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A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
This is a brief survey of recent results by the authors devoted to one of the most important operators of integral geometry. Basic facts about the analytic family of cosine transforms on the unit sphere and the corresponding Funk transform…
We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schr\"odinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schr\"odinger…
We show that the diagonal matrix elements $< Or^{p} >,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb…
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates…
We consider time discretization for score-based diffusion models to generate samples from a learned reverse-time dynamic on a finite grid. Uniform and hand-crafted grids can be suboptimal given a budget on the number of time steps. We…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
We demonstrate the relevance of an algorithm called generalized iterative scaling (GIS) or simultaneous multiplicative algebraic reconstruction technique (SMART) and its rescaled block-iterative version (RBI-SMART) in the field of optimal…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
Orbital angular momentum of photons is an intriguing system for the storage and transmission of quantum information, but it is rapidly degraded by atmospheric turbulence. We explore the ability of adaptive optics to compensate for this…
The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered…
Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…
We propose iterative inversion algorithms for weighted Radon transforms $R_W$ along hyperplanes in $R^3$. More precisely, expandingthe weight $W = W (x, \theta), x \in R^3 , \theta \in S^2$ , into the series of spherical harmonics in…
Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far…
We study the inversion of the conical Radon which integrates a function in three-dimensional space from integrals over circular cones. The conical Radon recently got significant attention due to its relevance in various imaging applications…
The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
Modular operads are a special type of operad: in fact, they bear the same relationship to operads that graphs do to trees (i.e. simply connected graphs). One of the basic examples of a modular operad is the collection of…
In [J. Math. Phys. 51 (2010) 022104] a self-adjoint operator was introduced that has the property that it indicates the direction of time within the framework of standard quantum mechanics, in the sense that as a function of time its…