Related papers: On Weak Separation Property for Affine Fractal Fun…
The fractal character of some quantum properties has been shown for systems described by continuous variables. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing,…
We prove that if a multiple trigonometric series is spherically Abel summable everywhere to an everywhere finite function $f(x)$ which is bounded below by an integrable function, then the series is the Fourier series of $f(x)$ if the…
We say that a function $\alpha(x)$ belongs to the set ${\bf A}^{(\gamma)}$ if it has an asymptotic expansion of the form $\alpha(x)\sim \sum^\infty_{i=0}\alpha_ix^{\gamma-i}$ as $x\to\infty$, which can be differentiated term by term…
A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids was presented and bilinear FIS was deduced by Ruan and Xu [Bull. Aust. Math. Soc. 91(3), 2015, pp. 435-446]. From the view point of operator theory…
We show that the values of a certain family of weakly holomorphic modular functions at points in the divisors of any meromorphic modular form with algebraic Fourier coefficients are algebraic. We use this to extend the classical result of…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…
We present a new approach to semi-inclusive hard processes in QCD by means of $\it Fracture\;Functions$, hybrids between structure and fragmentation functions. We briefly motivate and describe it together with a list of possible…
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions…
We construct a finitely presented group $G$ with non-quadratic Dehn function $f$ majorizable by a quadratic function on arbitrary long intervals.
The notion of weak tiling played a key role in the proof of Fuglede's spectral set conjecture for convex domains, due to the fact that every spectral set must weakly tile its complement. In this paper, we revisit the notion of weak tiling…
The natural kinship between classical theories of interpolation and approximation is well explored. In contrast to this, the interrelation between interpolation and approximation is subtle and this duality is relatively obscure in the…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
We develop the theory of weak Fraisse categories, where the crucial concept is the weak amalgamation property, discovered relatively recently in model theory. We show that, in a suitable framework, every weak Fraisse category has its unique…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
We show that any affine invariant function on the set of positive definite matrices must factor through the determinant function, as long as the restriction of the function to scalar matrices is surjective. A motivation from robust…
Let $S$ be the dyadic bi-parameter square function $$Sf(x)^{2} = \sum_{R \in \mathcal{D}} |\langle f, h_{R} \rangle|^{2} \frac{1_{R}(x)}{|R|}.$$ We prove that if $T$ is a bi-parameter martingale transform and $f,g$ are suitable test…
We define Schwartz functions, tempered functions and tempered distributions on (possibly singular) real algebraic varieties. We prove that all classical properties of these spaces, defined previously on affine spaces and on Nash manifolds,…
This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…