The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
On May 14th,following the U.S.adjustment of additional tariffs on Chinese goods,American buyers began stockpiling in earnest.Many cross-border e-commerce companies also received a surge of orders.At 7 PM,a bustling Ha...On May 14th,following the U.S.adjustment of additional tariffs on Chinese goods,American buyers began stockpiling in earnest.Many cross-border e-commerce companies also received a surge of orders.At 7 PM,a bustling Hangzhou-based cross-border e-commerce company was alive with multiple languages echoing through its live-streaming rooms as backend order numbers climbed steadily.展开更多
Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pa（n-1） ＋ qa（n-2） ＋ ra（n-3） with arbitrary initial conditions a0, a1 = 0, and a2 and their special cases of Pa...Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pa（n-1） ＋ qa（n-2） ＋ ra（n-3） with arbitrary initial conditions a0, a1 = 0, and a2 and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a0 = a1 = 0 and a2 = 1 and a0 = 3, a1 = 0, and a2 = 2, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.展开更多
In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our researc...In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.展开更多
The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social netwo...The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.展开更多
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
文摘On May 14th,following the U.S.adjustment of additional tariffs on Chinese goods,American buyers began stockpiling in earnest.Many cross-border e-commerce companies also received a surge of orders.At 7 PM,a bustling Hangzhou-based cross-border e-commerce company was alive with multiple languages echoing through its live-streaming rooms as backend order numbers climbed steadily.
文摘Here presented is a matrix representation of recursive number sequences of order 3 defined by an = pa（n-1） ＋ qa（n-2） ＋ ra（n-3） with arbitrary initial conditions a0, a1 = 0, and a2 and their special cases of Padovan number sequence and Perrin number sequence with initial conditions a0 = a1 = 0 and a2 = 1 and a0 = 3, a1 = 0, and a2 = 2, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.
基金This project is supported by Doctoral Fundation of National Educational Committee.
文摘In this paper, we study, mathematically speaking, the problem-the number of admissible preference orderings for the transitivity of simple majority vote(SMV) derived from Arrow’s Impossibility Theorem. In our research, we find, by computer enumerating, that some results given by Craven are not correct. By defining a set of constraints, we give the recurrence formula of the local maximal number of admissible preference orderings and some other useful results.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135partially supported by the National Natural Science Foundation of China under Grant No.11401239+1 种基金Funds of CCNU from the Colleges’s Basic Research and Operation of MOE(CCNU15A02032,CCNU15ZD011)a Fund from KLAS(130026507)
文摘The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.
