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中国科学院数学机械化重点实验室陈绍示副研究员科研进展-多变元幂级数的算术理论研究
多变元幂级数 算术理论 幂级数 多复变研究 Szego定理 Polya-Carlson定理
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2022/4/24
幂级数， 随处可见，在复分析、组合理论、代数几何等领域扮演着重要角色。在复分析中，多变元幂级数收敛域的几何结构开启了多复变研究的序幕。在组合理论中，序列的生成函数就是幂级数，其算术与代数性质可以揭示序列的内在结构。在代数几何中，幂级数被用于理解代数簇在奇点处的几何结构。 幂级数的算术理论始于Fatou，Eisenstein，Polya，Szego等人的工作，其中最著名的定理是Szego定理与Pol...
Twisted Weyl Group Multiple Dirichlet Series: The Stable Case
Stable Case Multiple Dirichlet Series
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2015/7/6
Weyl group multiple Dirichlet series were associated with a root system Φ and a number
field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] an...
Weyl Group Multiple Dirichlet Series I
Dirichlet Series Group
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2015/7/6
Given a root system Φ of rank r and a global field F containing the n-th
roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose
coefficients are n-th ...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
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2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
On one Laurent series ring over an extension of $\mathbb{Q}$
Laurent series ring
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2010/12/10
In this paper, using the general Mal’cev-Neumann construction of Laurent series rings, we construct a ring with a base ring which is an extension of the field Q of rational numbers. Further, we establ...
Various observations on angles proceeding in geometric progression
Various observations angles proceeding geometric progression
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2010/12/1
Since a great many well known properties found about angles, or arcs,and the sines, cosines, tangents, cotangents, secants and cosecants of them have been derived from the consideration of arcs increa...
Analysis of Width-$w$ Non-Adjacent Forms to Imaginary Quadratic Bases
-adic expansions non-adjacent forms redundant digit sets
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2010/11/29
We consider digital expansions to the base of , where is an algebraic integer. For a w 2, the set of admissible digits consists of 0 and one representative of every residue class modulo w which ...
Graded mutation in cluster categories coming from hereditary categories with a tilting object
Graded mutation cluster categories hereditary categories tilting object
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2010/12/13
We present a graded mutation rule for quivers of clustertilted algebras. Furthermore, we give a technique to recover a clustertilting object from its graded quiver in the cluster category of cohX.
Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method
Basket options pricing local volatility jump-diffusionmodel forward PIDE asymp-totic expansion
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2010/4/27
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We deri...
议认识无穷的三个误区
无穷 误区 认识
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2009/11/2
探讨了人们在认识无穷过程中存在的三个误区．第一个误区是由忽视无穷概念本身的重要性造成的，第二个误区是由对无穷概念及性质的理解偏差造成的，第三个误区是由把直观想象当推理依据造成的．并通过具体实例对其进行了分析．
p阶临界2-边连通图的最大边数(英文)
极值图 最大边数 边连通图
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2009/9/21
设G=(V,E)是2-边连通图,若对每个点v∈V,G-v不是2-边连通图,则称G是临界2-边连通图. 本文证明了p阶临界2-边连通图的最大边数是 7, P=6; (1/8)(P~2+4p) p=0(mod 4); f(p)= (1/8)(P~2+2p+13) p=1(mod 4); (1/8)(P~2+28) p=(2mod 4),p≠6 (1/8)(P~2+2p+9) p=3(mod 4)。并...
Sobolev方程的一类各向异性非协调有限元逼近
Sobolev方程 各向异性网格 非协调有限元 后处理技术 超逼近和超收敛
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2009/9/21
在各向异性网格下,分别讨论了Sobolev方程在半离散和全离散格式下的一类非协调有限元逼近,得到了与传统有限元方法相同的误差估计和一些超逼近性质.同时在半离散格式下,通过构造具有各向异性特征的插值后处理算子得到了整体超收敛结果.
可测函数序列关于弱收敛概率测度序列积分的极限定理
极限定理 控制收敛定理 弱等度胎紧 一致可积
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2009/9/21
研究了可测函数序列关于弱收敛概率测度序列积分的极限定理及其控制收敛定理,并给出了概率测度弱收敛的若干新的等价条件.
平面上的零级Dirichlet级数
Dirichlet级数 级 下级 零级 最大项指
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2009/9/18
应用最大项指标，在较宽的系数条件下,
对复平面上的零级数Dirichlet级数进行了深入的研究,得到关于它们增长性的两个定理,
即文中定理1和定理2.