Search results for "Combinatorics"
showing 10 items of 1770 documents
On finite T-groups
2003
[EN] Characterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.
Transitivity of Sylow permutability, the converse of Lagrange's theorem, and mutually permutable products
2008
This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G = AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every subgroup of the other factor. We prove that mutually permutable products of Y -groups (groups satisfying the converse of Lagrange's theorem) and SC-groups (groups whose chief factors are simple) are SC -groups. Next, we show that a product of pairwise mutually permutable Y -groups is supersoluble. Finally, we give a local version of the result stating that if a mutually permutable product of two groups is a PST - group (that is, a group in which every subnormal subgroup permutes …
Some subgroup embeddings in finite groups
2015
In this survey paper several subgroup embedding properties related to some types of permutability are introduced and studied.
Free Minor Closed Classes and the Kuratowski theorem
2009
Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered.
Pappus type theorems for motions along a submanifold
2004
Abstract We study the volumes volume( D ) of a domain D and volume( C ) of a hypersurface C obtained by a motion along a submanifold P of a space form M n λ . We show: (a) volume( D ) depends only on the second fundamental form of P , whereas volume( C ) depends on all the i th fundamental forms of P , (b) when the domain that we move D 0 has its q -centre of mass on P , volume( D ) does not depend on the mean curvature of P , (c) when D 0 is q -symmetric, volume( D ) depends only on the intrinsic curvature tensor of P ; and (d) if the image of P by the ln of the motion (in a sense which is well-defined) is not contained in a hyperplane of the Lie algebra of SO ( n − q − d ), and C …
The ∞-Eigenvalue Problem
1999
. The Euler‐Lagrange equation of the nonlinear Rayleigh quotient \( \left(\int_{\Omega}|\nabla u|^{p}\,dx\right) \bigg/ \left(\int_{\Omega}|u|^{p}\,dx\right)\) is \( -\div\left( |\nabla u|^{p-2}\nabla u \right)= \Lambda_{p}^{p} |u |^{p-2}u,\) where \(\Lambda_{p}^{p}\) is the minimum value of the quotient. The limit as \(p\to\infty\) of these equations is found to be \(\max \left\{ \Lambda_{\infty}-\frac{|\nabla u(x)|}{u(x)},\ \ \Delta_{\infty}u(x)\right\}=0,\) where the constant \(\Lambda_{\infty}=\lim_{p\to\infty}\Lambda_{p}\) is the reciprocal of the maximum of the distance to the boundary of the domain Ω.
Higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses
1999
The higher order statistics of the response of linear systems excited by polynomials of filtered Poisson pulses are evaluated by means of knowledge of the first order statistics and without any further integration. This is made possible by a coordinate transformation which replaces the original system by a quasi-linear one with parametric Poisson delta-correlated input; and, for these systems, a simple relationship between first order and higher order statistics is found in which the transition matrix of the dynamical new system, incremented by the correction terms necessary to apply the Ito calculus, appears.
The Integrated Nested Laplace Approximation for fitting Dirichlet regression models
2022
This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the data.These data, which mainly consist of proportions or percentages of disjoint categories, are widely known as compositional data and are common in areas such as ecology, geology, and psychology. We provide both the theoretical foundations and a description of how Laplace approximation can be implemented in the case of Dirichlet regression.The paper also introduces the package dirinla in the R-language that extends the RINLA package, which can not deal dire…
Novel 3D bio-macromolecular bilinear descriptors for protein science: Predicting protein structural classes
2015
In the present study, we introduce novel 3D protein descriptors based on the bilinear algebraic form in the ℝn space on the coulombic matrix. For the calculation of these descriptors, macromolecular vectors belonging to ℝn space, whose components represent certain amino acid side-chain properties, were used as weighting schemes. Generalization approaches for the calculation of inter-amino acidic residue spatial distances based on Minkowski metrics are proposed. The simple- and double-stochastic schemes were defined as approaches to normalize the coulombic matrix. The local-fragment indices for both amino acid-types and amino acid-groups are presented in order to permit characterizing fragme…
Posets That Locally Resemble Distributive Lattices
2000
Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.