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Based on the recently introduced uniform $\lambda-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely strictly singular operators to the sequences of closed subspaces and operators…
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal…
Blockwise determinantal ideals are those generated by the union of all the minors of specified sizes in certain blocks of a generic matrix, and they are the natural generalization of many existing determinantal ideals like the Schubert and…
Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
We use the idea of generic extensions to investigate the correspondence between the isomorphism classes of nilpotent representations of a cyclic quiver and the orbits in the corresponding representation varieties. We endow the set $\cal M$…
This paper deals with solutions to the equation \begin{equation*} -\Delta u = \lambda_+ \left(u^+\right)^{q-1} - \lambda_- \left(u^-\right)^{q-1} \quad \text{in $B_1$} \end{equation*} where $\lambda_+,\lambda_- > 0$, $q \in (0,1)$,…
We derive local boundedness estimates for weak solutions of a large class of second order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its…
We consider compactifications of the space of triples of distinct points in projective $n$-space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson;…
Our starting point is a basic problem in Hermite interpolation theory, namely determining the least degree of a homogeneous polynomial that vanishes to some specified order at every point of a given finite set. We solve this problem if the…
This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness of initial value problems for these equations are derived, and then the classification of them is obtained with a similar…
A basic problem in the theory of partially ordered vector spaces is to characterise those cones on which every order-isomorphism is linear. We show that this is the case for every Archimedean cone that equals the inf-sup hull of the sum of…
The main purpose of this study is to introduce the spaces $cs^{\lambda}, cs_0^{\lambda}$ and $bs^{\lambda}$ which are $BK-$spaces of non-absolute type. We prove that these spaces are linearly isomorphic to the spaces $cs, cs_0$ and $bs$,…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
Suppose $\Lambda$ is a special biserial algebra over an algebraically closed field. Schr\"oer showed that if $\Lambda$ is domestic then the radical of the category of finitely generated (left) $\Lambda$-modules is nilpotent, and the least…
Let $\Gamma$ be a smooth curve or finite disjoint union of smooth curves in the plane and $\Lambda$ be any subset of the plane. Let $\mathcal X(\Gamma)$ be the space of all finite complex-valued Borel measures in the plane which are…
We characterize the compactness properties of the product of \lambda\ copies of the space \omega\ with the discrete topology, dealing in particular with the case \lambda\ singular, using regular and uniform ultrafilters, infinitary…
Batanin and Leinster's work on globular operads has provided one of many potential defnitions of a weak $\omega$-category. Through the language of globular operads they construct a monad whose algebras encode weak $\omega$-categories. The…
Given an algebraic theory which can be described by a (possibly symmetric) operad $P$, we propose a definition of the \emph{weakening} (or \emph{categorification}) of the theory, in which equations that hold strictly for $P$-algebras hold…
This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix…