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For paired comparison experiments involving competing options described by two-level attributes several different methods of constructing designs having block paired observations under the main effects model are presented. These designs are…

We survey recent results on the boundedness of the moduli functor of stable pairs

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…

We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…

We study how the supporting hyperplanes produced by the projection process can complement the method of alternating projections and its variants for the convex set intersection problem. For the problem of finding the closest point in the…

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

In this paper we study the mapping properties of the averaging operator over a variety given by a system of homogeneous equations over a finite field. We obtain optimal results on the averaging problems over two dimensional varieties whose…

We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…

We study semicontinuous maps on varieties of modules over finite-dimensional algebras. We prove that truncated Euler maps are upper or lower semicontinuous. This implies that $g$-vectors and $E$-invariants of modules are upper…

We consider rational representations of a connected linear algebraic group $\mathbb G$ over a field $k$ of positive characteristic $p > 0$. We introduce a natural extension $M \mapsto \Pi(\mathbb G)_M$ to $\mathbb G$-modules of the…

We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…

We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to…

We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested.…

Expansion was introduced at the end of the 1970s for calculating principal typings for $\lambda$-terms in intersection type systems. Expansion variables (E-variables) were introduced at the end of the 1990s to simplify and help mechanise…

We prove that on a certain class of smooth complex varieties (those with "affine even stratifications"), the category of mixed Hodge modules is "almost" Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give…

In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves.…