In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather ar...In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
In this paper,we consider a semilinear difference equation in a Banach space.Under some suitable conditions on f,we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the e...In this paper,we consider a semilinear difference equation in a Banach space.Under some suitable conditions on f,we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.展开更多
In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic ...In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.展开更多
The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general...The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.展开更多
文摘In this paper, we prove an almost sure central limit theorem for weighted sums of mixing sequences of random variables without stationary assumptions. We no longer restrict to logarithmic averages, but allow rather arbitrary weight sequences. This extends the earlier work on mixing random variables
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
基金supported by Tianyuan Youth Foundations for Mathematics of NSFC(Grant No.11026150,11026098)the Doctor Scientific Research Foundation of Shandong Institute of Business and Technology(Grant No.521-014-306131)
文摘In this paper,we consider a semilinear difference equation in a Banach space.Under some suitable conditions on f,we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271380,11031002 and 11371058)Research Fund for the Doctoral Program of Higher Education(Grant No.20110003110004)+1 种基金the Grant of BeijingEducation Committee Key Project(Grant No.KZ201310028031)Natural Science Foundation of GuangdongProvince of China(Grant No.S2013010013212)
文摘In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.
基金supported by the National Natural Science Foundation of China under Grant No.11171366"the Fundamental Research Funds for the Central Universities"South-Central University for Nationalities under Grant No.CZY12014
文摘The weight hierarchy of a linear[n;k;q]code C over GF(q) is the sequence(d_1,d_2,…,d_k)where d_r is the smallest support of any r-dimensional subcode of C. "Determining all possible weight hierarchies of general linear codes" is a basic theoretical issue and has important scientific significance in communication system.However,it is impossible for g-ary linear codes of dimension k when q and k are slightly larger,then a reasonable formulation of the problem is modified as: "Determine almost all weight hierarchies of general g-ary linear codes of dimension k".In this paper,based on the finite projective geometry method,the authors study g-ary linear codes of dimension 5 in class IV,and find new necessary conditions of their weight hierarchies,and classify their weight hierarchies into6 subclasses.The authors also develop and improve the method of the subspace set,thus determine almost all weight hierarchies of 5-dimensional linear codes in class IV.It opens the way to determine the weight hierarchies of the rest two of 5-dimensional codes(classes III and VI),and break through the difficulties.Furthermore,the new necessary conditions show that original necessary conditions of the weight hierarchies of k-dimensional codes were not enough(not most tight nor best),so,it is important to excogitate further new necessary conditions for attacking and solving the fc-dimensional problem.
