Related papers: T-homotopy and refinement of observation (I) : Int…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
This paper serves as an introduction to the current book. It provides the basic notions of long-baseline optical/infrared interferome-try prior to reading all the subsequent chapters, and is not an extended introduction to the field.
I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
This paper presents a new algorithm for online estimation of a sequence of homographies applicable to image sequences obtained from robotic vehicles equipped with vision sensors. The approach taken exploits the underlying Special Linear…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
We introduce the persistent homotopy type distance dHT to compare real valued functions defined on possibly different homotopy equivalent topological spaces. The underlying idea in the definition of dHT is to measure the minimal shift that…
Nearness theory comes into play in homotopy theory because the notion of closeness between points is essential in determining whether two spaces are homotopy equivalent. While nearness theory and homotopy theory have different focuses and…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…
We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…
We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. The conditions for lifting the latter to the former are identified using obstruction theory in the form of Postnikov towers, where…
This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
We establish several fundamental properties of analysis-suitable T-splines which are important for design and analysis. First, we characterize T-spline spaces and prove that the space of smooth bicubic polynomials, defined over the extended…
There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build…
In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…
Controllability and observability are important properties of a distributed paramater systems.The equivalence between the notion of exact observability and exact controllability holds in general. In this work, we define a new notion of…
We review the construction and context of a stable homotopy refinement of Khovanov homology.