Related papers: Phi-transform on domains
We provide a novel approach to approximate bounded Lipschitz domains via a sequence of smooth, bounded domains. The flexibility of our method allows either inner or outer approximations of Lipschitz domains which also possess weakly defined…
Configurations of subspaces like equichordal and equiisoclinic tight fusion frames, which are in some sense optimally spread apart and which also have reconstruction properties emulating those of orthonormal bases, are useful in various…
We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma…
Domain generalization aims to learn a generalizable model from a known source domain for various unknown target domains. It has been studied widely by domain randomization that transfers source images to different styles in spatial space…
Ultrasound B-Mode images are created from data obtained from each element in the transducer array in a process called beamforming. The beamforming goal is to enhance signals from specified spatial locations, while reducing signal from all…
We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with…
Domain generalization aims to train models on multiple source domains so that they can generalize well to unseen target domains. Among many domain generalization methods, Fourier-transform-based domain generalization methods have gained…
New lower bounds on the minimum distance of quasi-twisted codes over finite fields are proposed. They are based on spectral analysis and eigenvalues of polynomial matrices. They generalize the Semenov-Trifonov and Zeh-Ling bounds in a…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
The present paper is devoted to studying of some weighted H\"older spaces. These spaces are designed in the way to serve as a framework for studying different statements for the thin film equations in weighted classes of smooth functions in…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
In the near-field context, the Fresnel approximation is typically employed to mathematically represent solvable functions of spherical waves. However, these efforts may fail to take into account the significant increase in the lower limit…
In this paper, we prove that the identity map for the smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^2$ extends to a bi-H\"{o}lder map between the Euclidean boundary and Gromov boundary. As an application, we show the…
In this article, the authors introduce Besov-type spaces with variable smoothness and integrability. The authors then establish their characterizations, respectively, in terms of $\varphi$-transforms in the sense of Frazier and Jawerth,…
This paper is concerned with the homogenization of Dirichlet problem of elliptic systems in a bounded, smooth domain of finite type. Both the coefficients of the elliptic operator and the Dirichlet boundary data are assumed to be periodic…
The object of the present paper is to study the locally $\phi $- semisymmetric Kenmotsu manifolds along with the characterization of such notion.