A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest pos...A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pn-periodic sequence.展开更多
A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of varia...A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.展开更多
Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and mini...Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.展开更多
Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear comp...Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear complexity,minimal polynomial,and autocorrelation are investigated.The results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey attack.Furthermore,the autocorrelation values are close to 0 with a probability of approximately 1?1/r.Therefore,when r is a big prime,the new sequence has a good autocorrelation.展开更多
The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show ...The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity.展开更多
Combining the theory of symbolic dynamics with the formal language theory, we determine the minimal deterministic finite automata (DFA) Aaccepting the formal languages generated by eventually periodic kneading sequenc...Combining the theory of symbolic dynamics with the formal language theory, we determine the minimal deterministic finite automata (DFA) Aaccepting the formal languages generated by eventually periodic kneading sequences of unimodal maps on an interval.展开更多
A nonincreasing sequence ( of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n. The set of all graphic sequences of n terms with even sum 2m and trace f is a pos...A nonincreasing sequence ( of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n. The set of all graphic sequences of n terms with even sum 2m and trace f is a poset G_(n,m,f) under majorization relation. The paper characterizes the minimal elements in the poset G_(n,m,f) and determines the number of minimal elements in various posets of graphic sequences.展开更多
The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert spa...The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.展开更多
This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity theory.Under some structural conditions,we derive that the minimizing sequence and ...This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity theory.Under some structural conditions,we derive that the minimizing sequence and the derivatives of the sequences have some regularity properties by using the Ekeland variational principle.展开更多
基金The National Natural Science Foundation of China (No.10971250,11171150)
文摘A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is given.Let p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=1.An algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et al.is employed to obtain the minimal polynomial of each pn-periodic sequence.
基金supported by the National Natural Science Foundation of China (No. 10671070)the Fund for E-Institute of Shanghai Universities (No. E03004)the Open Research Fund Program of LGISEM(No. 05PJ14040)
文摘A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.
基金Project supported by the National Natural Science Foundation of China(Grant No.60473028)the Natural Science Foundation of Fujian Province(Grant No.A0540011)the Science and Technology Fund of Educational Committee of Fujian Province(Grant No.JA04264)
文摘Minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.
基金supported by the National Key Research and Development Program of China(2016YFB0800601)the Natural Science Foundation of China(61303217+3 种基金61502372)the Fundamental Research Funds for the Central Universities(JB140115)the Natural Science Foundation of Shaanxi Province(2013JQ80022014JQ8313)
文摘Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear complexity,minimal polynomial,and autocorrelation are investigated.The results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey attack.Furthermore,the autocorrelation values are close to 0 with a probability of approximately 1?1/r.Therefore,when r is a big prime,the new sequence has a good autocorrelation.
基金Supported by the Natural Science Foundation of Hubei Province(2009CDZ004)the Scientific Research Fund of Hubei Provincial Education Department(B20104403)
文摘The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+1.The results show that this sequence has high linear complexity.
文摘Combining the theory of symbolic dynamics with the formal language theory, we determine the minimal deterministic finite automata (DFA) Aaccepting the formal languages generated by eventually periodic kneading sequences of unimodal maps on an interval.
文摘A nonincreasing sequence ( of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n. The set of all graphic sequences of n terms with even sum 2m and trace f is a poset G_(n,m,f) under majorization relation. The paper characterizes the minimal elements in the poset G_(n,m,f) and determines the number of minimal elements in various posets of graphic sequences.
文摘The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.
基金supported by National Natural Science Foundation of China(Grant No.12071021)Natural Science Foundation of Hebei Province(Grant No.A2019201120)+4 种基金the Key Science and Technology Project of Higher School of Hebei Province(Grant No.ZD2021307)supported by the Postgraduate Innovation Project of Hebei Province(Grant No.CXZZSS2020005)supported by Natural Science Foundation of Hebei Province(Grant No.A2018201285)Science and Technology Project of Hebei Education Department(Grant No.QN2020145)Research Funds of Hebei University(Grant No.8012605)。
文摘This paper deals with regularity properties for minimizing sequences of some integral functionals related to the nonlinear elasticity theory.Under some structural conditions,we derive that the minimizing sequence and the derivatives of the sequences have some regularity properties by using the Ekeland variational principle.
