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Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
An algorithm is proposed for the segmentation of image into multiple levels using mean and standard deviation in the wavelet domain. The procedure provides for variable size segmentation with bigger block size around the mean, and having…
The energy density method is generalized to include spin polarization with the full formalism derived based on spin-density functional theory, which aims at decomposing the total energy into well-defined atomic energies. The method involves…
The aim of the present contribution is to provide a framework for analyzing and visualizing the correlated many-electron dynamics of molecular systems, where an explicitly time-dependent electronic wave packet is represented as a linear…
We present a general method of constructing maximally localized Wannier functions. It consists of three steps: (1) picking a localized trial wave function, (2) performing a full band projection, and (3) orthonormalizing with the Lowdin…
Lennard-Jones clusters, while an easy system, have a significant number of non equivalent configurations that increases rapidly with the number of atoms in the cluster. Here, we aim at determining the cluster partition function; we use the…
The nonlinear Schrodinger (NLS) equation is considered on a periodic metric graph subject to the Kirchhoff boundary conditions. Bifurcations of standing localized waves for frequencies lying below the bottom of the linear spectrum of the…
$\delta$ Scuti stars are pulsating variable stars that exhibit both radial and non-radial pulsations, making them key objects for understanding stellar evolution and internal structures. The current classification of $\delta$ Scuti stars…
We define a set of operators that localise a radial image in radial space and radial frequency simultaneously. We find the eigenfunctions of this operator and thus define a non-separable orthogonal set of radial wavelet functions that may…
The non-localized cluster model provides a new perspective on nuclear cluster effects and has been applied successfully to study cluster structures in various bound states and quasi-bound states (i.e., long-lived resonant states). In this…
Single encoder-decoder methodologies for semantic segmentation are reaching their peak in terms of segmentation quality and efficiency per number of layers. To address these limitations, we propose a new architecture based on a decoder…
In this paper, we propose a simple yet effective method for multiple music source separation using convolutional neural networks. Stacked hourglass network, which was originally designed for human pose estimation in natural images, is…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We propose a scalable tensorization framework for neural network compression based on slice-wise feature distillation. Unlike conventional tensor decomposition methods that rely on costly global finetuning, our approach decomposes the…
The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
A new method for elimination of the 'spurious' states comprising reguirement of translational invariance and simplicity of the enumeration scheme of antisymmetric A-particle states has been developed. The method presented enables one to…
The direct calculation of magnetoelastic wave dispersion in layered media is presented using an efficient, accurate computational technique. The governing, coupled equations for elasticity and magnetism, the Navier and Landau-Lifshitz…