相关论文: Strongly almost disjoint sets and weakly uniform b…

Consider a smooth, projective family of canonically polarized varieties over a smooth, quasi-projective base manifold Y, all defined over the complex numbers. It has been conjectured that the family is necessarily isotrivial if Y is special…

Principal Component Analysis (PCA) and its exponential family extensions have three components: observations, latents and parameters of a linear transformation. We consider a generalised setting where the canonical parameters of the…

Two approaches to Lipschitz structures for any set are presented, studied and compared. The first approach is similar to the one proposed in Fraser, Jr. R. B., Axiom systems for Lipschitz structures, Fundamenta Mathematicae, (1970), where…

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-\v{S}emrl…

The hypergraph container lemma is a powerful tool in probabilistic combinatorics that has found many applications since it was first proved a decade ago. Roughly speaking, it asserts that the family of independent sets of every uniform…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

We call a space $X$ {\it weakly linearly Lindel\"of} if for any family $\mathcal{U}$ of non-empty open subsets of $X$ of regular uncountable cardinality $\kappa$, there exists a point $x\in X$ such that every neighborhood of $x$ meets…

The aim of this paper is to determine the logical and computational strength of instances of the Bolzano-Weierstra{\ss} principle (BW) and a weak variant of it. We show that BW is instance-wise equivalent to the weak K\"onig's lemma for…

Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case…

We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special…

We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…

This paper builds model-theoretic tools to detect changes in complexity among the simple theories. We develop a generalization of dividing, called shearing, which depends on a so-called context c. This leads to defining c-superstability, a…

We introduce the notion of \tau-like partial order, where \tau is one of the linear order types \omega, \omega*, \omega+\omega*, and \zeta. For example, being \omega-like means that every element has finitely many predecessors, while being…

We argue that we solved Hilbert's first problem positively (after reformulating it just to avoid the known consistency results) and give some applications. Let lambda to the revised power of kappa, denoted lambda^{[kappa]}, be the minimal…

A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a…

Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose here a structure for the set \Pi_u(G) of equivalence classes of irreducible unitary representations of G. (The subscript u will be used throughout to indicate…

The space of weak expectations for a given representation of a (unital) separable C*-algebra is a compact convex set of (unital) completely positive maps in the BW topology, when it is non-empty. An application of the classical Choquet…

To do dimensionality reduction on the datasets with outliers, the $\ell_1$-norm principal component analysis (L1-PCA) as a typical robust alternative of the conventional PCA has enjoyed great popularity over the past years. In this work, we…

In the present note we focus on conic line arrangements in the plane with quasihomogeneous ordinary singularities from the perspective of weak Ziegler pairs. The foundations of this article come from an active area of research devoted to…