Related papers: Foliation Theory and it's applications
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
This is a review of the results related to generalizations of the notion of $\tau$-function and integrable hierarchies and to their interpretation within the group theory framework that admits an immediate quantization procedure. Different…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
We survey aspects of prediction theory in infinitely many dimensions, with a view to the theory and applications of functional time series.
We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's…
This work presents a framework for control theory based on constructive analysis to account for discrepancy between mathematical results and their implementation in a computer, also referred to as computational uncertainty. In control…
Suppose that $\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\mathcal F$ has continuous tangent plane field and is {\sl taut}; that is, closed smooth…
We introduce a new kind of foliated quantum field theory (FQFT) of gapped fracton orders in the continuum. FQFT is defined on a manifold with a layered structure given by one or more foliations, which each decompose spacetime into a stack…
In this contribution we establish a dictionary between terms in two different areas in order to show that many of the topics studied are common ones - just with a different terminology. We further analyze the relations between the…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its…
The dissertation provides a comparative analysis of a number of variability tools currently in use. It serves as a catalogue for practitioners interested in the topic. We compare a range of modelling, configuring, and management tools for…
We attempt to review all trustworthy and well-controlled de Sitter compactifications of string theory.
The purpose of this work is to introduce the reader to the Woods Hole trace formula and to show how several well-known index theorems for foliations, vector fields and endomorphisms can be rephrased as particular cases of such formula. The…
Haga's fold in paper folding is generalized. Recent generalization of Haga's theorems and problems in Wasan geometry involving Haga's fold are also generalized.
As a first step towards a microscopic understanding of the effective interaction between colloidal particles suspended in a solvent we study the wetting behavior of one-component fluids at spheres and fibers. We describe these phenomena…
We prove a squeezing/stability theorem for delta-epsilon controlled L-groups when the control map is a fibration on a finite polyhedron. A relation with boundedly-controlled L-groups is also discussed.
The normal distribution and its perturbation has left an immense mark on the statistical literature. Hence, several generalized forms were developed to model different skewness, kurtosis, and body shapes. However, it is not easy to…
A foliation is said to admit a foliated contact structure if there is a codimension 1 distribution in the tangent space of the foliation such that the restriction to any leaf is contact. We prove a version of the Weinstein conjecture in the…