We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with...We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with m, n, p positive integers: and the bisymmetric positive semidefinite solution of the matrix equation D^T XD=C, where D is a given real n×m matrix. C is a given real m×m matrix, with m. n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions.展开更多
Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present...Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.展开更多
Drought is one of the severe natural disasters to impact human society and occurs widely and frequently in China,causing considerable damage to the living environment of humans.The Yellow River basin(YRB)of China show...Drought is one of the severe natural disasters to impact human society and occurs widely and frequently in China,causing considerable damage to the living environment of humans.The Yellow River basin(YRB)of China shows great vulnerability to drought in the major basins;thus,drought monitoring in the YRB is particularly important.Based on monthly data of 124 meteorological stations from 1961 to 2015,the Standardized Precipitation Evapotranspiration Index(SPEI)was used to explore the temporal and spatial patterns of drought in the YRB.The periods and trends of drought were identified by Extreme-point Symmetric Mode Decomposition(ESMD),and the research stages were determined by Bernaola-Galvan Segmentation Algorithm(BGSA).The annual and seasonal variation,frequency and intensity of drought were studied in the YRB.The results indicated that(1)for the past 55 years,the drought in the YRB has increased significantly with a tendency rate of-0.148(10 a)^(-1),in which the area Lanzhou to Hekou was the most vulnerable affected(-0.214(10 a)^(-1));(2)the drought periods(2.9,5,10.2 and 18.3 years)and stages(1961–1996,1997–2002 and 2003–2015)were characterized and detected by ESMD and BGSA;(3)the sequence of drought frequency was summer,spring,autumn and winter with mean values of 71.0%,47.2%,10.2%and 6.9%,respectively;and(4)the sequence of drought intensity was summer,spring,winter and autumn with mean values of 0.93,0.40,0.05 and 0.04,respectively.展开更多
In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally conv...In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions.展开更多
In the light of the theory on moist potential vorticity (MPV) investigation was undertaken of the 700 hPa vertical (horizontal) component MP1 (MPV2) for the heavy rain event occurring in July 5–6, 1991. Results show ...In the light of the theory on moist potential vorticity (MPV) investigation was undertaken of the 700 hPa vertical (horizontal) component MP1 (MPV2) for the heavy rain event occurring in July 5–6, 1991. Results show that the distribution features of the two components were closely related to the development of a mesoscale cyclone as a rainstorm-causing weather system in the lower troposphere in such a way that the ambient atmosphere of which MPV1 > 0 and MPV2 < 0 with |MPV1| ≥ |MPV2| favored the genesis of conditional symmetric instability (CSI) and that, as indicated by calculations, a CSI sector was really existent in the lower troposphere during the heavy rain happening and contributed greatly to its development.展开更多
A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The conv...A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.展开更多
In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequa...In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.展开更多
A novel carbon foam with microporous structure(CFMS),with the advantages of a simple fabrication process,low energy consumption,large specific surface area and high conductivity,has been prepared by a facile one-step ...A novel carbon foam with microporous structure(CFMS),with the advantages of a simple fabrication process,low energy consumption,large specific surface area and high conductivity,has been prepared by a facile one-step carbonization.In addition,the carbon foam possesses suitable interlayer spacing in short range which is flexible to accommodate the deformation of carbon layer caused by the ion insertion and deinsertion at the charge and discharge state.Furthermore,a low cost carbon-based symmetric potassium dual-ion capacitor(PDIC),which integrates the virtues of potassium ion capacitors and dual-ion batteries,is successfully established with CFMS as both the battery-type cathode and the capacitor-type anode.PDIC displays a superior rate performance,an ultra-long cycle life(90%retention after 10000 cycles),and a high power density of 7800 W kg^-1 at an energy density of 39Whkg^-1.The PDIC also exhibits excellent ultrafast charge and slow discharge properties,with a full charge in just 60 s and a discharge time of more than 3000 s.展开更多
Dynamically encircling an exceptional point(EP)in parity-time(PT)symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes...Dynamically encircling an exceptional point(EP)in parity-time(PT)symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes.The counterpart symmetry-broken modes(i.e.,each eigenmode is localized in one waveguide only),which are more useful for applications such as on-chip optical signal processing,exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching.Here,we solve this problem by resorting to anti-parity-time(anti-PT)symmetric systems and utilizing their unique topological structure,which is very different from that of PT-symmetric systems.We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics.As a result,symmetry-broken modes can be used for asymmetric mode switching,which is a phenomenon and application unique to anti-PT-symmetric systems.We perform experiments to demonstrate the new wave-manipulation scheme,which may pave the way towards designing on-chip optical systems with novel functionalities.展开更多
The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtaine...The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.展开更多
A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric g...A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.展开更多
Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk...Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper.展开更多
基金Subsidized by the Special Funds for Major State Basic Research Projects G1999032803
文摘We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with m, n, p positive integers: and the bisymmetric positive semidefinite solution of the matrix equation D^T XD=C, where D is a given real n×m matrix. C is a given real m×m matrix, with m. n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions.
基金Subsidized by The Special Funds For Major State Basic Research Project G1999032803.
文摘Least-squares solution of AXB = D with respect to symmetric positive semidefinite matrix X is considered. By making use of the generalized singular value decomposition, we derive general analytic formulas, and present necessary and sufficient conditions for guaranteeing the existence of the solution. By applying MATLAB 5.2, we give some numerical examples to show the feasibility and accuracy of this construction technique in the finite precision arithmetic.
基金supported by the Henan Province Scientific and Technological Project (Grant Nos. 162102410066 & 172102410075)the National Key Research and Development Plan (Grant No. 2016YFC0401407)the open research fund of the State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin at the China Institute of Water Resources and Hydropower Research (Grant No. IWHR-SKL-201701)
文摘Drought is one of the severe natural disasters to impact human society and occurs widely and frequently in China,causing considerable damage to the living environment of humans.The Yellow River basin(YRB)of China shows great vulnerability to drought in the major basins;thus,drought monitoring in the YRB is particularly important.Based on monthly data of 124 meteorological stations from 1961 to 2015,the Standardized Precipitation Evapotranspiration Index(SPEI)was used to explore the temporal and spatial patterns of drought in the YRB.The periods and trends of drought were identified by Extreme-point Symmetric Mode Decomposition(ESMD),and the research stages were determined by Bernaola-Galvan Segmentation Algorithm(BGSA).The annual and seasonal variation,frequency and intensity of drought were studied in the YRB.The results indicated that(1)for the past 55 years,the drought in the YRB has increased significantly with a tendency rate of-0.148(10 a)^(-1),in which the area Lanzhou to Hekou was the most vulnerable affected(-0.214(10 a)^(-1));(2)the drought periods(2.9,5,10.2 and 18.3 years)and stages(1961–1996,1997–2002 and 2003–2015)were characterized and detected by ESMD and BGSA;(3)the sequence of drought frequency was summer,spring,autumn and winter with mean values of 71.0%,47.2%,10.2%and 6.9%,respectively;and(4)the sequence of drought intensity was summer,spring,winter and autumn with mean values of 0.93,0.40,0.05 and 0.04,respectively.
基金supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010)Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200)
文摘In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally complementary solution to the monotone SCCP under some assumptions.
文摘In the light of the theory on moist potential vorticity (MPV) investigation was undertaken of the 700 hPa vertical (horizontal) component MP1 (MPV2) for the heavy rain event occurring in July 5–6, 1991. Results show that the distribution features of the two components were closely related to the development of a mesoscale cyclone as a rainstorm-causing weather system in the lower troposphere in such a way that the ambient atmosphere of which MPV1 > 0 and MPV2 < 0 with |MPV1| ≥ |MPV2| favored the genesis of conditional symmetric instability (CSI) and that, as indicated by calculations, a CSI sector was really existent in the lower troposphere during the heavy rain happening and contributed greatly to its development.
基金Subsidized by The Special Funds For Major State Basic Research Projects G1999032803.
文摘A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.
基金supported by NSFC (60850005)NSF of Zhejiang Province(D7080080, Y7080185, Y607128)
文摘In this article, we prove that the symmetric function Fn（x,r）=∑i1＋i2＋……in=r（x1（i1x2^i2……xn^in）1/r is Schur harmonic convex for x ∈ R＋n and r ∈N -=（1, 2, 3,...} As its applications, some analytic inequalities are established.
基金financially supported by the National Natural Science Foundation of China(Nos.51672078 and 21473052)Hunan University State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Independent Research Project(No.71675004)+2 种基金the Fundamental Research Funds for the Central UniversitiesHunan Natural Science Foundation(2019JJ40031)Foundation of State Key Laboratory of Coal Conversion(Grant J1718-903)。
文摘A novel carbon foam with microporous structure(CFMS),with the advantages of a simple fabrication process,low energy consumption,large specific surface area and high conductivity,has been prepared by a facile one-step carbonization.In addition,the carbon foam possesses suitable interlayer spacing in short range which is flexible to accommodate the deformation of carbon layer caused by the ion insertion and deinsertion at the charge and discharge state.Furthermore,a low cost carbon-based symmetric potassium dual-ion capacitor(PDIC),which integrates the virtues of potassium ion capacitors and dual-ion batteries,is successfully established with CFMS as both the battery-type cathode and the capacitor-type anode.PDIC displays a superior rate performance,an ultra-long cycle life(90%retention after 10000 cycles),and a high power density of 7800 W kg^-1 at an energy density of 39Whkg^-1.The PDIC also exhibits excellent ultrafast charge and slow discharge properties,with a full charge in just 60 s and a discharge time of more than 3000 s.
基金supported by the National Natural Science Foundation of China(grant no.61605056)the China Postdoctoral Science Foundation(grant no.2019T120234)supported by the Hong Kong Research Grants Council through grant no.AoE/P-02/12.
文摘Dynamically encircling an exceptional point(EP)in parity-time(PT)symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes.The counterpart symmetry-broken modes(i.e.,each eigenmode is localized in one waveguide only),which are more useful for applications such as on-chip optical signal processing,exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching.Here,we solve this problem by resorting to anti-parity-time(anti-PT)symmetric systems and utilizing their unique topological structure,which is very different from that of PT-symmetric systems.We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics.As a result,symmetry-broken modes can be used for asymmetric mode switching,which is a phenomenon and application unique to anti-PT-symmetric systems.We perform experiments to demonstrate the new wave-manipulation scheme,which may pave the way towards designing on-chip optical systems with novel functionalities.
基金Supported by the National Natural Science Foundation of China(Grant No.60573028)the Open Founds of Key Lab of Fujian Province University Network Security and Cryptology(Grant No. 07A003)the Basic Research Foundation of National University of Defense Technology(Grant No.JC07-02-03)
文摘The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.
基金This work was supported partly by the National Natural Science Foundation of China(Grant Nos.19831050,10171006)the Doctoral Program Foundation of Institutions of Higher Education of China(Grant No.2000000102).
文摘A graph Γ is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Γ) acting transitively on its edge set but not on its vertex set. In the case of G = A, we call Γ a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.
基金Project 19771020 supported by National Science Foundation of China.
文摘Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper.
