We obtain several estimates for bilinear forms with exponential sums with binomials mx(k) + nx(l). In particular we show the existence of nontrivial cancellations between such sums when the coefficients m and n vary over rather sparse sets of general nature. (C) 2018 Published by Elsevier Inc.

We obtain an asymptotic formula for the average value of the divisor function over the integers n <= x in an arithmetic progression n a mod q, where q = p(k) for a prime p >= 3 and a sufficiently large integer k. In particular, we break the classical barrier q <= x(2/3-epsilon) (with an arbitrary epsilon > 0) for such formulas, and, using some new arguments, generalise and strengthen a recent result of R. Khan (2015), making it uniform in k. (C) 2017 Elsevier Inc. All rights reserved.

We give nontrivial upper bounds in various ranges for Kloosterman sums of the formSigma'(n is an element of S(x,y)) exp(27 pi ia (n) over bar /m),where m, a are integers with m >= 2, (a, m) = 1, and S(x, y) is the set of y-smooth numbers up to x. We also obtain a better bound on average over m asSigma(m similar to M) ((a, m)=1) max vertical bar Sigma'(n is an element of S(x,y)) exp(27 pi ia (n) over bar /m),where m similar to M means M < m <= 2M. (C) 2017 Elsevier Inc. All rights reserved.

By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.

针对二维不规则实物碎片,提出了一种基于多种碎片特征的碎片匹配算法.对碎片进行预处理,提取碎片的轮廓特征以及文字特征.文中主要采用高斯滤波对图像进行平滑,基于数学形态学边缘检测算法进行边缘检测,基于曲率尺度空间进行角点检测

Let q > 2 be an integer, n >= 2 be a fixed integer with (n, q) = 1, psi be a non-principal Dirichlet character modq. An upper bound estimate for character sums of the formSigma(a is an element of C(1,q)) psi(a)is given, where C(1, q) = {a vertical bar 1 <= a <= q - 1, (a) over bara equivalent to 1(mod q), n inverted iota (a + (a) over bar)}.

Text. By using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function, a hybrid mean value problem involving certain Hardy sum and Kloosterman sum is studied. Two exact computational formulae are given, through which the cancellation phenomenon is revealed.Video. For a video summary of this paper, please visit https://youtu.be/d-X81xErU7Q. (C) 2016 Elsevier Inc. All rights reserved.

Let q >= 2 be a fixed integer, A = A(q) <= q, B = B(q) <= q, and H <= H(q) = q. Define(h) over bar (A, B, H) = {a is an element of vertical bar Z vertical bar (a, q) = 1, ab 1 (modq), 1 <= a <= A, 1 <= b <= B, vertical bar a - b vertical bar <= H}.With the aid of the estimates for the general Kloosterman sums and the properties of trigonometric sums, we obtain an upper bound of the general partial Gaussian sums over the number set (h) over bar (A, B, H).

针对现有机械制造领域网格模型分割结果缺少工程含义的现状,提出了一种三角网格模型体素特征分割方法。首先在对三角网格模型分割的基础上,对由网格分割得到的每个子网格进行曲面类型识别,然后在基本体素及典型结构显著特征表示的基础上,把识别出的曲面集合与基本体素及典型结构进行匹配,从而将分割结果分类为自由曲面、基本体素和复杂体素,实现具有工程含义的体素特征分割。该方法可以降低模型重构的难度,加快模型重构的速度。