In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power s...In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.展开更多
By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the inf...By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.展开更多
An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form?t+(t2)?is called a unipotent substitution with pre-function. Such operators, denoted by a p...An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form?t+(t2)?is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ,σ )? , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .展开更多
In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and pr...In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and prove convergence of formal so- lutions under conditions. -We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.展开更多
Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation bet ween the z-ideals of A and t hose of the formal power series rings in an infinite set of indetermiii...Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation bet ween the z-ideals of A and t hose of the formal power series rings in an infinite set of indetermiiiates over A.Consider A[[Xa]]3 and its subrings A[[X_(A)]]_(1),A[[X_(A)]]_(2),and A[[X_(A)]]_(α),where a is an infinite cardinal number.In fact,a z-ideal of the rings defined above is of the form I+(X_(A))i,where i=1,2,3 or an infinite cardinal number and I is a z-ideal of A.In addition,we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients.As a natural result,we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.展开更多
设shx,chx和sinβ,cosβ是双曲正、余弦函数和三角函数,用发生函数的方法得到双曲正,余弦函数方幂与等比序列乘积之和sum (dksh'kx)from k=0 to n ,sum (dkch'kx)from k=0 to n 和双曲正、余弦函数带有三角函数方幂sum (sh'...设shx,chx和sinβ,cosβ是双曲正、余弦函数和三角函数,用发生函数的方法得到双曲正,余弦函数方幂与等比序列乘积之和sum (dksh'kx)from k=0 to n ,sum (dkch'kx)from k=0 to n 和双曲正、余弦函数带有三角函数方幂sum (sh'kxsinkβ)from k=0 to n,sum (sh'kxcoskβ)from k=0 to n的计算公式.展开更多
设Tn(x),Un(x)是Chebyshev多项式,复数d≠0,利用发生函数方法给Chebyshev多项式方幂和sum from k=1 to n U_k^r dk,sum from k=0 to n T_k^r dk计算公式,并进一步得到方幂和sum from k=1 to n U_k^r sin ka,sum from k=0 to n T_k^r sin...设Tn(x),Un(x)是Chebyshev多项式,复数d≠0,利用发生函数方法给Chebyshev多项式方幂和sum from k=1 to n U_k^r dk,sum from k=0 to n T_k^r dk计算公式,并进一步得到方幂和sum from k=1 to n U_k^r sin ka,sum from k=0 to n T_k^r sin ka计算公式,展开更多
文摘In this paper, we study self-dual permutation codes over formal power series rings and finite principal ideal rings. We first give some results on the torsion codes associated with the linear codes over formal power series rings. These results allow for obtaining some conditions for non-existence of self-dual permutation codes over formal power series rings. Finally, we describe self-dual permutation codes over finite principal ideal rings by examining permutation codes over their component chain rings.
基金Supported by the NNSF of China(10771093)Supported by the NSF of Henan Province(0511010300)
文摘By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the infinite series Σr≥m tn＋r/（n＋rr）.
文摘An operator on formal power series of the form S μS , where μ is an invertible power series, and σ is a series of the form?t+(t2)?is called a unipotent substitution with pre-function. Such operators, denoted by a pair (μ ,σ )? , form a group. The objective of this contribution is to show that it is possible to define a generalized powers for such operators, as for instance fractional powers σ for every .
文摘In this article, we study on the existence of solution for a singularities of a system of nonlinear fractional differential equations （FDE）. We construct a formal power series solution for our considering FDE and prove convergence of formal so- lutions under conditions. -We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function.
文摘Let A be a ring.In this paper we generalize some results introduced by Aliabad and Mohamadian.We give a relation bet ween the z-ideals of A and t hose of the formal power series rings in an infinite set of indetermiiiates over A.Consider A[[Xa]]3 and its subrings A[[X_(A)]]_(1),A[[X_(A)]]_(2),and A[[X_(A)]]_(α),where a is an infinite cardinal number.In fact,a z-ideal of the rings defined above is of the form I+(X_(A))i,where i=1,2,3 or an infinite cardinal number and I is a z-ideal of A.In addition,we prove that the same condition given by Aliabad and Mohamadian can be used to get a relation between the minimal prime ideals of the ring of the formal power series in an infinite set of indeterminates and those of the ring of coefficients.As a natural result,we get a relation between the z°-ideals of the formal power series ring in an infinite set of indeterminates and those of the ring of coefficients.
文摘设shx,chx和sinβ,cosβ是双曲正、余弦函数和三角函数,用发生函数的方法得到双曲正,余弦函数方幂与等比序列乘积之和sum (dksh'kx)from k=0 to n ,sum (dkch'kx)from k=0 to n 和双曲正、余弦函数带有三角函数方幂sum (sh'kxsinkβ)from k=0 to n,sum (sh'kxcoskβ)from k=0 to n的计算公式.
文摘设Tn(x),Un(x)是Chebyshev多项式,复数d≠0,利用发生函数方法给Chebyshev多项式方幂和sum from k=1 to n U_k^r dk,sum from k=0 to n T_k^r dk计算公式,并进一步得到方幂和sum from k=1 to n U_k^r sin ka,sum from k=0 to n T_k^r sin ka计算公式,
