Related papers: A short note on containment of cores
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositions of these ideals and, for certain subclasses of models,…
In this note we consider two simplicial arrangements of lines and ideals $I$ of intersection points of these lines. There are $127$ intersection points in both cases and the numbers $t_i$ of points lying on exactly $i$ configuration lines…
This paper shows that the interpolation theorem fails in the intuitionistic logic of constant domains. This result refutes two previously published claims that the interpolation property holds.
We establish the primary decomposition and uniqueness of primary decomposition for k-ideals in commutative Noetherian semirings.
Our main result is that possibly some non-null set of reals cannot be divided to uncountably many non-null sets. We deal also with a non-null set of reals, the graph of any function from it is null and deal with our iterations somewhat more…
The role of ion-ion correlations in suppressing neutrino-nucleus elastic scattering during stellar core collapse is reinvestigated, using two different equations of state. We test the improved description by Itoh et al. against the…
Observations of dark cloud cores have been carried out in the mid-infrared using ISOCAM and in the far-infrared using ISOPHOT, both aboard the Infrared Space Observatory. The cores are in most cases detected in emission at 200 and 170…
We show that there is a point on a computable arc that does not belong to any computable rectifiable curve. We also show that there is a point on a computable rectifiable curve with computable length that does not belong to any computable…
This paper has been withdrawn by the authors, due a crucial error in the proof of the main theorem.
This note introduces some bijections relating core partitions and tuples of integers. We apply these bijections to count the number of cores with various types of restriction, including fixed number of parts, limited size of parts, parts…
We demonstrate that in calculation, where unitarity constraints are properly imposed, the deeply bound hadronic molecules recently proposed by Close and Downum do not exist.
We prove that certain modules are faithful. This enables us to draw consequences about the reduction number and the integral closure of some classes of ideals.
In this note we address the relation between symbolic and ordinary powers of the ideal of a reduced set or points in projective space: the so-called containment problem. In particular, we obtain sharp lower bounds on the Waldschmidt…
The purpose of this note is to find an elemenary explanation of a surprising result of Ein--Lazarsfeld--Smith \cite{ELS} and Hochster--Huneke \cite{HH} on the containment between symbolic and ordinary powers of ideals in simple cases. This…
We present an algorithm to decide whether a given ideal in the polynomial ring contains a monomial without using Gr\"obner bases, factorization or sub-resultant computations.
We show that interactions violating the conservation of lepton numbers in the neutrino sector could significantly alter the standard low entropy picture for the pre-supernova collapsing core of a massive star. A rapid neutrino-antineutrino…
In this short note, we give basic enumerative results on colored integer partitions.
We show that a determinantal ideal generated by $t$-minors does not contain any nonzero polynomials with $t!/2$ or fewer terms. Geometrically this means that any nonzero polynomial vanishing on all matrices of rank at most $t-1$ has more…
The paper is withdrawn. The proof has an error and it requires a different approach.
In the Letter, Xu et al. reported that edge modes disappear in the expanded structure of Wu-Hu model characterized by $\mathbb{Z}_2$ topological index, while appear in the trivial shrunken structure, when the edge cuts through the hexagonal…