Search results for "normal"
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An extension of the algebra of sets
1973
We shall explain the aim which leads us in the construction of an extended system of the algebra of sets1. The symbol 1. {*:?(*)} denoting the set of these and only these elements of domain of the variable x which satisfy the propositional condition (propositional function or form) ?9 (x)" is in com? mon use nowadays, so that it is adopted in school courses of mathematics in many countries, and in Poland as well. This condition will be said to define the set 1. However, if we admit propositional conditions which are meaningless for some values of their variables then we encounter some difficulties connected with the ex? pression 1. The formulae 2. {x : 9 (*)} = {x : 9 (*)}' 3. {x : 9 (s) v …
On sigma-subnormal subgroups of factorised finite groups
2020
Abstract Let σ = { σ i : i ∈ I } be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called σ-subnormal in G if there is chain of subgroups X = X 0 ⊆ X 1 ⊆ ⋯ ⊆ X n = G with X i − 1 normal in X i or X i / C o r e X i ( X i − 1 ) is a σ i -group for some i ∈ I , 1 ≤ i ≤ n . In the special case that σ is the partition of P into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. If a finite soluble group G = A B is factorised as the product of the subgroups A and B, and X is a subgroup of G such that X is σ-subnormal in 〈 X , X g 〉 for all g ∈ A ∪ B , we prove that X is σ-subnormal in G. This is an extension…
New Refinements of the McKay Conjecture for Arbitrary Finite Groups
2004
Let $G$ be an arbitrary finite group and fix a prime number $p$. The McKay conjecture asserts that $G$ and the normalizer in $G$ of a Sylow $p$-subgroup have equal numbers of irreducible characters with degrees not divisible by $p$. The Alperin-McKay conjecture is a version of this as applied to individual Brauer $p$-blocks of $G$. We offer evidence that perhaps much stronger forms of both of these conjectures are true.
Degrees of rational characters of finite groups
2010
Abstract A classical theorem of John Thompson on character degrees states that if the degree of any complex irreducible character of a finite group G is 1 or divisible by a prime p, then G has a normal p-complement. In this paper, we consider fields of values of characters and prove some improvements of this result.
On finite soluble groups in which Sylow permutability is a transitive relation
2003
A characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding properties enjoyed by all the subgroups is proved in the paper. The key point is an extension of a subnormality criterion due to Wielandt.
Domains of Convergence of Kam Type Iterations for Eigenvalue Problems
1999
The KAM technique was first introduced to deal with small denominator problems appearing in perturbation of invariant tori in classical mechanics [1, 2]. Similar methods were later applied to many different problems, like e.g. eigenvalue problems for time dependent problems in the Floquet representation [3, 4, 5, 6]. Most of the known results are valid for sufficiently small perturbation of some simple (integrable) system. The phenomena arising for large perturbations, in particular critical perturbations at which a given torus loses its stability, have been discussed in the framework of some approximate schemes inspired in renormalization group ideas [7, 8, 9]. In this framework, an iterat…
Analysis of microsphere oblique impact with planar surfaces based on the independent friction-restitution approach
2020
The independent friction restitution closure (IFR) previously applied to describe planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is applied here to microsphere collisions and is extended to describe horizontal launch experiments. The model provides analytical solutions of the motion equations based on a unique set of values of the coefficients of normal and tangential restitution and friction. Comparison with experimental data in literature for the impact of microspheres of diameter <100 mu m yields a satisfactory agreement between experimentation and theory.
Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder
2013
Publised version of an article from the journal: Physics of Fluids. Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Article appears in Volume 25 issue 4 of the journal: http://dx.doi.org/10.1063/1.4799253 The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper b…
Using the ARP-03 for high-resolution mapping of calcic horizons
2013
A b s t r a c t. The aim of this work is to present a fast and cheap method for high-resolution mapping of calcic horizons in vineyards based on geoelectrical proximal sensing. The study area, 45 ha located in southern Sicily (Italy), was characterized by an old, partially dismantled marine terrace and soils with a calcic horizon at different depths. The geoelectrical investigation consisted of a survey of the soil electrical resistivity recorded with the Automatic Resistivity Profiling-03 sensor. The electrical resistivity values at three pseudo-depths, 0-50, 0-100 and 0-170 cm, were spatialized by means of ordinary kriging. A principal component analysis of the three electrical resistivit…
Local thermal non-equilibrium effects in the Darcy–Bénard instability of a porous layer heated from below by a uniform flux
2013
Abstract The influence of the lack of thermal equilibrium between the solid phase and the fluid phase on the convective instability in a porous medium is studied. A horizontal layer with parallel and impermeable bounding walls is considered. The lower wall is assumed to be isoflux, and the upper wall isothermal. The basic motionless state is perturbed with small-amplitude disturbances, so that a linear analysis of the instability is carried out with a streamfunction-temperature formulation of the local balance equations. Then, the governing equations are solved for the normal modes, leading to an eigenvalue problem for the neutral stability. This eigenvalue problem is solved analytically, t…