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本文研究了一类基于非线性抛物变分不等式问题，
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其中L表示变指数退化抛物算子.通过新的惩罚函数和微分不等式级数，证明了该变分不等式解的存在性和唯一性.
基于反正切函数权值累加生成的DGM (1,1)atan模型及其应用
序列预测 DGM (1, 1) 变权累加生成算子 振荡序列
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2018/2/7
传统DGM （1，1）模型的累加生成算子没有考虑数据振荡对数据序列发展趋势的影响，模型预测结果往往呈现齐次指数增长的趋势.该局限性使得DGM （1，1）模型不适用于本身存在随机振动特征的序列分析与预测.针对这一问题，本文提出基于原始数据均值像序列的随机波动特征分析方法，设计出均值像反正切函数变权形式的累加生成算子；在此基础上建立了基于均值像反正切函数变权累加的DGM （1，1）atan模型，该模型...
On self-consistent estimators and kernel density estimators with doubly censored data
Asymptotic normality Failure rate function Right censored data: Survival distribution Uniform strong consistency
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2015/12/11
We study the detailed structure (in a large sample) of the self-consistent estimators of the survival functions with doubly censored data. We also introduce the kernel-type density estimators based on...
Generalized eigenfunctions and a Borel Theorem on the Sierpinski Gasket
Generalized eigenfunctions Borel Theorem Sierpinski Gasket
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2015/12/10
There is a well developed theory (see [5, 9]) of analysis on certain types of fractal sets, of which the Sierpinski Gasket (SG) is the simplest non-trivial example. In this theory the fractals are vie...
SZEGO LIMIT THEOREMS ON THE SIERPINSKI GASKET
Analysis on Fractals equally distributed sequences Laplacian localized eigenfunctions Sierpinski gasket strong Szego limit theorem
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2015/12/10
We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket (SG) to formulate and prove analogues of the strong Szego limit theorem in this fractal setting.Furthermore, ...
SOME SPECTRAL PROPERTIES OF PSEUDO-DIFFERENTIAL OPERATORS ON THE SIERPINSKI GASKET
Analysis on fractals localized eigenfunctions Sierpiński gasket Szego limit theorem
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2015/12/10
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
The Dehn function of SLn(Z)
function L'Enseignement Mathématique
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2015/8/26
This is a brief expository article on the problem of determining the Dehn function of SLn(Z). It appeared in a volume that was presented to G.Mislin on his retirement from ETHZ and was then published ...
The gallery length filling function and a geometric inequality for filling length
filling length filling function
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2015/8/26
We exploit duality considerations in the study of singular combinatorial 2-discs ("diagrams") and are led to the following innovations concerning the geometry of the word problem for finite presentati...
Isoperimetric inequalities for nilpotent groups
nilpotent groups Isoperimetric inequalities
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2015/8/26
We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function.
Higher connectedness of asymptotic cones
asymptotic cones function
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2015/8/26
We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions which are defined recursively on dim...
Digital Implementation of Ridgelet Packets
Wavelets. Ridge function Ridgelets
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2015/8/21
The Ridgelet Packets library provides a large family of orthonormal bases for functions f(x, y) in L2(dxdy) which includes orthonormal ridgelets as well as bases deriving from tilings reminiscent from...
Recovering Edges in Ill-Posed Inverse Problems: Optimality of Curvelet Frames
Ill-Posed Inverse Problems Regularization
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2015/8/21
We consider a model problem of recovering a function f(x1; x2) from noisy Radon
data. The function f to be recovered is assumed smooth apart from a discontinuity
along a C2 curve { i.e. an edge. We ...
Sobol' indices and Shapley value
Sobol' indices Shapley value
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2015/8/21
Global sensitivity analysis measures the importance of some input variables to a function f by looking at the impact on f of making large random
perturbations to subsets of those variables. Using mea...
Effective dimension for weighted function spaces
function spaces weighted
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2015/8/21
This paper introduces some notions of e ective dimension for weighted
function spaces. A space has low e ective dimension if the smallest ball
in it that contains a function of variance 1, has no fu...
Solving Schubert Problems with Littlewood-Richardson Homotopies
Littlewood-Richardson Homotopies Schubert Problems
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2015/7/14
We present a new numerical homotopy continuation algorithm for finding all solutions to
Schubert problems on Grassmannians. This Littlewood-Richardson homotopy is based on
Vakil’s geometric pr...