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The problem of resolving point-like light sources not only serves as a benchmark for optical resolution but also holds various practical applications ranging from microscopy to astronomy. In this research, we aim to resolve two thermal…

In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket (SG). As…

Functional Analysis · Mathematics 2016-11-02 Xiao-Hui Li , Huo-Jun Ruan

We present a categorical formulation of the Hamiltonian renormalisation programme for quantum field theories, establishing a systematic bridge between functional and lattice renormalisation. To this end, we introduce two categories, $Seq$…

General Relativity and Quantum Cosmology · Physics 2025-11-20 M. Rodriguez Zarate

We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic…

High Energy Physics - Theory · Physics 2008-11-26 Sergey Krivonos , Armen Nersessian , Vadim Ohanyan

Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…

Numerical Analysis · Mathematics 2016-08-16 Robert Eymard , Thierry Gallouët , Raphaèle Herbin

We consider Backus's problem in geophysics. This consists in reconstructing a harmonic potential outside the Earth when the intensity of the related field is measured on the Earth's surface. Thus, the boundary condition is (severely)…

Analysis of PDEs · Mathematics 2021-08-30 Toru Kan , Rolando Magnanini , Michiaki Onodera

Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…

Numerical Analysis · Mathematics 2019-03-08 Stefano De Marchi , Wolfgang Erb , Francesco Marchetti , Emma Perracchione , Milvia Rossini

Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outwards are introduced. Their $3\times3$ cross-spectral density matrix is given through expansions of the field components in terms of basis…

In this paper, we formulate black hole solutions through extended gravitational decoupling scheme in the framework of self-interacting Brans-Dicke theory. The addition of a new source in the matter distribution increases the degrees of…

General Relativity and Quantum Cosmology · Physics 2021-04-14 M. Sharif , Amal Majid

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has…

Numerical Analysis · Mathematics 2022-04-21 Oded Stein , Eitan Grinspun , Alec Jacobson , Max Wardetzky

We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…

Numerical Analysis · Mathematics 2023-01-25 Jennifer E. Fromm , Nils Wunsch , Ru Xiang , Han Zhao , Kurt Maute , John A. Evans , David Kamensky

Dirac semimetals can be classified into types I, II, and III based on the topological charge of their Dirac points. If a three-dimensional (3D) system can be sliced into a family of kz-dependent normal and topological insulators, type I…

Mesoscale and Nanoscale Physics · Physics 2025-10-13 Hong Wu , Jia-Ji Zhu , Jian Li , Xue-Min Yang , Jiang-Shan Chen , Mu Zhou

In this paper, we consider weighted Dirichlet spaces $\cD_\omega$, where $\omega$ is a positive superharmonic weight on the unit disc $\DD$. These spaces include the standard weighted Dirichlet spaces $\cD_\alpha$ and appear in the…

Functional Analysis · Mathematics 2026-05-14 H. Bahajji-El Idrissi , O. El-Fallah , Y. Elmadani , A. Hanine

The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described…

Quantum Physics · Physics 2007-10-31 Martijn Wubs , L. G. Suttorp , A. Lagendijk

Recent advancements in finite element methods allows for the implementation of mesh cells with curved edges. In the present work, we develop the tools necessary to employ multiply connected mesh cells, i.e. cells with holes, in planar…

Numerical Analysis · Mathematics 2023-03-15 Jeffrey S. Ovall , Samuel E. Reynolds

The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied,…

Complex Variables · Mathematics 2024-10-17 Bo-Yong Long

A new Hardy space Hardy space approach of Dirichlet type problem based on Tikhonov regularization and Reproducing Hilbert kernel space is discussed in this paper, which turns out to be a typical extremal problem located on the upper…

Numerical Analysis · Mathematics 2017-05-31 Zhulin Liu , C. L. Philip Chen

We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of…

Analysis of PDEs · Mathematics 2018-01-26 Hubert Grzebuła , Sławomir Michalik

Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…

Probability · Mathematics 2025-12-10 Shiping Cao , Zhen-Qing Chen

The intrinsically hierarchical and blended structure of interstellar molecular clouds, plus the always increasing resolution of astronomical instruments, demand advanced and automated pattern recognition techniques for identifying and…

Computer Vision and Pattern Recognition · Computer Science 2017-11-28 Martín Villanueva , Mauricio Araya