Distribution of Primitive A-Roots of Composite Moduli Ⅱ

Abstract We improve estimates for the distribution of primitive λ-roots of a composite modulus q yielding an asymptotic formula for the number of primitive λ-roots in any interval I of length ∣I∣ ≫ q ^1/2+∈. Similar results are obtained for the distribution of ordered pairs (x, x ⁻¹) with x a primitive λ-root, and for the number of primitive λ-roots satisfying inequalities such as |x − x ⁻¹| ≤ B. (Dedicated to Professor Wang Yuan on the occasion of his 75th birthday) *Project supported by the National Natural Science Foundation of China (No.19625102) and the 973 Project of the Ministry of Science and Technology of China.     

On the Distribution of Weakly Composite Numbers

ＯｎｔｈｅＤｉｓｔｒｉｂｕｔｉｏｎｏｆＷｅａｋｌｙＣｏｍｐｏｓｉｔｅＮｕｍｂｅｒｓ王天泽，李国强ＯｎｔｈｅＤｉｓｔｒｉｂｕｔｉｏｎｏｆＷｅａｋｌｙＣｏｍｐｏｓｉｔｅＮｕｍｂｅｒｓ￥ＷａｎｇＴｉａｎｚｅ；ＬｉＧｕｏｑｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭ...     

L(d1, d2,..., dt)-Number λ(Cn; d1, d2,...,dt) of Cycles

An L(d1,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0, 1,..., k} for some positive integer k such that {f(x) - f(y)| ≥ di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,... ,dt)labeling with max{f(x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2,1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2,1,..., 1)     

Value‐Distribution of General Dirichlet Series. II

In the paper, a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved.     

On the Convergence Acceleration of Composite Sequence Transformation

ＯｎｔｈｅＣｏｎｖｅｒｇｅｎｃｅＡｃｃｅｌｅｒａｔｉｏｎｏｆＣｏｍｐｏｓｉｔｅＳｅｑｕｅｎｃｅＴｒａｎｓｆｏｒｍａｔｉｏｎ￥ＴａｎｇＳｈｕｏ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＨｅｆｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏ...     

Complete Space-like λ-surfaces in the Minkowski Space R1^3 with the Second Fundamental Form of Constant Length

In this paper we study the complete space-like λ-surfaces in the three dimensional Minkowski space R1^3.As the result,we obtain a complete classification theorem for all the complete space-like λ-surfaces x:M^2→R1^3 with the second fundamental form of constant length.This is a natural extension to the λ-surfaces in R1^3 of a recent interesting classification theorem by Cheng and Wei forλ-surfaces in the Euclidean space R^3.     

Convergence of the Iterated Aluthge Transform Sequence for Diagonalizable Matrices II: λ-Aluthge Transform

Let λ ∈ (0, 1) and let T be a r × r complex matrix with polar decomposition T = U|T|. Then the λ-Aluthge transform is defined by

Classification of Flag-Transitive Primitive Symmetric(v,k, λ) Designs with PSL(2, q) as Socle

Let D be a nontrivial symmetric(v, k, λ) design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on D and Soc(G) = PSL(2, q), then D has parameters(7, 3, 1),(7, 4, 2),(11, 5, 2),(11, 6, 3) or(15, 8, 4).     

Exact solutions of accelerated flows for a Burgers’ fluid II. The cases γ = λ2/4 and γ > λ2/4

The purpose of this study is to provide the exact analytic solutions of accelerated flows for a Burgers’ fluid when the relaxation times satisfy the conditions γ = λ²/4 and γ > λ²/4. The velocity field and the adequate tangential stress that is induced by the flow due to constantly accelerating plate and flow due to variable accelerating plate are determined by means of Laplace transform. All the solutions that have been obtained are presented in the form of simple or multiple integrals in terms of Bessel functions. A comparison between Burgers’ and Newtonian fluids for the velocity and the shear stress is also made through several graphs.