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An old friend revisited: Countable models of ω-stable theories
Countable models ω-stable theories
2015/9/25
We work in the context of ω-stable theories. We obtain a natural,
algebraic equivalent of ENI-NDOP and discuss recent joint proofs with
S. Shelah that if an ω-stable theory has either ENI-DOP or is ...
We characterize the stable theories T for which the saturated
models of T admit decompositions. In particular, we show that
countable, shallow, stable theories with NDOP have this property.
Descriptive set theory and uncountable model theory
Descriptive set theory uncountable model theory
2015/9/25
In the early days of the development of model theory it was considered
natural and was certainly beneficial to assume that the theories under investigation
were in a countable language. The primary ...
Every countable, strictly stable theory either has the Dimensional
Order Property (DOP), is deep, or admits an ‘abelian group witness
to unsuperstability’. To obtain this and other results, we devel...
The Schr鰀er-Bernstein property for a-saturated models
Schr鰀er-Bernstein property a-saturated models
2015/9/25
A first-order theory T has the Schr╫der-Bernstein (SB) property
if any pair of elementarily bi-embeddable models are isomorphic. We prove
that T has an expansion by constants with the SB property if...
On mathematical foundation of the Brownian motor theory
Brownian motors diffusion effective drift effective diffusivity Bloch decomposition
2015/9/25
The paper contains mathematical justification of basic facts concerning the Brownian motor theory. The homogenization theorems are proved for the Brownian motion in periodic tubes with a constant drif...
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 ...
By a classifiable theory we shall mean a theory which is superstable, without
the dimensional order property, which has prime models over pairs. In order
to define what we mean by unique decompositi...
局部剖分邻接冠图的谱
无符号Laplacian矩阵 图的谱 局部剖分邻接冠图
2018/2/6
设$G_1,G_2$是两个简单连通图,图$G_1,G_2$的局部剖分邻接冠图$G_1 \overline{\star G_2}$是指复制一个$G_1$和$|V(G_1)|$个$G_2$,图$G_1$的第$i$个点的邻点与复制的第$i$个图$G_2$的每一个点相连接,然后在$G_1$每一条边上插入一个新的点而得到的图类.本文利用两个图$G_1,G_2$的邻接谱、Laplacian谱和无符号Lapla...
second moment but satisfying some weaker finite moment condition. For
any locally compact unimodular group G and any positive function :G→
[0,+∞], we introduce a function G, which describes the ...
ASB/ISB award paper Manipulating the edge of instability
Feedback Motor control Time-delay Hand Biomechanics
2015/8/25
We investigate the integration of visual and tactile sensory input for dynamic manipulation. Our experimental data and computational
modeling reveal that time-delays are as critical to task-optimal m...
For an equilibrium of a general dynamical system, the
domain of stability of a linear feedback controller is enlarged by the use
of a general "hybrid" or "switching" strategy. The strategy is illust...
Towards a Global Theory of Singularly Perturbed Dynamical Systems
Perturbed Dynamical System Theory
2015/8/25
Dynamical systems with multiple time scales arise naturally in many domains.
Models of neural systems provide the principal motivation for this
paper. Most of the previous mathematical analysis of q...
Serving as SIAM President was a unique opportunity for me to observe and participate
in the process by which we establish scienti c policy in this country. As is
inevitable in such circumstances, I ...
This paper is a commentary on the experimental observation observa-
tions of Bensimon et al. [1] of convection of a binary
uid mixture in a
uid annulus. They observed a convective pattern that is ...