Related papers: Frame multiplication theory and a vector-valued DF…
The continued miniaturization of semiconductor devices, represented by Moore's law, has reached the atomic scale limit, requiring nanoscale quantum mechanical effects to be included in device simulations without empirical parameters. For…
In many practical problems it is not necessary to compute the DFT in a perfect manner including some radar problems. In this article a new multiplication free algorithm for approximate computation of the DFT is introduced. All…
Density functional theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. Last year, at least 30,000 papers used DFT to make useful predictions or give…
Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…
While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly…
Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…
The Discrete Fourier Transform (DFT) is widely utilized for signal analysis but is plagued by spectral leakage, leading to inaccuracies in signal approximation. Window functions play a crucial role in mitigating spectral leakage by…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
Density functional theory is a successful branch of numerical simulations of quantum systems. While the foundations are rigorously defined, the universal functional must be approximated resulting in a `semi'-ab initio approach. The search…
The low-T part of the phase diagram in self-assembling systems is correctly predicted by the known versions of the density functional theory (DFT). The high-T part obtained in DFT, however, does not agree with simulations even on the…
We introduce a method for the estimation of uncertainties in density-functional-theory (DFT) calculations for atomistic systems. The method is based on the construction of an uncertainty-aware functional distribution (UAFD) in a space…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
We present a theoretical framework based on an extension of dynamical density functional theory (DDFT) for describing the structure and dynamics of cells in living tissues and tumours. DDFT is a microscopic statistical mechanical theory for…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
By doubling the target space of a canonical Courant algebroid and subsequently projecting down to a specific subbundle, we identify the data of double field theory (DFT) and hence define its algebroid structure. We specify the properties of…
Density Functional Theory (DFT) is widely used for first-principles simulations in chemistry and materials science, but its computational cost remains a key limitation for large systems. Motivated by recent advances in ML-based…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
Molecular-level understanding of the interactions between the constituents of an atomic structure is essential for designing novel materials in various applications. This need goes beyond the basic knowledge of the number and types of…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…