Related papers: Fracture functions from cut vertices
We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…
We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case…
I review recent progress in analysing deep inelastic scattering structure functions in global analyses. The new ingredients are new data and attempts to incorporate heavy quarks consistently. A new way of including the resummation of large…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
This article discusses the notion of convergence of sequences of iterated function systems. The technique of iterated function systems is one of the several methods to construct objects with fractal nature, and the fractals obtained with…
Dual feasible functions (DFFs) have been used to provide bounds for standard packing problems and valid inequalities for integer optimization problems. In this paper, the connection between general DFFs and a particular family of…
Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of…
Coverage functions are an important subclass of submodular functions, finding applications in machine learning, game theory, social networks, and facility location. We study the complexity of partial function extension to coverage…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
Structure functions of rough fracture surfaces in isotropic materials exhibit complicated scaling properties due to the broken isotropy in the fracture plane generated by a preferred propagation direction. Decomposing the structure…
We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [{\it Fract. Calc. Appl. Anal.} {\bf 21} (2018) 1156--1169]. We extend the…
Partitioned neural network functions are used to approximate the solution of partial differential equations. The problem domain is partitioned into non-overlapping subdomains and the partitioned neural network functions are defined on the…
The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation.…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously…
This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).
The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require…
Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…
We discuss semi-inclusive Deep Inelastic Scattering (DIS) in the z -> 1 limit, in particular the relationship between fracture functions, generalised cut vertices and Green functions of the composite operators arising in the OPE. The…
The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…