Search results for "GEOMETRIA"

Ideas for using GeoGebra and Origami in Teaching Regular Polyhedrons Lessons

2018

The approach of combining GeoGebra and origami is well accepted among students in the school "Petro Kuzmjak" where it is used to teach geometry lessons. This article elaborates on how to introduce students (upper elementary and high school students, age 14-18) to Platonic solids and their properties through combination of GeoGebra and origami activities. Some of the important mathematical concepts related to these well-known geometrical solids can be explained to students applying hands-on activities along with educational software. peerReviewed

Limiting Carleman weights and conformally transversally anisotropic manifolds

2020

We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, 3 3 -manifolds, and 4 4 -manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that there are only three basic such weights up to the action of the conformal group. In dimension three we show that if the manifold is not conformally flat, there could be one or two limiting Carleman weights. We also characterize the metrics that have more than one limiting Carleman weight. In dimension four we obtain a complete spectrum of examples according to the structure of the Weyl tensor. In particular, we construct unimodular Lie groups whose …

Volume preserving mean curvature flows near strictly stable sets in flat torus

2021

In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus $\mathbb T^n$ in low dimensions $n=3,4$. The result says roughly that if the initial set is near to a strictly stable set in $\mathbb T^n$ in $H^3$-sense, then the corresponding flow has infinite lifetime and converges exponentially fast to a translate of the strictly stable (critical) set in $W^{2,5}$-sense.

Whitney forms and their extensions

2021

Whitney forms are widely known as finite elements for differential forms. Whitney’s original definition yields first order functions on simplicial complexes, and a lot of research has been devoted to extending the definition to nonsimplicial cells and higher order functions. As a result, the term Whitney forms has become somewhat ambiguous in the literature. Our aim here is to clarify the concept of Whitney forms and explicitly explain their key properties. We discuss Whitney’s initial definition with more depth than usually, giving three equivalent ways to define Whitney forms. We give a comprehensive exposition of their main properties, including the proofs. Understanding of these propert…

The action of a compact Lie group on nilpotent Lie algebras of type {{n,2}}

2015

Abstract We classify finite-dimensional real nilpotent Lie algebras with 2-dimensional central commutator ideals admitting a Lie group of automorphisms isomorphic to SO 2 ⁢ ( ℝ ) ${{\mathrm{SO}}_{2}(\mathbb{R})}$ . This is the first step to extend the class of nilpotent Lie algebras 𝔥 ${{\mathfrak{h}}}$ of type { n , 2 } ${\{n,2\}}$ to solvable Lie algebras in which 𝔥 ${{\mathfrak{h}}}$ has codimension one.

Permutations of zero-sumsets in a finite vector space

2020

Abstract In this paper, we consider a finite-dimensional vector space 𝒫 {{\mathcal{P}}} over the Galois field GF ⁡ ( p ) {\operatorname{GF}(p)} , with p being an odd prime, and the family ℬ k x {{\mathcal{B}}_{k}^{x}} of all k-sets of elements of 𝒫 {\mathcal{P}} summing up to a given element x. The main result of the paper is the characterization, for x = 0 {x=0} , of the permutations of 𝒫 {\mathcal{P}} inducing permutations of ℬ k 0 {{\mathcal{B}}_{k}^{0}} as the invertible linear mappings of the vector space 𝒫 {\mathcal{P}} if p does not divide k, and as the invertible affinities of the affine space 𝒫 {\mathcal{P}} if p divides k. The same question is answered also in the case where …

Klassista projektiivista geometriaa

2017

Generalized wave propagation problems and discrete exterior calculus

2018

We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…

Laddove c’era l’erba…la rappresentazione come governo delle modificazioni del paesaggio

2004

obiettivo del paper è quello di mostrare come l'opportuno utilizzo delle tecniche di rappresentazione siano indispensabili per la rappresentazione del territorio. Non sempre, infatti, si sanno utilizzare con destrezza ed abilità le nozioni geometriche e le relative ricadute sui software per rappresentare un territorio nella sua modificazione antropologica e sostanziale.

Combinatorics of Mumford-Morita-Miller classes in low genus

2003

Here we use elementary combinatorial arguments to give explicit formulae and relations for some cohomology classes of moduli spaces of stable curves of low genus.