Search results for "Theorem"
showing 10 items of 1250 documents
Classical and quantum aspects of electric-magnetic duality rotations in curved spacetimes
2018
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, $\mathrm{F}\ensuremath{\rightarrow}\mathrm{F}\mathrm{cos}\ensuremath{\theta}+^{\ensuremath{\star}}\mathrm{F}\mathrm{sin}\ensuremath{\theta}$. These transformations are indeed a symmetry of the theory in the Noether sense. The associated constant of motion is the difference in the intensity between self-dual and anti-self-dual components of the electromagnetic field or, equivalently, the difference between the right and left circularly polarized components. This conservation law holds even if the electromagnetic field interacts with an arbitrary classical gravitational background.…
A computer program suitable for analysis of choice of categories in biomedical data recognition problems.
1980
The optimum choice of categories in problems of medical data recognition is governed by the choice of categories, the selection of appropriate features, and by the choice of a loss function. Under these circumstances it is often difficult to find out the suitable classification scheme. The computer program described here serves for the design of the optimum recognition procedure. The Bayes rule is used as decision rule. A criterion for the comparison of different choice of categories is given. The program can be performed after estimation of the underlying prior probabilities and the conditional densities obtained from a training set, and before testing the decision rule with real data.
Permutability of injectors with a central socle in a finite solvable group
2017
In response to an Open Question of Doerk and Hawkes [5, IX Section 3, page 615], we shall show that if Zπ is the Fitting class formed by the finite solvable groups whose π-socle is central (where π is a set of prime numbers), then the Zπ-injectors of a finite solvable group G permute with the members of a Sylow basis in G. The proof depends on the properties of certain extraspecial groups [4].
On a class of supersoluble groups
2014
A subgroup H of a finite group G is said to be S-semipermutable in G if H permutes with every Sylow q-subgroup of G for all primes q not dividing |H|. A finite group G is an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable in G. The aim of the present paper is to characterise the finite MS-groups.
Solutions of nonlinear PDEs in the sense of averages
2012
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .
Homomorphs and wreath product extensions
1982
A homomorph is a class of (finite soluble) groups closed under the operation Q of taking epimorphic images. (All groups considered in this paper are finite and soluble.) Among those types of homomorphs that have found particular interest in the theory of finite soluble groups are formations and Schunck classes; the reader is referred to (2), § 2, for a definition of those classes. In the present paper we are interested in homomorphs satisfying the following additional closure property:(W0) if A is abelian with elementary Sylow subgroups, then each wreath product A G (with respect to an arbitrary permutation representation of G) with G ∊ is contained in .
A Note on Locally ??-compact Spaces
1995
: The local version of the concept of ℰτ-compactness (where ℰ is a class of Hausdorff spaces and ℰ is a cardinal) introduced by the first author as a generalization of Her-rlich's concept of ℰ-compactness (and hence, also of Mrowka's E-compactness) is defined and the corresponding theory is initiated. An essential part of the theory is developed under the additional assumption that all spaces from ℰ are absolute extensors for spaces under consideration. The theory contains as a special case the classical theory of local compactness.
A lower bound for the Bloch radius of 𝐾-quasiregular mappings
2004
We give a quantitative proof to Eremenko’s theorem (2000), which extends Bloch’s classical theorem to the class of n n -dimensional K K -quasiregular mappings.
Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
2021
Abstract We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.
A delay time bound for distributed parameter circuits with bipolar transistors
1990
We prove here a stability theorem concerning a parabolic system of equations with non-linear boundary conditions that governs the behaviour of a class of networks in which the bipolar transistors operating under large-signal conditions are interconnected with reg-lines modelled by telegraph equations