By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral dela...By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.展开更多
Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial s...Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.展开更多
By using the generalized PoincarE index theorem it is proved that if the n2 critical points of an n-polynomial system form a configuration of type (2n -1) - (2n - 3) +(2n- 5) -…+ (- 1 )n- 1, and the 2n -1 outmost ant...By using the generalized PoincarE index theorem it is proved that if the n2 critical points of an n-polynomial system form a configuration of type (2n -1) - (2n - 3) +(2n- 5) -…+ (- 1 )n- 1, and the 2n -1 outmost anti-saddles form the venices of a convex (2n -1)-polygon, then among these 2n-1 anti-saddles at least one must be a node.展开更多
It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q...It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.展开更多
We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the a...We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the associated polynomial Poisson algebras with their algebraic dependence relations are exhibited.展开更多
基金Supported by the Natural Science Foundation of Gansu Province(1606RJZA038) the Scientific Study Project for Gansu Province Institutes of Higher Learning(2017B-41) the National Statistical Scientific Research Projects(2017LZ41)
文摘By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.
文摘Finding all zeros of polynomial systems is very interesting and it is also useul for many applied science problems.In this paper,based on Wu's method,we give an algorithm to find all isolated zeros of polynomial systems (or polynomial equations).By solving Lorenz equations,it is shown that our algo-rithm is efficient and powerful.
文摘By using the generalized PoincarE index theorem it is proved that if the n2 critical points of an n-polynomial system form a configuration of type (2n -1) - (2n - 3) +(2n- 5) -…+ (- 1 )n- 1, and the 2n -1 outmost anti-saddles form the venices of a convex (2n -1)-polygon, then among these 2n-1 anti-saddles at least one must be a node.
基金supported by Natural Science Foundation of Hebei Province(Grant No.A2012205079)Science Foundation of Hebei Normal University(Grant No.L2011B02)the 100 Talents Program of the Chinese Academy of Sciences for support
文摘It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11771352 and 11371293
文摘We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the associated polynomial Poisson algebras with their algebraic dependence relations are exhibited.
