Related papers: Certain representations of the Cuntz relations, an…
We study representations of the Cuntz algebras $\O_N$. While, for fixed $N$, the set of equivalence classes of representations of $\O_N$ is known not to have a Borel cross section, there are various subclasses of representations which can…
The Hecke algebra $\mathbb{C}_q[W]$ of a Coxter group $W$, associated to parameter $q$, can be completed to a von Neumann algebra $\mathcal{N}_q(W)$. We study such algebras in case where $W$ is right-angled. We determine the range of $q$…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
It has been recently conjectured that the exact eigenfunctions of quantum mirror curves can be obtained by combining their WKB expansion with the open topological string wavefunction. In this paper we give further evidence for this…
We suggest a physical definition of the confinement mass scale in QCD in the framework of non-perturbative, gauge invariant QCD, where all possible gluons exchanged between any pair of quark lines are included; and we insist that a stable,…
In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix…
We study unbounded 2-dimensional metric polytopes such as those arising as K\"ahler quotients of complete K\"ahler 4-manifolds with two commuting symmetries and zero scalar curvature. Under a mild closedness condition, we obtain a complete…
Quantum Measure Theory (QMT) is a generalization of quantum theory where physical predictions are computed from a matrix known as \emph{decoherence functional} (DF). Previous works have noted that, in its original formulation, QMT exhibits…
We study certain $q$-deformed analogues of the maximal abelian subalgebras of the group von Neumann algebras of free groups. The radial subalgebra is defined for Hecke deformed von Neumann algebras of the Coxeter group…
As an attempt to give an unified description of quark and lepton mass matrices M_f, the following mass matrix form is proposed: the form of the mass matrices are invariant under a cyclic permutation (f_1 \to f_2, f_2 \to f_3, f_3 \to f_1)…
We show that a Krein-Feller operator is naturally associated to a fixed measure $\mu$, assumed positive, $\sigma$-finite, and non-atomic. Dual pairs of operators are introduced, carried by the two Hilbert spaces, $L^{2}\left(\mu\right)$ and…
We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure…
To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor…
Motivated by the existence problem of Fourier frames on fractal measures, we introduce Bessel and frame measures for a given finite measure on $\br^d$, as extensions of the notions of Bessel and frame spectra that correspond to bases of…
Oscillating shapes of the primordial bispectrum are present in many inflationary models. The Planck experiment has recently published measurements of oscillating shapes, which were however limited to the efficient frequency range of the…
Like the continous shearlet transform and their relatives, discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more…
We propose a strategy to compute the CKM matrix based on the conjecture, recently put forward in the literature, according to which elementary particle masses are not generated like in the standard Higgs scenario, but emerge from a…
Conditions for the existence of K\"ahler-Einstein metrics and central K\"ahler metrics [MS] along with examples, both old and new, are given on classes of Lorentzian $4$-manifolds with two distinguished vector fields. The results utilize…
In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the…
It is known that in $\mathbb{R}^n,n\geq 2$, a compact set which contains $n-1$ spheres with all radii in $[1/2,1]$ or with all possible centres in $[0,1]^n$ has full Hausdorff dimension. In fact the later set has positive Lebesgue measure.…