We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the q...We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including integral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.展开更多
A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are al...A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.展开更多
Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p...Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.展开更多
Denoteby <sub>n</sub>（f） the degree of copositive approximation to f（x） by polynomials of degree≤n. For function f（x） ∈ C<sup>k</sup>[-1, 1] which alternates in sign finitely many times...Denoteby <sub>n</sub>（f） the degree of copositive approximation to f（x） by polynomials of degree≤n. For function f（x） ∈ C<sup>k</sup>[-1, 1] which alternates in sign finitely many timesin [-1, 1], the author obtains the following Jackson type estimates<sub>n</sub>（f）≤Cn<sup>-k</sup>w(f<sup>k</sup>, 1/n)foa any positive integer k.展开更多
It is well known that interleavers play a critical role in Turbo coding/decoding schemes, and contention-free interleaver design has become a serious problem in the paraUelization of Turbo decoding, which is indispens...It is well known that interleavers play a critical role in Turbo coding/decoding schemes, and contention-free interleaver design has become a serious problem in the paraUelization of Turbo decoding, which is indispensable to meet the demands for high throughput and low latency in next generation mobile communication systems. This paper unveils the fact that interleavers based on permutation polynomials modulo N are contention-free for every window size W, a factor of the intedeaver length N, which, also called maximum contention-free interleavers.展开更多
Let f（x）=a<sub>k</sub>X<sup>k</sup>+…+a<sub>1</sub>x+a<sub>0</sub> be a polynomial with integral coefficients such that （a<sub>1</sub>,…,a<sub>k&l...Let f（x）=a<sub>k</sub>X<sup>k</sup>+…+a<sub>1</sub>x+a<sub>0</sub> be a polynomial with integral coefficients such that （a<sub>1</sub>,…,a<sub>k</sub>, q）=1, where q is a positive integer. We proved that for k≥3,展开更多
The authors obtain,among other things,the following result:Let f be a transcendentalmeromorphic function,then there exists an integer n,such that the setα∈C;f(z)z^n(z-α)is not prime}is an at most countable set.
基金Supported by National Natural Science Foundation of China(Nos.11971274,12061074,11671344).
文摘We introduce the notion of a quadratic graph,which is a graph whose eigenvalues are integral or quadratic algebraic integral,and we determine nine infinite families of quadratic starlike trees,which are just all the quadratic starlike trees including integral starlike trees.Thus,the quadratic starlike trees are completely characterized.The expressions for characteristic polynomials of quadratic starlike trees are also given.
文摘A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.
文摘Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.
文摘Denoteby <sub>n</sub>（f） the degree of copositive approximation to f（x） by polynomials of degree≤n. For function f（x） ∈ C<sup>k</sup>[-1, 1] which alternates in sign finitely many timesin [-1, 1], the author obtains the following Jackson type estimates<sub>n</sub>（f）≤Cn<sup>-k</sup>w(f<sup>k</sup>, 1/n)foa any positive integer k.
基金Project (No. 60332030) supported by the National Natural ScienceFoundation of China
文摘It is well known that interleavers play a critical role in Turbo coding/decoding schemes, and contention-free interleaver design has become a serious problem in the paraUelization of Turbo decoding, which is indispensable to meet the demands for high throughput and low latency in next generation mobile communication systems. This paper unveils the fact that interleavers based on permutation polynomials modulo N are contention-free for every window size W, a factor of the intedeaver length N, which, also called maximum contention-free interleavers.
文摘Let f（x）=a<sub>k</sub>X<sup>k</sup>+…+a<sub>1</sub>x+a<sub>0</sub> be a polynomial with integral coefficients such that （a<sub>1</sub>,…,a<sub>k</sub>, q）=1, where q is a positive integer. We proved that for k≥3,
文摘The authors obtain,among other things,the following result:Let f be a transcendentalmeromorphic function,then there exists an integer n,such that the setα∈C;f(z)z^n(z-α)is not prime}is an at most countable set.
