Related papers: A note on construction of the Leech lattice
We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade…
In this paper we give the generalization of lifted codes over any finite chain ring. This has been done by using the construction of finite chain rings from $p$-adic fields. Further we propose a lattice construction from linear codes over…
In this paper I show a geometrical method to obtain construction of the Nikodym type set.
A series of integral lattices parametrised by integers $k,m,n$ are introduced and investigated, where $n$ is the rank of the lattice, including the root lattices described in a uniform way and unimodular lattices such as the Niemeier…
A method for successive synthesis of the Weyl matrix on the square lattice is proposed. It allows one to compute the Weyl matrix of a large graph by adding new edges and solving elementary systems of linear algebraic equations at each step.…
In this short review we compare different ways to construct solutions of the periodic Toda lattice. We give two recipes that follow from the projection method and compare them with the algebra-geometric construction of Krichever.
The twist construction is a method to build new interesting examples of geometric structures with torus symmetry from well-known ones. In fact it can be used to construct arbitrary nilmanifolds from tori. In our previous paper, we presented…
We develop the method for constructing Lax representations of PDEs via the twisted extensions of their algebras of contact symmetries by generalizing the construction to the Lie--Rinehart algebras. We present examples of application of the…
We show that the free Banach lattice $\mathrm{FBL}(A)$ may be constructed as the completion of $\mathrm{FVL}(A)$ with respect to the maximal lattice seminorm $\nu$ on $\mathrm{FVL}(A)$ with $\nu(a)\le 1$ for all $a\in A$. We present a…
The main results of the paper points out the connection between the weak ordered relations and factor lattices defined by tolerances. It is proved that for any tolerance $T$ of a lattice $L$ the Dedekind-Mac Neille completion of $L/T$ is…
We describe a method to put chiral gauge theories on the lattice. Our method makes heavy use of the effective action for chiral fermions in the continuum, which is in general complex. As an example we discuss the chiral Schwinger model.
In this paper, we give a constructive method for linear extensions of Zadeh's fuzzy orders. We also characterize Zadeh's fuzzy orders by their linear extensions.
We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler action requires to choose the lattice structure having both orientabilities…
After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations.
A lattice version of the Dirac-Kaehler equation (DKE) describing fermions was discussed in articles by Becher and Joos. The decomposition of lattice Dirac-Kaehler fields (inhomogeneous cochains) to lattice Dirac fields remained as an open…
In this thesis, we construct and analyze multiple-description codes based on lattice vector quantization.
Another approach to constructing an upper bound for the Riemann-Farey sum is described.
We construct a Cauchy type formula on open subdomains of Riemann surfaces
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.