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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Gauss maps of complete minimal surfaces in Rm
Rm 完全极小曲面 高斯映射
2023/12/11
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Minimal model program for generalized pairs
广义对 最小 模型程序
2023/4/23
Generalized pairs are a natural structure in birational geometry that first appeared in Kodaira’s canonical bundle formula for elliptic fibrations. They were formally introduced by Birkar and Zhang in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds
8流形 最小超曲面 通用规则性
2023/5/5
The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on stable minimal hypercones. It ...
In this paper, we study VC-minimal theories and explore related concepts. We
first define the notion of convex orderablity and show that this lies strictly between VCminimality
and dp-minimality. To...
Compression schemes, stable definable families, and o-minimal structures
Compression schemes stable definable families o-minimal structures
2015/9/28
We show that any family of sets uniformly definable in an ominimal
structure has an extended compression scheme of size equal
to the number of parameters in the defining formula.
The elementary diagram of a trivial, weakly minimal structure is near model complete
elementary diagram model complete
2015/9/28
We prove that if M is any model of a trivial, weakly minimal theory,
then the elementary diagram T(M) eliminates quantifiers down
to Boolean combinations of certain existential formulas.
On the computability-theoretic complexity of trivial, strongly minimal models
computability-theoretic strongly minimal models
2015/9/28
We show the existence of a trivial, strongly minimal (and thus
uncountably categorical) theory for which the prime model is computable and
each of the other countable models computes 0
00. This res...
Trivial, strongly minimal theories are model complete after naming constants
model complete naming constants
2015/9/25
We prove that if M is any model of a trivial, strongly
minimal theory, then the elementary diagram Th(MM ) is a model
complete LM -theory. We conclude that all countable models of
a trivial, strong...
The Schr鰀er-Bernstein property for weakly minimal theories
The Schr鰀er-Bernstein property weakly minimal theories
2015/9/25
For a countable, weakly minimal theory T, we show that the SchröderBernstein
property (any two elementarily bi-embeddable models are isomorphic)
is equivalent to each of the following:
1. For ...
For Most Large Underdetermined Systems of Equations, the Minimal ` 1 -norm Near-Solution Approximates the Sparsest Near-Solution
Solution of Underdetermined Linear Systems Approximate Sparse Solution of Linear equations
2015/8/21
We consider inexact linear equations y ≈ Φα where y is a given vector in R
n
, Φ is a
given n by m matrix, and we wish to find an α0, which is sparse and gives an approximate
solution, obey...
For Most Large Underdetermined Systems of Linear Equations the Minimal ` 1 -norm Solution is also the Sparsest Solution
Solution of Underdetermined Linear Systems Overcomplete Representations
2015/8/21
We consider linear equations y = Φα where y is a given vector in R
n
, Φ is a given n by m
matrix with n < m ≤ An, and we wish to solve for α ∈ Rm. We suppose that the columns
of Φ are normalized ...
ω1 and −ω1 May Be the Only Minimal Uncountable Linear Orders
ω1 and − ω1 May Only Minimal Uncountable Linear Orders
2015/8/17
In 1971 Laver proved the following result, confirming a long-standing conjecture of Fraïssé. Theorem 1.1 [10]. If Li (i < ω) is a sequence of σ-scattered linear orders, then there exist i < j suc...
Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements
Matrix completion The Dantzig selector oracle inequalities norm of random matrices convex optimization and semidefinite programming
2015/6/17
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3
Allen-Cahn Equation Embedded Minimal Surfaces Finite Total Curvature in R3
2015/4/3
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3.
An Inclusion-Exclusion Algorithm for Network Reliability with Minimal Cutsets
Inclusion-Exclusion Formula Network Reliability Minimal Cutset Dynamic Programming
2013/1/30
The inclusion-exclusion formula (IEF) is a fundamental tool for evaluating network reliability with known minimal paths or minimal cuts. However, the formula contains many pairs of terms which cancel....