Search results for "Geometria"

Multiplicative Loops of Quasifields Having Complex Numbers as Kernel

2017

We determine the multiplicative loops of locally compact connected 4-dimensional quasifields Q having the field of complex numbers as their kernel. In particular, we turn our attention to multiplicative loops which have either a normal subloop of dimension one or which contain a subgroup isomorphic to $$Spin_3({\mathbb {R}})$$ . Although the 4-dimensional semifields Q are known, their multiplicative loops have interesting Lie groups generated by left or right translations. We determine explicitly the quasifields Q which coordinatize locally compact translation planes of dimension 8 admitting an at least 16-dimensional Lie group as automorphism group.

On $MC$-hypercentral triply factorized groups

2007

A group G is called triply factorized in the product of two subgroups A, B and a normal subgroup K of G ,i fG = AB = AK = BK. This decomposition of G has been studied by several authors, investigating on those properties which can be carried from A, B and K to G .I t is known that if A, B and K are FC-groups and K has restrictions on the rank, then G is again an FC-group. The present paper extends this result to wider classes of FC-groups. Mathematics Subject Classification: 20F24; 20F14

Le Geometrie dei numeri duali

I numeri duali furono introdotti per la prima volta da William Kingdon Clifford (1845-1879) nel 1873, come estensione dei quaternioni (biquaternioni), nell’ambito dello studio dei numeri ipercomplessi. In seguito, furono chiamati così da Eduard Study (1862-1930) [Study 1902], il quale ne fece poi oggetto di studio [Study 1903]. Già nel 1885 Arthur Buchheim (1859-1888) [Buchheim 1885], aveva rintracciato l’origine dei duali in Clifford e si era soffermato sulla (sostanziale) differenza tra l’introduzione dei biquaternioni in Hamilton e in Clifford. Nel 1906, in perfetto accordo alle teorie esposte da Study nel 1903, Joseph Grünwald (1876-1911), introdusse i numeri duali come u+vε, dove u e v…

Two-step nilpotent Leibniz algebras

2022

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. In particular, we describe the complex and the real case of the indecomposable Heisenberg Leibniz algebras as a generalization of the classical $(2n+1)-$dimensional Heisenberg Lie algebra $\mathfrak{h}_{2n+1}$. Then we use the Leibniz algebras - Lie local racks correspondence proposed by S. Covez to show that nilpotent real Leibniz algebras have always a global integration. As an application, we integrate the indecomposable nilpotent real Leibniz algebras with one-dimensional commutator ideal. We also show that every Lie quandle integr…

L’idea di iperspazio e l’evoluzione del pensiero geometrico al quadridimensionale

Attraverso un viaggio storico di quasi due secoli, lo scritto vuole analizzare le situazioni in cui lo studio della geometria iperdimensionale ha avuto la sua genesi e la sua evoluzione. Colui il quale approfondisce in modo analitico la questione è Ludwig Schläfli che con il suo Theorie der vielfachen Kontinuität, a partire dallo studio di un integrale, analizza lo spazio pluridimensionale senza cercare una immagine nel mondo circostante di ciò che descrive in modo molto sistematico attraverso i coefficienti che prendono il suo nome. L’aspetto divulgativo della questione viene affrontata a partire dagli anni ’70 del XIX secolo da Beltrami, Casorati e Stringham, da un punto di vista merament…

Covering by discrete and closed discrete sets.

2008

Say that a cardinal number $\kappa$ is \emph{small} relative to the space $X$ if $\kappa <\Delta(X)$, where $\Delta(X)$ is the least cardinality of a non-empty open set in $X$. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire $\sigma$-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces.

On the volume of unit vector fields on spaces of constant sectional curvature

2004

A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.

Fixed points for weak alpha-psi-contractions in partial metric spaces

2013

Recently, Samet et al. (2012) introduced the notion of $\alpha $ - $\psi $ -contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak $\alpha $ - $\psi $ -contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Radial conformal motions in Minkowski space–time

1999

A study of radial conformal Killing fields (RCKF) in Minkowski space-time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.

A singular (p,q)-equation with convection and a locally defined perturbation

2021

We consider a parametric Dirichlet problem driven by the (p,q)-Laplacian and a reaction which is gradient dependent (convection) and the competing effects of two more terms, one a parametric singular term and a locally defined perturbation. We show that for all small values of the parameter the problem has a positive smooth solution.