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新的梯度算法求解单位球笛卡尔积约束优化问题
单位球 梯度算法 Chambolle算法
2019/4/17
本文主要研究了单位球笛卡尔积作为约束的优化问题，给出了此类问题的最优性条件.同时将求解此问题的一些经典的梯度算法推广到了更加一般的形式，并证明了新算法的收敛性.随机二次规划问题和求解图像变分去噪模型的数值结果表明新算法并不弱于一些经典的算法，特别是在精度要求较高的情形下.
无$K_4$-图子式的图的邻和可区别边染色
邻和可区别边染色 组合零点定理 无$K_4$-图子式的图
2018/2/6
给定图 ~$G$ 的一个正常 ~$k$- 边染色$\phi:E(G)\rightarrow\{1,2,\cdots,k\}$, 记$f(v)$是与点$v$相关联的边的颜色的加和. 若对$G$的每条边$uv$都有$f(u)\neq f(v)$, 则称$\phi$是图$G$的$k$-邻和可区别边染色. 图$G$存在$k$-邻和可区别边染色的$k$的最小值称为图$G$的邻和可区别边色数, 记作$\chi...
素变量混合幂丢番图逼近
丢番图不等式 素数 Davenport-Heilbronn方法
2019/4/17
设λ1，λ2，λ3，λ4为不全为负的非零实数，λ1/λ2是无理数和代数数.V是具有良好间隔的序列，δ>0.本文证明了：对于任意ε>0及v∈V，v≤X，使得不等式|λ1p12+λ2p22+λ3p33+λ4p43-v|
PERIODIC BOXCAR DECONVOLUTION AND DIOPHANTINE APPROXIMATION
BOXCAR DECONVOLUTION DIOPHANTINE APPROXIMATION
2015/8/20
We consider the nonparametric estimation of a periodic function that is
observed in additive Gaussian white noise after convolution with a “boxcar,”
the indicator function of an interval. This is an...
Diophantine Geometry over Groups X: The Elementary Theory of Free Products of Groups
Diophantine Geometry Groups X Elementary Theory of Free Products of Groups
2011/1/14
This paper is the 10th in a sequence on the structure of sets of solutions to systems of equations over groups, projections of such sets (Diophantine sets), and the structure of definable sets over fe...
Transference inequalities for multiplicative Diophantine exponents
Transference inequalities multiplicative Diophantine exponents
2011/1/20
In this paper we prove inequalities for multiplicative analogues of Diophantine exponents, similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if...
Exponents for three-dimensional simultaneous Diophantine approximations
three-dimensional simultaneous Diophantine approximations
2010/11/30
Let = (1, 2, 3) ∈ R3. Suppose that 1, 1, 2, 3 are linearly independent over Z.
Inhomogeneous theory of dual Diophantine approximation on manifolds
Metric Diophantine approximation extremal manifolds
2010/12/14
The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is e...
On Delannoy numbers and Schröder numbers
Congruences central Delannoy numbers Euler numbers Schr¨oder numbers
2010/12/6
The nth Delannoy number and the nth Schr¨oder number given by Dn = n Xk=0 n kn + k k and Sn =n Xk=0 n kn + k k 1 k + 1espectively arise naturally from enumer tive combinatorics. Let p be an ...
Polynomial estimates, exponential curves and Diophantine approximation
Polynomial estimates exponential curves Diophantine approximation
2010/12/10
Let ∈ (0, 1) \ Q and K = {(ez, e z) : |z| ≤ 1} ⊂ C2. If P is a polynomial of degree n in C2, normalized by kPkK = 1, we obtain sharp estimates for kPk2 in terms of n, where 2 is the closed u...
一类连分数的有理逼近
有理逼近 连分数 下界估计
2008/7/21
设$f(n)$是非负函数, $\kappa,b,s_{i},t_{i}(i=1,2,\cdots)$是正常数,研究形如$$[a_{0},a_{1},a_{2},\cdots]=[\overline{\kappa n+b}]_{n=0}^{\infty}\mbox{~~和~~}[\overline{s_{n},f(n),t_{n}}]_{n=1}^{\infty}$$的连分数有理逼近的下界.
设$D$ 是不能被$3$ 整除的正整数. 本文证明了：当$D>10^{12}$ 时, 如果Pell 方程${U^2}- DV^2 =-1$ 有解$(U,V)$, 则方程${x^2}-D=3^n$ 至多有2 组正整数解$(x, n)$.
丢番图方程与实二次域类数的可除性
2007/12/13
设ｄ无平方因子,h(d)是二次域$Q\sqrt{d}$的类数。本文证明了：在方程$U^2-dV^2=4,(u,V)=1$有整数解时，丢番图方程$4x^{2n}-dy^2=-1,n>2$无$|y|>1$的整数解；如果正整数ａ，ｋ，ｎ满足$a\geqk^{\frac{n}{2}},k>1,n>2$且$2k^n$而是Ｐｅｌｌ方程$x^2-dy^2=-1$的基本解，则$h(d)\equiv0$(mod n...
关于丢番图方程$x^2-D=p^n$的解数
2007/12/13
设D是正整数,p是适合$p\aleph D$的奇素数。本文证明了:当$max(D,p)≥10^{190}$时,方程$x^2-D=p^n$至多有3组正整数解(x,n)。