Related papers: Nested Cantor sets
We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems {with} jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set…
Semantic sentence embedding models encode natural language sentences into vectors, such that closeness in embedding space indicates closeness in the semantics between the sentences. Bilingual data offers a useful signal for learning such…
Non-linear parametric resonances occur frequently in nature. Here we summarize how they can be studied by means of perturbative methods. We show in particular how resonances can affect the motion of a test particle orbiting in the vicinity…
The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative…
In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-rank tensors is generally a hard problem, however, the set of…
For a two parameter family of two-dimensional piecewise linear maps and for every natural number $ n $ we prove not only the existence of intervals of parameters for which the respective maps are $ n $ times renormalizable but also we show…
We numerically study energy spectra and localization properties of the double exchange model at irrational filling factor. To obtain variational ground state, we use a mumerical technique in momentum space by ``embedded'' boundary condition…
A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set $K\subseteq \mathbb{R}$ is constructed such that every set definable in $(\mathbb{R},<,+,\cdot,K)$ is Borel. In addition, we…
The ever-growing size of the foundation language model has brought significant performance gains in various types of downstream tasks. With the existence of side-effects brought about by the large size of the foundation language model such…
The main purpose of this note is to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we derive the existence theorems on a…
We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.
We consider the problem of existence of bound entangled states with non-positive partial transpose (NPT). As one knows, existence of such states would in particular imply nonadditivity of distillable entanglement. Moreover it would rule out…
We give sufficient conditions for a first order expansion of the real line to define the standard model of the monadic second order theory of one successor. Such an expansion does not satisfy any of the combinatorial tameness properties…
Machine Translation models are trained to translate a variety of documents from one language into another. However, models specifically trained for a particular characteristics of the documents tend to perform better. Fine-tuning is a…
This study describes such a situation that a Cantor set emerges as a result of the exploration of sufficient conditions for the property which is generalized from fundamental chaotic maps, and the Cantor set even guarantees infinitely many…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
Considering the sets of subsums of series (or achievement sets) we show that for conditionally convergent series the multidimensional case is much more complicated than that of the real line. Although we are far from the full topological…
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer.…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of numerical results is increasingly important. This presentation concerns the development of another benchmark for…