Related papers: Topics on nonlinear generalized functions
We study the smooth structure of convex functions by generalizing a powerful concept so-called self-concordance introduced by Nesterov and Nemirovskii in the early 1990s to a broader class of convex functions, which we call generalized…
These Lecture Notes are devoted to an introductory description of some of the most widely applied statistical methods for the analysis of the Large-Scale Structure (LSS) of the Universe. Rather than providing technical details about the…
A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.
The main purpose of this paper is to study the generalized squeezing functions and Fridman invariants of some special domains. As applications, we give the precise form of generalized squeezing functions and Fridman invariants of various…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
Recent work on dissimilarity-based hierarchical clustering has led to the introduction of global objective functions for this classical problem. Several standard approaches, such as average linkage, as well as some new heuristics have been…
We consider the fractional Laplace framework and provide models and theorems related to nonlocal diffusion phenomena. Some applications are presented, including: a simple probabilistic interpretation, water waves, crystal dislocations,…
We study the geometry of functions from the plane to the plane. For a large special class we are able to count preimages and compute them. Both numerical and theoretical aspects are discussed. Some of the tools used are Whitney's…
Notes from a course taught by Palle Jorgensen in the fall semester of 2009. The course covered central themes in functional analysis and operator theory, with an emphasis on topics of special relevance to such applications as representation…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of…
We introduce and analyze spaces and algebras of generalized functions which correspond to H\" older, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are…
The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…
The plenary presentations of the conference are summarised, highlighting some aspects that were of particular interest and attempting to link a few of the topics covered. Particular emphasis is placed on the problem of deep-inelastic…
We introduce a general context involving a presheaf A and a subpresheaf B of A. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as…
We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
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…