The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theore...The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.展开更多
This paper presents equations for estimating limiting stand density for Z undulata plantations grown in hot desert areas of Raj asthan State in India. Five different stand level basal area projection models, belonging...This paper presents equations for estimating limiting stand density for Z undulata plantations grown in hot desert areas of Raj asthan State in India. Five different stand level basal area projection models, belonging to the path invariant algebraic difference form of a non-linear growth function, were also tested and compared. These models can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are necessary for reviewing different silvicultural treatment options. Data from 22 sample plots were used for modelling. An all possible growth intervals data structure was used. Both, qualitative and quantitative criteria were used to compare alternative models. The Akaike＇s information criteria differ- ence statistic was used to analyze the predictive ability of the models. Results show that the model proposed by Hui and Gadow performed best and hence this model is recommended for use in predicting basal area development in 12 undulata plantations in the study area. The data used were not from thinned stands, and hence the models may be less accurate when used for predictions when natural mortality is very significant.展开更多
We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
The trace inverse functions Tr(λx^(-1)) over the finite field F_(2~n) are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS,RAKAPOSHI,the simple counter stream cipher(SCSC...The trace inverse functions Tr(λx^(-1)) over the finite field F_(2~n) are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS,RAKAPOSHI,the simple counter stream cipher(SCSC) presented by Si W and Ding C(2012),etc.In order to evaluate the security of those ciphers in resistance to(fast) algebraic attacks,the authors need to characterize algebraic properties of Tr(λx^(-1)).However,currently only some bounds on algebraic immunity of Tr(λx^(-1)) are given in the public literature,for example,the NGG upper bound and the Bayev lower bound,etc.This paper gives the exact value of the algebraic immunity of Tr(λx^(-1)) over F_(2~n),that is,AI(Tr(λx^(-1))) =[2n^(1/2)]- 2,where n ≥ 2,A ∈ F_(2~n) and λ≠ 0,which shows that Dalai's conjecture on the algebraic immunity of Tr(λx^(-1)) is correct.What is more,the authors demonstrate some weak properties of Tr(λx^(-1)) against fast algebraic attacks.展开更多
Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares,which was the first Hermitian analogue of...Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares,which was the first Hermitian analogue of Hilbert s seventeenth problem in the nondegenerate case.Later Catlin-D’Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator.The arguments of Catlin-D’Angelo involve subtle asymptotic estimates of the Bergman kernel.In this article,the authors give an elementary and geometric proof of the eventual positivity of this integral operator,thereby yielding another proof of the corresponding positivstellensatz.展开更多
This paper discusses all cases of second order linear singular defferential difference equations with delay and different coefficients, and prensents the conditionsfor existence and uniqueness of solutions nearly in a...This paper discusses all cases of second order linear singular defferential difference equations with delay and different coefficients, and prensents the conditionsfor existence and uniqueness of solutions nearly in all cases.展开更多
Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm...Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm）q（x1,x2,…,xe）^1/lwe＋1^xe＋1…wm^xm, where g∈ F, q ∈ C（x1,x2,…,xe）,t∈Z^＋ and we＋1,…,wm are roots of unity. Furthermore,we present an algorithm for determining whether a hyperexponential function is algebraic over F.展开更多
In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n,...In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(O K) of K in the series all have a factor n.[展开更多
Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace ...Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.展开更多
In this letter, we present a kind of new trap-door one-way function over algebraic integers. We shall first prove the following theorems. Theorem 1. Suppose that Q（i） is a complex number field,D={a+bi: a, b∈Z} wher...In this letter, we present a kind of new trap-door one-way function over algebraic integers. We shall first prove the following theorems. Theorem 1. Suppose that Q（i） is a complex number field,D={a+bi: a, b∈Z} where Z denotes the domain of rational integers. Let m=q1n1…qknk, qj（?）3 （mod 4） （j=1, …, k）, where q1,…,qk are distinct primes. Let s>0,展开更多
基金Supported by Guangdong Natural Science Foundation(2015A030313628,S2012010010376)Training plan for Distinguished Young Teachers in Higher Education of Guangdong(Yqgdufe1405)+1 种基金Guangdong Education Science Planning Project(2014GXJK091,GDJG20142304)the National Natural Science Foundation of China(11301140,11101096)
文摘The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.
基金the State Forest Department,Rajasthan for providing financial support for conducting this study and to their officials for rendering necessary assistance during fieldwork
文摘This paper presents equations for estimating limiting stand density for Z undulata plantations grown in hot desert areas of Raj asthan State in India. Five different stand level basal area projection models, belonging to the path invariant algebraic difference form of a non-linear growth function, were also tested and compared. These models can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are necessary for reviewing different silvicultural treatment options. Data from 22 sample plots were used for modelling. An all possible growth intervals data structure was used. Both, qualitative and quantitative criteria were used to compare alternative models. The Akaike＇s information criteria differ- ence statistic was used to analyze the predictive ability of the models. Results show that the model proposed by Hui and Gadow performed best and hence this model is recommended for use in predicting basal area development in 12 undulata plantations in the study area. The data used were not from thinned stands, and hence the models may be less accurate when used for predictions when natural mortality is very significant.
文摘We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
基金supported by the National Natural Science Foundation of China under Grant No.61572491the 973 Program under Grant No.2011CB302401the open project of the SKLOIS in Institute of Information Engineering,Chinese Academy of Sciences under Grant No.2015-MS-03
文摘The trace inverse functions Tr(λx^(-1)) over the finite field F_(2~n) are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS,RAKAPOSHI,the simple counter stream cipher(SCSC) presented by Si W and Ding C(2012),etc.In order to evaluate the security of those ciphers in resistance to(fast) algebraic attacks,the authors need to characterize algebraic properties of Tr(λx^(-1)).However,currently only some bounds on algebraic immunity of Tr(λx^(-1)) are given in the public literature,for example,the NGG upper bound and the Bayev lower bound,etc.This paper gives the exact value of the algebraic immunity of Tr(λx^(-1)) over F_(2~n),that is,AI(Tr(λx^(-1))) =[2n^(1/2)]- 2,where n ≥ 2,A ∈ F_(2~n) and λ≠ 0,which shows that Dalai's conjecture on the algebraic immunity of Tr(λx^(-1)) is correct.What is more,the authors demonstrate some weak properties of Tr(λx^(-1)) against fast algebraic attacks.
基金partially supported by the Singapore Ministry of Education Academic Research Fund Tier 1 grant R-146-000-142-112。
文摘Quillen proved that repeated multiplication of the standard sesquilinear form to a positive Hermitian bihomogeneous polynomial eventually results in a sum of Hermitian squares,which was the first Hermitian analogue of Hilbert s seventeenth problem in the nondegenerate case.Later Catlin-D’Angelo generalized this positivstellensatz of Quillen to the case of Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds by proving the eventual positivity of an associated integral operator.The arguments of Catlin-D’Angelo involve subtle asymptotic estimates of the Bergman kernel.In this article,the authors give an elementary and geometric proof of the eventual positivity of this integral operator,thereby yielding another proof of the corresponding positivstellensatz.
文摘This paper discusses all cases of second order linear singular defferential difference equations with delay and different coefficients, and prensents the conditionsfor existence and uniqueness of solutions nearly in all cases.
基金The research is supported in part by the 973 project of China(2004CB31830).
文摘Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm）q（x1,x2,…,xe）^1/lwe＋1^xe＋1…wm^xm, where g∈ F, q ∈ C（x1,x2,…,xe）,t∈Z^＋ and we＋1,…,wm are roots of unity. Furthermore,we present an algorithm for determining whether a hyperexponential function is algebraic over F.
文摘In this paper, we study the real quadratic function fields K=k(D), given a necessary and sufficient condition for the ideal class group H(K) of any real quadratic function field K to have a cyclic subgroup of order n, and obtained eight series of such fields. The ideal class numbers h(O K) of K in the series all have a factor n.[
基金The second author is supported by National Natural Science Foundation of China(Grant Nos.11550110172 and 11771164)。
文摘Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.
基金Project supported by the Science Fund of Academia Sinica
文摘In this letter, we present a kind of new trap-door one-way function over algebraic integers. We shall first prove the following theorems. Theorem 1. Suppose that Q（i） is a complex number field,D={a+bi: a, b∈Z} where Z denotes the domain of rational integers. Let m=q1n1…qknk, qj（?）3 （mod 4） （j=1, …, k）, where q1,…,qk are distinct primes. Let s>0,
