Related papers: Several comments about the combinatorics of tau-co…

We will study some possible non universal corrections that could affect single measurements of the Weinberg angle sin^2(theta) (leaving the full average essentially unchanged). We will concentrate on the class of the models that introduces…

Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further…

In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…

The challenge of selecting the most relevant features of a given dataset arises ubiquitously in data analysis and dimensionality reduction. However, features found to be of high importance for the entire dataset may not be relevant to…

The general notion of a Hausdorff-type operator with a kernel depending on an external variable is introduced and generalizations and analogs of classical results on the regularity of various summation methods are proved for the case of…

This thesis proposes a combinatorial generalization of a nilpotent operator on a vector space. The resulting object is highly natural, with basic connections to a variety of fields in pure mathematics, engineering, and the sciences. For the…

We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…

Hurwitz numbers count ramified covers of a Riemann surface with prescribed monodromy. As such, they are purely combinatorial objects. Tautological classes, on the other hand, are distinguished classes in the intersection ring of the moduli…

In this paper, using the classical covering theory, we introduce a generalization of covering maps of a space $X$ with respect to a topology $\tau$ on the fundamental group of $X$. We show that the famous notions, covering, semicovering,…

We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `reduced' versions of the notions of higher Fitting…

We prove that for any tau-symmetric bihamiltonian deformation of the tau-cover of the Principal Hierarchy associated with a semisimple Frobenius manifold, the deformed tau-cover admits an infinite set of Virasoro symmetries.

We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain fixed points of the involution $\omega$ on the ring of…

For a smooth toric variety X over a field of positive characteristic, a T-equivariant \'{e}tale cover Y \rightarrow T^*X^{(1)} trivializing the sheaf of crystalline differential operators on X is constructed. This trivialization is used to…

We generalize the results from "P. Lipparini, Productive $[\lambda,\mu]$-compactness and regular ultrafilters, Topology Proceedings, 21 (1996), 161--171"; in particular the present results apply to singular cardinals, too.

We construct Menger subsets of the real line whose product is not Menger in the plane. In contrast to earlier constructions, our approach is purely combinatorial. The set theoretic hypothesis used in our construction is far milder than…

We study the generalized Volterra-type integral and composition operators acting on the classical Fock spaces. We first characterize various properties of the operators in terms of growth and integrability conditions which are simpler to…

We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…

The non-Leibniz formalism is introduced in this article. The formalism is based on the generalized differentiation operator (kappa-operator) with a non-zero Leibniz defect. The Leibniz defect of the introduced operator linearly depends on…

This article is devoted to the interplay between forcing with fusion and combinatorial covering properties. We discuss known instances of this interplay as well as present a new one, namely that in the Laver model for the consistency of the…

We define two tau functions, $\tau$ and $\hat{\tau}$ , on moduli spaces of spectral covers of $GL(n)$ Hitchin's systems. Analyzing the properties of $\tau$, we express the divisor class of the universal Hitchin's discriminant in terms of…