Related papers: Metric Regularity. Theory and Applications - a sur…
This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…
In this thesis, set-valued maps are considered to model the $i-v$ characteristics of semiconductors like diode, and transistor. Using the circuit theory laws, a generalized equation is obtained. The main concern of the thesis is to…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
Motivated by the local theory of Banach spaces we introduce a notion of finite representability for metric spaces. This allows us to develop a new technique for comparing the generalized roundness of metric spaces. We illustrate this…
We revisit the well-established regularity estimates on harmonic maps on surfaces to question their independence with respect to the dimension of the target manifold. We are mainly interested in harmonic maps into target ellipsoids, that we…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The…
We develop a framework for regularly varying measures on complete separable metric spaces $\mathbb{S}$ with a closed cone $\mathbb{C}$ removed, extending material in Hult & Lindskog (2006), Das, Mitra & Resnick (2013). Our framework…
The Two-Measure theory (TMT) has been developing since 1998 and has yielded a number of highly interesting results, including those not realized in traditional field theory models. The most important advantage of TMT as an alternative…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…