Consider the nonautonomous delay logistic equation △yn=pnyn（1-yn-ln/k）,n≥0, where {Pn}n≥0 is a sequence of nonnegative real numbers, {In}n≥0 is a sequence of positive integers satisfying n→∞lim（n-ln）=∞, and...Consider the nonautonomous delay logistic equation △yn=pnyn（1-yn-ln/k）,n≥0, where {Pn}n≥0 is a sequence of nonnegative real numbers, {In}n≥0 is a sequence of positive integers satisfying n→∞lim（n-ln）=∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of （1） to oscillate about k which contains the corresponding result in [2] when i = 1.展开更多
In this paper we extend the concept of Sλ^L（I）- asymptotically statistical equivalence which is a natural combination of λ - statistical convergence and asymptotically I -equivalence. We use the sequence P = （Pk...In this paper we extend the concept of Sλ^L（I）- asymptotically statistical equivalence which is a natural combination of λ - statistical convergence and asymptotically I -equivalence. We use the sequence P = （Pk） which is the sequence of positive real numbers.展开更多
Let a and b be positive integers, with a not perfect square and b > 1. Recently, He, Togband Walsh proved that the Diophantine equation x2-a((bk-1)/(b-1))2=1 has at most three solutions in positive integers. Moreov...Let a and b be positive integers, with a not perfect square and b > 1. Recently, He, Togband Walsh proved that the Diophantine equation x2-a((bk-1)/(b-1))2=1 has at most three solutions in positive integers. Moreover, they showed that if max{a,b} > 4.76·1051, then there are at most two positive integer solutions (x,k). In this paper, we sharpen their result by proving that this equation always has at most two solutions.展开更多
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are ...Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.展开更多
文摘Consider the nonautonomous delay logistic equation △yn=pnyn（1-yn-ln/k）,n≥0, where {Pn}n≥0 is a sequence of nonnegative real numbers, {In}n≥0 is a sequence of positive integers satisfying n→∞lim（n-ln）=∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of （1） to oscillate about k which contains the corresponding result in [2] when i = 1.
文摘In this paper we extend the concept of Sλ^L（I）- asymptotically statistical equivalence which is a natural combination of λ - statistical convergence and asymptotically I -equivalence. We use the sequence P = （Pk） which is the sequence of positive real numbers.
基金the first two authors has been partially supported by a LEA Franco-Roumain Math-Mode projectPurdue University North Central for the support
文摘Let a and b be positive integers, with a not perfect square and b > 1. Recently, He, Togband Walsh proved that the Diophantine equation x2-a((bk-1)/(b-1))2=1 has at most three solutions in positive integers. Moreover, they showed that if max{a,b} > 4.76·1051, then there are at most two positive integer solutions (x,k). In this paper, we sharpen their result by proving that this equation always has at most two solutions.
基金supported by the National Natural Science Foundation of China(Nos.11471097,11271257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20121303110005)+1 种基金the Natural Science Foundation of Hebei Province(No.A2013205021)the Key Fund Project of Hebei Normal University(No.L2012Z01)
文摘Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.
