Related papers: A note on lattice coverings
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.
These informal notes are concerned with sums and averages in various situations in analysis.
These are notes from a basic course in Several Complex Variables
We consider two constructions of an envelope for a finite locally distributive strong upper semilattice. The first is based on Birkhoff's representation of finite distributive lattices and the second on valuations on lattices. We show that…
We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.
A new geometry of optical lattice is proposed, namely a lattice made of a 1D stack of ring traps. It is obtained though the interference pattern of two counterpropagating beams: one of the beam is a standard gaussian beam, while the other…
It is our aim in this note to give a counter example to an argument used in the proof of the main theorem of the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…
We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric…
There are examples of branched surfaces that do not fully carry laminations, but their preimage in a finite cover does fully carry a lamination
In this note, we shall give an improved lower bound for the argument of a power of a given algebraic number which has absolute value one but is not a root of unity.
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
The aim of this note is to give a sufficient condition for pairs of functions to have a convex separator when the underlying structure is a Cartan--Hadamard manifold, or more generally: a reduced Birkhoff--Beatley system. Some exotic…
These notes are connected to a "potpourri" topics class and deal with some special cases of norms of various objects which arise in classical analysis.
Replaced by a shorter version which appeared in press.
I present here another example of a lattice fibration, a discrete version of the highest dimensional Hopf fibration: $S^{7}\longrightarrow S^{15} \longrightarrow S^{8}$.
We study the spectrum and stationary states in a ring-shaped lattice potential in the context of ultracold atoms with attractive interatomic interactions. We determine analytical solutions in the absence of a lattice by mapping them to…