Related papers: Inversion formula and Parsval theorem for complex …
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Localized wave packet treatments of neutrino oscillations by various groups lead to mutually inconsistent predictions. The neutrino wave packet description arises as an approximate substitute for the evolution of an entangled state which is…
A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
We construct a diffusive matrix model for the $\beta$-Wishart (or Laguerre) ensemble for general continuous $\beta\in [0,2]$, which preserves invariance under the orthogonal/unitary group transformation. Scaling the Dyson index $\beta$ with…
The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for…
In this work we introduce a class of discrete groups containing subgroups of abstract translations and dilations, respectively. A variety of wavelet systems can appear as $\pi(\G)\psi$, where $\pi$ is a unitary representation of a wavelet…
Any triple $(W,L,\rho)$, where $W$ is a compact closed oriented 3-manifold, $L$ is a link in $W$ and $\rho$ is a flat principal $B$-bundle over $W$ ($B$ is the Borel subgroup of upper triangular matrices of $SL(2,\mc)$), can be encoded by…
This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape interrogation with special attention given to the Hausdorff…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
We address the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
We discuss various properties of the variational class of continuous matrix product states, a class of ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful…
This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification…
The orbital angular momentum of light, unlike spin, is an infinite-dimensional discrete variable and may hence offer enhanced performances for encoding, transmitting, and processing information in the quantum regime. Hitherto, this degree…
In this work, a group theory-based formulation that introduces new classes of dihedral-symmetric beams is presented. Our framework leverages the algebraic properties of the dihedral group of rotations and reflections to transform input…
Let $a$, $b$ be two fixed positive constants. A function $g\in L^2({\mathbb R})$ is called a \textit{mother Weyl-Heisenberg frame wavelet} for $(a,b)$ if $g$ generates a frame for $L^2({\mathbb R})$ under modulates by $b$ and translates by…
We give an overview over the higher torsion invariants of Bismut-Lott, Igusa-Klein and Dwyer-Weiss-Williams, including some more or less recent developments.