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For countably infinite IFSs on $\mathbb R^2$ consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower…

We investigate the set of invariant idempotent probabilities for countable idempotent iterated function systems (IFS) defined in compact metric spaces. We demonstrate that, with constant weights, there exists a unique invariant idempotent…

We investigate advanced CMOS-compatible Graphene/Silicon active metasurfaces based on guided-mode resonance filters. The simulated results show a high extinction ratio (>25 dB), narrow linewidth (~1.5 nm @1550 nm), quality factor of Q~1000,…

Assume that $X$ and $Y$ are locally compact and locally doubling metric spaces, which are also generalized $n$-manifolds, that $X$ is locally linearly locally $n$-connected, and that $Y$ has bounded turning. In this paper, addressing…

In this article, we further develop the thermodynamic formalism of affine iterated function systems with countably many transformations by showing the existence and extending earlier characterisations of the equilibrium states of finite…

In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…

Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting…

For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…

This paper introduces a new class of iterated function systems (IFSs) called R-IFSs, which include both rotation/reflection maps and contraction maps. The study of R-IFSs is motivated by the recent research direction on enriching IFSs by…

The standard (``fine-grained'') interpretation of quantum density functional theory, in which densities are specified with infinitely-fine spatial resolution, is mathematically unruly. Here, a coarse-grained version of DFT, featuring…

Iterated Function Systems (IFSs) have been at the heart of fractal geometry almost from its origin, and several generalizations for the notion of IFS have been suggested. Subdivision schemes are widely used in computer graphics and attempts…

We investigate usage of nonlinear wave chaotic amorphous silicon (a-Si) cavities as physically unclonable functions (PUF). Machine learning attacks on integrated electronic PUFs have been demonstrated to be very effective at modeling PUF…

Directional couplers are essential components in integrated photonics. Given their widespread use, accurate characterization of directional couplers is crucial for ensuring optimal performance. However, it is challenging due to the coupling…

Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in $\mathbb{R}$ does not equal its expected value, then the underlying iterated function system contains an exact…

The attractors of iterated function systems are usually obtained as the Hausdorff limit of any non-empty compact subset under iteration. In this note we show that an iterated function system on a boundedly compact metric space has compact,…

Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but…

This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X,d,m_n), m_n weakly convergent to m. In particular, under…

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…

In the present work we study the behavior of sequences of smooth global isothermic immersions of a given closed surface and having a uniformly bounded total curvature. We prove that, if the conformal class of this sequence is bounded in the…

Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework…