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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principles
Caffarelli Kohn-Nierberg不等式 不确定性原理
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2023/11/13
In this talk we introduce some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on ?n, which is a further study of the results given i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on holomorphic Morse inequalities
全纯 Morse不等式 CR流形
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2023/11/13
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Identities, inequalities and congruences for odd ranks and k-marked odd Durfee symbols
奇数秩 k标记 奇数杜菲符号 恒等式 不等式 全等
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2023/4/23
In 2007, Andrews introduced the odd rank of odd Durfee symbols. Let N^0 (m,n) denote the number of odd Durfee symbols of n with odd rank m, and N^0 (r,m;n) be the number of odd Durfee symbols of n wit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum Inequalities and Their Extremisers
量子不等式 极端值 量子对称性
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2023/4/14
In this talk, we shall present a series of inequalities for quantum symmetries such as Hausdorff-Young inequalities, Young's inequalities, uncertainty principles, sumset estimation and entropic inequa...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Heintze Karcher type inequalities on capillary hypersurfaces in hyperbolic space
双曲空间 毛细管超表面 海因茨·卡彻型不等式
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2023/4/23
In this talk, I will introduce our recent result on Heintze Karcher type inequalities for capillary hypersurfaces supported on different types of umbilical hypersurfaces in hyperbolic space. I will in...
A Posteriori Error Analysis for A Class of Integral Equations and Variational Inequalities
Integral Equations Variational Inequalities
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2015/12/11
We consider elliptic and parabolic variational equations and inequalities governed by
integro-differential operators of order 2s ∈ (0,2]. Our main motivation is the pricing of European
or Amer...
A POSTERIORI ERROR ANALYSIS FOR PARABOLIC VARIATIONAL INEQUALITIES
variational inequality American option pricing
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2015/12/11
Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain Ω ⊂ Rd with a continuous piecewise smooth obstacle.
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The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra
generalized triangle inequalities symmetric spaces and buildings applications to algebra
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2015/10/14
In this paper we apply our results on the geometry of polygons in infinitesimal symmetric spaces, symmetric spaces and buildings, [KLM1, KLM2], to four problems in algebraic group theory. Two of these...
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.
Nash Inequalities for Finite Markov Chains
Finite Markov Chains Inequalities
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2015/8/26
This paper develops bounds on the rate of decay of powers of Markov kernels
on finite state spaces. These are combined with eigenvalue estimates to give
good bounds on the rate of convergence to sta...
A NOTE ON POINCARI, SOBOLEV, AND HARNACK INEQUALITIES
HARNACK INEQUALITIES SOBOLEV
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2015/8/26
Let M be a cg-connected manifold. Let L be a second-order
differential operator with real cg(R) coefficients on M and such that L1 0 (i.e., L
has no zero-order term). Assume that there exists a posi...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Sobolev inequality MARKOV CHAINS
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2015/8/26
This is an expository paper on the use of logarithmic Sobolev inequalities
for bounding rates of convergence of Markov chains on finite state
spaces to their stationary distributions. Logarithmic So...
Sobolev Inequalities in Disguise
Disguise functional inequalities
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2015/8/26
We present a simple and direct proof of the equivalence of various
functional inequalities such as Sobolev or Nash inequalities. This
proof applies in the context of Riemannian or sub-elliptic geome...
Pseudo-Poincar¶e Inequalities and Applications to Sobolev Inequalities
Sobolev Inequalities Inequalities
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2015/8/26
Most smoothing procedures are via averaging. Pseudo-Poincar¶e in-
equalities give a basic Lp-norm control of such smoothing procedures in terms
of the gradient of the function involved. When av...
INEQUALITIES FOR THE H-AND FLAG H-VECTORS OF GEOMETRIC LATTICES
H-AND FLAG H-VECTORS GEOMETRIC LATTICES
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2015/8/25
We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if ∆(L) is the order complex of a rank (r +1) geometric lattice L, then the for all i ≤ r...