Related papers: A note on lattice coverings

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.

We consider a graph called a lattice diagram, which is a graph in the $xy$-plane such that each edge is parallel to the $x$-axis or the $y$-axis. In [4], we investigated transformations of certain lattice diagrams, and we considered the…

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

A problem involving a square in the curvilinear triangle made by two touching congruent circles and their common tangent is generalized.

This note gives an example of closed smooth manifolds $M$ and $N$ for which the rank of $M\times N$ is strictly greater than $rank M + rank N$.

This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…

New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…

The ``crumpling" transition, between rigid and crumpled surfaces, has been object of much discussion over the past years. The common lore is that such transition should be of second order. However, some lattice versions of the rigidity term…

These notes are a self-contained short proof of the stability of persistence diagrams.

This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.

Icosahedral tilings, although non-periodic, are known to be characterized by their configurations of some finite size. This characterization has also been expressed in terms of a simple alternation condition. We provide an alternative proof…

Ultra-thin optical structures, known as metasurfaces, have shown promising light controlling capability at the nanoscale. In this paper, we study their particular case, a periodic array of high-refractive-index nanoparticles with electric…

We exhibit an example of covering surface of C*, arising from analytical continuation of a holomorphic germ and failing to be a topological covering, due to singular points and regular ones being projected over the same slits in C*.

We study a harmonic triangular lattice, which relaxes in the presence of a weak, short-wavelength periodic potential. Monte Carlo simulations reveal that the elastic lattice has only short-ranged positional correlations, despite the absence…

We propose a new formulation of lattice theory. It is given by a matrix form and suitable for satisfying Leibniz rule on lattice. The theory may be interpreted as a multi-flavor system. By realizing the difference operator as a commutator,…

The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.

Designing the shape of silicon nanoparticles has been shown to be an effective approach to increasing overlap between electric and magnetic dipole resonances thereby achieving directional scattering and decrease of reflection. Variations of…