Search results for "Algebra"

On the algebraic representation of projectively embeddable affine geometries

1995

The main result of this article is an application of [1] and [2] which yields that an at least 2-dimensional affine geometry is module-induced if and only if it is projectively embeddable into an Arguesian projective lattice geometry.

A SIMPLE CULTIVATION CHAMBER FOR THE STUDY OF AERIAL REPRODUCTIVE ELEMENTS OF FUNGI

1970

Finite-element design sensitivity analysis for non-linear potential problems

1990

Design sensitivity analysis is performed for the finite-element system arising from the discretization of non-linear potential problems using isoparametric Lagrangian elements. The calculated sensitivity formulae are given in a simple matrix form. Applications to the design of electromagnets and airfoils are given.

The exact bounds for the degree of commutativity of a p-group of maximal class, II

2004

AbstractLet G be a p-group of maximal class. Since the pioneer work of Blackburn in 1958 (cf. [N. Blackburn, Acta Math. 100 (1958) 45–92]), several authors have obtained information about the degree of commutativity c of G, in order to precise which the defining relations of G are (cf. [N. Blackburn, Acta Math. 100 (1958) 45–92; R. Shepherd, PhD Thesis, University of Chicago, 1970; C.R. Leedham-Green, S. McKay, Quart. J. Math. Oxford Ser. (2) 27 (1976) 297–311, Quart. J. Math. Oxford Ser. (2) 29 (1978) 175–186, 281–299; G.A. Fernández-Alcober, J. Algebra 174 (1995) 523–530; A. Vera-López, J.M. Arregi, F.J. Vera-López, Comm. Algebra 23 (1995) 2765–2795, Math. Proc. Cambridge Philos. Soc. 122…

An improvement of a bound of Green

2012

A p-group G of order pn (p prime, n ≥ 1) satisfies a classic Green's bound log p |M(G)| ≤ ½n(n - 1) on the order of the Schur multiplier M(G) of G. Ellis and Wiegold sharpened this restriction, proving that log p |M(G)| ≤ ½(d - 1)(n + m), where |G′| = pm(m ≥ 1) and d is the minimal number of generators of G. The first author has recently shown that log p |M(G)| ≤ ½(n + m - 2)(n - m - 1) + 1, improving not only Green's bound, but several other inequalities on |M(G)| in literature. Our main results deal with estimations with respect to the bound of Ellis and Wiegold.

Additivity of affine designs

2020

We show that any affine block design $$\mathcal{D}=(\mathcal{P},\mathcal{B})$$ is a subset of a suitable commutative group $${\mathfrak {G}}_\mathcal{D},$$ with the property that a k-subset of $$\mathcal{P}$$ is a block of $$\mathcal{D}$$ if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design $$\mathcal{D}$$ is the group of automorphisms of $${\mathfrak {G}}_\mathcal{D}$$ that leave $$\mathcal P$$ invariant. Whenever k is a prime p,  $${\mathfrak {G}}_\mathcal{D}$$ is an elementary abelian p-group.

A coincidence-point problem of Perov type on rectangular cone metric spaces

2017

We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using alpha-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.

A descendent tropical Landau–Ginzburg potential for $\mathbb{P}^2$

2016

Bhabha Scattering and a special pencil of K3 surfaces

2018

We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Ap\'ery--Fermi pencil, that was related to Ap\'ery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.

Supersymmetric structures for second order differential operators

2012

Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different.