Related papers: Divisorial Multiplicative Lattices
We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth variety whose sets of integral points are never…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent…
There have been many works on proving the integrals in the table of integrals compiled by Gradshteyn and Ryzhik, and in this paper we prove some doubly logarithmic integral identities in the Gradshteyn and Ryzhik table.
In this paper we construct examples of irrational behavior of multiplicities and mixed multiplicities of divisorial filtrations. The construction makes essential use of anti-positive intersection products.
Implicational bases are a well-known representation of closure spaces and their closure lattices. This representation is not unique, though, and a closure space usually admits multiple bases. Among these, the canonical base, the canonical…
We propose a diagrammatic notation for matrix differentiation. Our new notation enables us to derive formulas for matrix differentiation more easily than the usual matrix (or index) notation. We demonstrate the effectiveness of our notation…
We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain…
Some recent existence, multiplicity, and uniqueness results for singular p-Laplacian systems either in bounded domains or in the whole space are presented, with a special attention to the case of convective reactions. A extensive…
A classification of commutative integral domains consisting of ordinary differential operators with matrix coefficients is established in terms of morphisms between algebraic curves.
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extension's derivatives with bounds on the original…
We investigate the performance of multigrid preconditioners for solving linear systems arising from finite element discretizations of elliptic interface problems using the Fictitious Domain with Distributed Lagrange Multipliers (FD-DLM)…
We present new sharp results concerning multipliers and distance estimates in various spaces of harmonic functions in the unit ball of $R^n$.
We obtain multirelative connectivity statements about spaces of smooth embeddings, deducing these from analogous results about spaces of Poincare embeddings that were established in our previous paper.
We consider divisorial filtration on the rings of functions on hypersurface singularities associated with Newton diagrams and their analogues for plane curve singularities. We compute the multi-variable Poincar\'e series for the latter…
The first part of the paper is a survey of some of the results previously obtained by the authors concerning the $L^p$-dissipativity of scalar and matrix partial differential operators. In the second part we give new necessary and,…
The concept of integral as an inverse to that of derivation was already introduced for rings and recently also for lattices. Since semirings generalize both rings and bounded distributive lattices, it is natural to investigate integration…
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…
We discuss factorization of the hypergeometric-type difference equations on the uniform lattices and show how one can construct a dynamical algebra, which corresponds to each of these equations. Some examples are exhibited, in particular,…
We show that in high dimensions the set of stable lattices is almost of full measure in the space of unimodular lattices.