相关论文: Ordinal and Horizontal Sums Constructing PBZ*-latt…
We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…
Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associate with it a Foulis quantale Lin(X) consisting of its…
A recent result of G. Cz\'edli relates the ordered set of principal congruences of a bounded lattice $L$ with the ordered set of principal congruences of a~bounded sublattice $K$ of $L$. In this note, I sketch a new proof.
Let $A$ be an associative unital algebra, $B_k$ its successive quotients of lower central series and $N_k$ the successive quotients of ideals generated by lower central series. The geometric and algebraic aspects of $B_k$ and $N_k$ have…
In this paper, we study three representations of lattices by means of a set with a binary relation of compatibility in the tradition of Plo\v{s}\v{c}ica. The standard representations of complete ortholattices and complete perfect Heyting…
The $OS$ algebra $A$ of a matroid $M$ is a graded algebra related to the Whitney homology of the lattice of flats of $M$. In case $M$ is the underlying matroid of a hyperplane arrangement \A in $\C^r$, $A$ is isomorphic to the cohomology…
We study the covolumes of arithmetic lattices in $PSL_2(\mathbb R)^n$ for $n\geq 2$ and identify uniform and non-uniform irreducible lattices of minimal covolume. More precisely, let $\mu$ be the Euler-Poincar\'e measure on $PSL_2(\mathbb…
We study the module $C^r(\mathcal{P})$ of piecewise polynomial functions of smoothness $r$ on a pure $n$-dimensional polytopal complex $\mathcal{P}\subset\mathbb{R}^n$, via an analysis of certain subcomplexes $\mathcal{P}_W$ obtained from…
A lattice reduction is an algorithm that transforms the given basis of the lattice to another lattice basis such that problems like finding a shortest vector and closest vector become easier to solve. Some of the famous lattice reduction…
Two sets in $\mathbb{R}^d$ are called homometric if they have the same covariogram, where the covariogram of a finite subset $K$ of $\mathbb{R}^d$ is the function associating to each $u \in \mathbb{R}^d$ the cardinality of $K \cap (K+u)$.…
We prove that cocompact arithmetic lattices in a simple Lie group are uniformly discrete if and only if the Salem numbers are uniformly bounded away from $1$. We also prove an analogous result for semisimple Lie groups. Finally, we shed…
This paper has two objectives. First, we study lattices with skew-Hermitian forms over division algebras with positive involutions. For division algebras of Albert types I and II, we show that such a lattice contains an "orthogonal" basis…
For finite dimensional algebras over algebraically closed fields, we study the sets of pairwise Hom-orthogonal modules and obtain new results on some open conjectures on the behaviour of bricks and several related problems, which we…
In this note we show, roughly speaking, that if $\mathcal{B}$ is a Boolean algebra included in the natural way in the collection $\mathcal{D}/_\sim$ of all equivalence classes of natural density sets of the natural numbers, modulo null…
For a closure space (P,f) with f(\emptyset)=\emptyset, the closures of open subsets of P, called the regular closed subsets, form an ortholattice Reg(P,f), extending the poset Clop(P,f) of all clopen subsets. If (P,f) is a finite convex…
Let $\mathscr N$ be a two step nilpotent Lie algebra endowed with non-degenerate scalar product $\langle\cdot\,,\cdot\rangle$ and let $\mathscr N=V\oplus_{\perp}Z$, where $Z$ is the center of the Lie algebra and $V$ its orthogonal…
We show that lattice polytopes cut out by root systems of classical type are normal and Koszul, generalizing a well-known result of Bruns, Gubeladze, and Trung in type A. We prove similar results for Cayley sums of collections of polytopes…
This paper deals with lattice congruences of the weak order on the symmetric group, and initiates the investigation of the cover graphs of the corresponding lattice quotients. These graphs also arise as the skeleta of the so-called…
Bloch oscillations (BOs) describe the coherent oscillatory motion of electrons in a periodic lattice under a constant external electric field. Deviations from pure harmonic wave packet motion or irregular Bloch oscillations can occur due to…
Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek's basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative…