Related papers: A short note on containment of cores
A criticism against the conception adopted by some textbook's authors concerning ideal constraints is presented. The criticism is strengthen with two traditional examples.
Given an ideal $\mathcal{I}$ on $\omega$ and a bounded real sequence $\textbf{x}$, we denote by $\text{core}_{\textbf{x}}(\mathcal{I})$ the smallest interval $[a,b]$ such that $\{n \in \omega: x_n \notin [a-\varepsilon,b+\varepsilon]\} \in…
We present a few results about (non)pathology of submeasures and ideals.
The purpose of this note is twofold. We present first a vanishing theorem for families of linear series with base ideal being a fat points ideal. We apply then this result in order to give a partial proof of a conjecture raised by Bocci,…
A special case of an elegant result due to Anderson proves that the number of $(s,s+1)$-core partitions is finite and is given by the Catalan number $C_s$. Amdeberhan recently conjectured that the number of $(s,s+1)$-core partitions into…
We give a proof of Theorem 2.10 from [8] that eliminates the use of Shelah's nice filters and associated rank functions, and instead uses only the well-foundedness of reduced products of ordinals modulo countably complete filters. This…
Motivated by recent result of P\'erez and R.G. on equality of test ideal of module closure operation and trace ideal, and the well-known result by Smith that parameter test ideal cannot be contained in parameter ideals, we study the…
We prove that cancellation of reflexive modules over affine rings holds under some restrictions. We construct examples to show that this is false even over polynomial rings without the extra assumptions.
We conduct an analysis of the shapes of molecular cloud cores using recently compiled catalogs of observed axis ratios of individual cores mapped in ammonia or through optical selection. We apply both analytical and statistical techniques…
This paper contains some immature results. It have been withdrawn.
In this note we consider two configurations of twelve lines with nineteen triple points (i.e., points where three lines meet). Both of them have the same combinatorial features. In both configurations nine of twelve lines have five triple…
We develop a new approach to non-Hausdorff \'etale groupoids and their algebras based on Timmermann's construction of Hausdorff covers. As an application, we completely characterise when singular ideals vanish in Steinberg algebras over…
In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central…
The symbolic powers $I^{(n)}$ of a radical ideal $I$ in a polynomial ring consist of the functions that vanish up to order $n$ in the variety defined by $I$. These do not necessarily coincide with the ordinary algebraic powers $I^n$, but it…
Let $K$ be a local field of characteristic $p$. We consider the local Langlands correspondence for tori, and construct examples for which depth is not preserved.
We show that the regularity of monomial ideals whose associated prime ideals are totally ordered by inclusion is linearly bounded.
We present the first detailed classification of the structures of Class 0 cores in a high resolution simulation of a giant molecular cloud. The simulated cloud contains 10^4 solar masses and produces over 350 cores which allows for…
We consider the problem of neutral inclusions for two-dimensional conductivity and anti-plane elasticity. The neutral inclusion, when inserted in a matrix having a uniform field, does not disturb the field outside the inclusion. The…
We show that a prominent counterexample for the completeness of first order RUE-resolution does not apply to the higher order RUE-resolution approach EXTRUE.
We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [ER21], extending our previous results to the expanded context. We apply…