO） systems model, and a closed-form of average error probability upper bo...The space time spreading, superimposed training sequences, and space-time coding are used to present a multiple input and multiple output （MIMO） systems model, and a closed-form of average error probability upper bound expression for MIMO correlated frequency-selective channel in the presence of interference （co-channel interference and jamming signals） is derived. Moreover, the correlation at both ends of the wireless link that can be incorporated equivalently into correlation at the transmit end is also derived, which is significant to analyze space-time link algorithm of MIMO systems.展开更多
Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 fo...Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.展开更多
In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bou...In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.展开更多
The space-time spreading （SIS）, superimposed training sequences and space-time coding （STC） are adopted to obtain a closed-form of average error probability upper bound and maximum likelihood esti- mation expressi...The space-time spreading （SIS）, superimposed training sequences and space-time coding （STC） are adopted to obtain a closed-form of average error probability upper bound and maximum likelihood esti- mation expression for multiple input and multiple output （MIMO） correlated frequency-selective channel in the presence of interference （colored interference）. Moreover, the correlation at both ends of the wire- less link that can be incorporated equivalently into correlation at the transmit end is derived. Finally, the mean square error （MSE） of the maximum likelihood estimate is also derived.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
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 a展开更多
A variant of Robinson-Ursescu Theorem is given in normed spaces. Several error bound theorems for convex inclusions are proved and in particular a positive answer to Li and Singer's conjecture is given under weake...A variant of Robinson-Ursescu Theorem is given in normed spaces. Several error bound theorems for convex inclusions are proved and in particular a positive answer to Li and Singer's conjecture is given under weaker assumption than the assumption required in their conjecture. Perturbation error bounds are also studied. As applications, we study error bounds for convex inequality systems.展开更多
In certain computational systems the amount of space required to execute an algorithm is even more restrictive than the corresponding time necessary for solution of a problem. In this paper an algorithm for modular mu...In certain computational systems the amount of space required to execute an algorithm is even more restrictive than the corresponding time necessary for solution of a problem. In this paper an algorithm for modular multiplicative inverse is introduced and its computational space complexity is analyzed. A tight upper bound for bit storage required for execution of the algorithm is provided. It is demonstrated that for range of numbers used in public-key encryption systems, the size of bit storage does not exceed a 2K-bit threshold in the worst-case. This feature of the Enhanced-Euclid algorithm allows designing special-purpose hardware for its implementation as a subroutine in communication-secure wireless devices.展开更多
We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obn...We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.展开更多
In this paper,we study and analyze the regularized least squares for function-on-function regression model.In our model,both the predictors(input data)and responses(output data)are multivariate functions(with d variab...In this paper,we study and analyze the regularized least squares for function-on-function regression model.In our model,both the predictors(input data)and responses(output data)are multivariate functions(with d variables andd variables respectively),and the model coefficient lies in a reproducing kernel Hilbert space(RKHS).We show under mild condition on the reproducing kernel and input data statistics that the convergence rate of excess prediction risk by the regularized least squares is minimax optimal.Numerical examples based on medical image analysis and atmospheric point spread function estimation are considered and tested,and the results demonstrate that the performance of the proposed model is comparable with that of other testing methods.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 10931001,10901076 and 11171345)Shanghai Leading Academic Discipline Project(Grant No.J50101)supported by the Key Laboratory of Mathematics and Complex System(Beijing Normal University),Ministry of Education,China
文摘In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.
基金supported by the National Natural Science Foundation of China(Nos.12234007,12221004,12321161645,62325501,62135001,12074049,and 12147102)the National Key R and D Program of China(Nos.2022YFA1404804,2021YFA1400603,and 2023YFA1406900)+4 种基金the Major Program of National Natural Science Foundation of China(Nos.T2394480 and T2394481)the Science and Technology Commission of Shanghai Municipality(Nos.22142200400,21DZ1101500,2019SHZDZX01,and 23DZ2260100)the Fundamental Research Funds for the Central Universities(No.2022CDJQY-007)supported by the China National Postdoctoral Program for Innovative Talents(No.BX20230079)the China Postdoctoral Science Foundation(No.2023M740721).
文摘Optical bound states in the continuum(BICs)have recently stimulated a research boom,accompanied by demonstrations of abundant exotic phenomena and applications.With ultrahigh quality(Q)factors,optical BICs have powerful abilities to trap light in optical structures from the continuum of propagation waves in free space.Besides the high Q factors enabled by the confined properties,many hidden topological characteristics were discovered in optical BICs.Especially in periodic structures with well-defined wave vectors,optical BICs were discovered to carry topological charges in momentum space,underlying many unique physical properties.Both high Q factors and topological vortex configurations in momentum space enabled by BICs bring new degrees of freedom to modulate light.BICs have enabled many novel discoveries in light-matter interactions and spin-orbit interactions of light,and BIC applications in lasing and sensing have also been well explored with many advantages.In this paper,we review recent developments of optical BICs in periodic structures,including the physical mechanisms of BICs,explored effects enabled by BICs,and applications of BICs.In the outlook part,we provide a perspective on future developments for BICs.
基金the National Basic Research Program of China "973"(2008CB317109)the National "863" High-Tech Research and Development Program (2002AA123032)+2 种基金the National Natural Science Foundation of China (60572054)the Innovative Research Team Program of University of Electronic and Technology of Chinathe Doctor Foundation of Guilin University of Electronic Technology.
文摘The space time spreading, superimposed training sequences, and space-time coding are used to present a multiple input and multiple output （MIMO） systems model, and a closed-form of average error probability upper bound expression for MIMO correlated frequency-selective channel in the presence of interference （co-channel interference and jamming signals） is derived. Moreover, the correlation at both ends of the wireless link that can be incorporated equivalently into correlation at the transmit end is also derived, which is significant to analyze space-time link algorithm of MIMO systems.
基金Supported by the NNSF of China(11971165)the Natural Science Foundation of Zhejiang Province(LY21A010003)。
文摘Let C be the familiar class of normalized close-to-convex functions in the unit disk.In[17],Koepf demonstrated that,as to a function■in the class C,■By applying this inequality,it can be proven that‖a3|-|a2‖≤1 for close-to-convex functions.Now we generalized the above conclusions to a subclass of close-to-starlike mappings defined on the unit ball of a complex Banach space.
基金supported by National Natural Science Foundation of China (Grant No.11871452)Beijing Information Science and Technology University Foundation (Grant No.2025031)+1 种基金Natural Science Foundation of Henan Province (Grant No.202300410338)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University.
文摘In this paper,we calculate the sharp bound for the generalized m-linear n-dimensional Hardy-Littlewood-Polya operator on power weighted central and non-central homogeneous Morrey spaces.As an application,the sharp bound for the Hardy-Littlewood-Polya operator on power weighted central and noncentral homo-geneous Morrey spaces is obtained.Finally,we also find the sharp bound for the Hausdorff operator on power weighted central and noncentral homogeneous Morrey spaces,which generalizes the previous results.
基金supported by the Key Laboratory on Mathematics and Complex System (at Beijing Normal University) from the Ministry of Education,Chinasupported by NSFC(No.10931001)
基金the National High Technology Research and Development Program of China(2002AA123032)
文摘The space-time spreading （SIS）, superimposed training sequences and space-time coding （STC） are adopted to obtain a closed-form of average error probability upper bound and maximum likelihood esti- mation expression for multiple input and multiple output （MIMO） correlated frequency-selective channel in the presence of interference （colored interference）. Moreover, the correlation at both ends of the wire- less link that can be incorporated equivalently into correlation at the transmit end is derived. Finally, the mean square error （MSE） of the maximum likelihood estimate is also derived.
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 a
基金This work was supported by the National Natural Science Foundation of China(Grant No.19861004)the Natural Science Foundation of Yunnan Province.
文摘A variant of Robinson-Ursescu Theorem is given in normed spaces. Several error bound theorems for convex inclusions are proved and in particular a positive answer to Li and Singer's conjecture is given under weaker assumption than the assumption required in their conjecture. Perturbation error bounds are also studied. As applications, we study error bounds for convex inequality systems.
文摘In certain computational systems the amount of space required to execute an algorithm is even more restrictive than the corresponding time necessary for solution of a problem. In this paper an algorithm for modular multiplicative inverse is introduced and its computational space complexity is analyzed. A tight upper bound for bit storage required for execution of the algorithm is provided. It is demonstrated that for range of numbers used in public-key encryption systems, the size of bit storage does not exceed a 2K-bit threshold in the worst-case. This feature of the Enhanced-Euclid algorithm allows designing special-purpose hardware for its implementation as a subroutine in communication-secure wireless devices.
基金supported by the Danish Council for Independent Research(Grant No.DFF–4002-00367),supported by the Danish Council for Independent Research(Grant No.DFF–6108-00362)supported by the Research Council of Norway(Project No.280731)supported by IRCC Award grant 12IRAWD009 from IIT Bombay
文摘We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these generators form a universal Gr¨obner basis of the ideal. Further we give a projective analogue for the so-called footprint bound, and a version of it that is suitable for estimating the number of rational points of projective algebraic varieties over finite fields. An application to Serre’s inequality for the number of points of projective hypersurfaces over finite fields is included.
文摘In this paper,we study and analyze the regularized least squares for function-on-function regression model.In our model,both the predictors(input data)and responses(output data)are multivariate functions(with d variables andd variables respectively),and the model coefficient lies in a reproducing kernel Hilbert space(RKHS).We show under mild condition on the reproducing kernel and input data statistics that the convergence rate of excess prediction risk by the regularized least squares is minimax optimal.Numerical examples based on medical image analysis and atmospheric point spread function estimation are considered and tested,and the results demonstrate that the performance of the proposed model is comparable with that of other testing methods.
