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ON THE GENERAL QUADRATIC GAUSS SUMS WEIGHTED BY CHARACTER SUMS OVER A SHORT INTERVAL
Zhang, Tianping Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
By using the analytic methods, the mean value of the general quadratic Gauss sums weighted by the first power mean of character sums over a short interval is investigated. Several sharp asymptotic formulae are obtained, which show that these sums enjoy good distributive properties. Moreover, interesting connections among them are established.
On the $r$-th hyper-Kloosterman sums and its hybrid mean value
Tianping Zhang,Wenpeng Zhang 대한수학회 2006 대한수학회지 Vol.43 No.6
The main purpose of this paper is using the propertiesof Gauss sums, primitive characters and the mean value theoremsof Dirichlet L-functions to study the hybrid mean value of the r-thhyper-Kloosterman sums Kl (h;k+1 ;r;q) and the hyper Cochranesums C(h;q;m;k);and give an interesting mean value formula.
On the r-th hyper-Kloosterman sums and a problem of D. H. Lehmer
Zhang Tianping,Xue Xifeng 대한수학회 2009 대한수학회지 Vol.46 No.4
For any integer k≥2, let P(c,k+1;q) be the number of all k+1-tuples with positive integer coordinates (a_1, a_2,…,a_{k+1}) such that 1≤a_i≤q, (a_i, q)=1,a_1 a_2…a_{k+1}≡ c(mod q) and 2│(a_1+a_2+…+a_{k+1}), and E(c,k+1;q)=P(c,k+1;q)-Φi^{k}(q)}/{2}. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula. For any integer k≥2, let P(c,k+1;q) be the number of all k+1-tuples with positive integer coordinates (a_1, a_2,…,a_{k+1}) such that 1≤a_i≤q, (a_i, q)=1,a_1 a_2…a_{k+1}≡ c(mod q) and 2│(a_1+a_2+…+a_{k+1}), and E(c,k+1;q)=P(c,k+1;q)-Φi^{k}(q)}/{2}. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.
ON MIXED TWO-TERM EXPONENTIAL SUMS
Zhang Tianping 대한수학회 2010 대한수학회지 Vol.47 No.6
In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r,Â; q), and give several sharp asymptotic formulae
ON MIXED TWO-TERM EXPONENTIAL SUMS
Tianping, Zhang Korean Mathematical Society 2010 대한수학회지 Vol.47 No.6
In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r, $\chi$; q), and give several sharp asymptotic formulae.
ON THE r-TH HYPER-KLOOSTERMAN SUMS AND ITS HYBRID MEAN VALUE
Zhang, Tianping,Zhang, Wenpeng Korean Mathematical Society 2006 대한수학회지 Vol.43 No.6
The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the T-th hyper-Kloosterman sums Kl(h, k+1, r;q) and the hyper Cochrane sums C(h, q; m, k), and give an interesting mean value formula.
On the general quadratic Gauss sums weighted by character sums over a short interval
Tianping Zhang 대한수학회 2013 대한수학회보 Vol.50 No.3
By using the analytic methods, the mean value of the general quadratic Gauss sums weighted by the first power mean of character sums over a short interval is investigated. Several sharp asymptotic formulae are obtained, which show that these sums enjoy good distributive properties. Moreover, interesting connections among them are established.
ON THE γ-TH HYPER-KLOOSTERMAN SUMS AND A PROBLEM OF D. H. LEHMER
Tianping, Zhang,Xifeng, Xue Korean Mathematical Society 2009 대한수학회지 Vol.46 No.4
For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.
城市会展产业发展的支持要素对来访客商的 影响研究 - 以河北省为例 -
Shen Hej iang,Zhang Tianping,Sang-Yup Lee 한국자치행정학회 2010 한국자치행정학보 Vol.24 No.2
컨벤션은 상품 전시, 무역과 경제 기술 합작 기능뿐만 아니라, 정보 문의, 투자 서비스와 비즈니스 지원 등 기능을 가지고 있다. 한 지역의 컨벤션산업이 지속가능한 성장을 이루려면 외부 지원 요소로서 우수한 사회경제발전환경, 지리인문환경, 교통구역조건, 정책조건과 관련 업계의 지원 조건 등을 갖춰야 하고, 내부 지원 요소로서 전시회장, 주관기관, 주관기업, 참여인원, 전시회 프로젝트 등이 체계적으로 구비되어야 한다. 허베이성은 베이징 주변에 있으면서 지리적으로 유리한 위치에 있고, 전시회의 발전에 여러 가지로 객관적인 요건을 갖추고 있다. 본 논문에서는 최근 허베이성 컨벤션산업의 전반적인 환경을 검토하고 발전방안을 모색하였다. 허베이성에는 전시 장소가 부족하여 외래 참석 고객의 규모가 제한되고 있는 형편이다. 전시 소프트 환경의 경쟁력이 뒷받침되지 않아 고객의 구매 욕구를 충족해 주지 못하고 있다. 전시회 소프트 환경의 열악, 관리체계 소홀, 정책 지원의 한계, 자금의 한계, 전문 인력 부족 등이 전시회의 지속적인 발전을 제한하고 있다. 분석 결과 전시산업 발전의 환경은 방문한 고객의 구조와 밀접한 상관관계가 있음을 알 수 있었다. 고객 규모는 컨벤션 관광 환경과 正의 상관관계가 있고, 고객의 동기는 컨벤션 관광 프로젝트의 영향력에 영향을 미치며, 고객 구조는 전시회 요소 배치 구조와 전시 방문 배분과 밀접하게 관련되며, 고객의 몰입은 전시상품의 특색과 밀접한 관련이 있다는 점을 알 수 있었다.
Multi-agent Formation Control in Switching Networks using Backstepping Design
Qin Wang,Qingguang Hua,Yang Yi,Tianping Zhang 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.4
A rigid formation control problem of n agents described by double integrators is proposed in this paper. At the same time, the arbitrary switching topology with no dwell time between consecutive switches is considered. Then the nonsmooth analysis, the backstepping technique and the adaptive perturbation method are employed todesign the globally stable rigid formation control strategy. The main result is that regardless of the topology switching,the global stabilization of the rigid formation, the convergence to a common velocity vector and the collisionavoidance between communicating agents are still guaranteed as long as the graph topology remains rigid all thetime. Simulations are given to demonstrate the effectiveness of the proposed control algorithm.