Search results for "outer"
showing 10 items of 252 documents
Two graphs with a common edge
2014
Let G = G1 ∪ G2 be the sum of two simple graphs G1,G2 having a common edge or G = G1 ∪ e1 ∪ e2 ∪ G2 be the sum of two simple disjoint graphs G1,G2 connected by two edges e1 and e2 which form a cycle C4 inside G. We give a method of computing the determinant det A(G) of the adjacency matrix of G by reducing the calculation of the determinant to certain subgraphs of G1 and G2. To show the scope and effectiveness of our method we give some examples
A Classification of all Symmetric Block Designs of Order Nine with an Automorphism of Order Six
2006
We complete the classification of all symmetric designs of order nine admitting an automorphism of order six. As a matter of fact, the classification for the parameters (35,17,8), (56,11,2), and (91,10,1) had already been done, and in this paper we present the results for the parameters (36,15,6), (40,13,4), and (45,12,3). We also provide information about the order and the structure of the full automorphism groups of the constructed designs. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 301–312, 2006
Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39
1997
AbstractIn this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a non-abelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1320 non-isomorphic designs. The orders of the full automorphism groups of these designs all divide 8 · 3 · 13.
Measure and dimension functions: measurability and densities
1997
During the past several years, new types of geometric measure and dimension have been introduced; the packing measure and dimension, see [Su], [Tr] and [TT1]. These notions are playing an increasingly prevalent role in various aspects of dynamics and measure theory. Packing measure is a sort of dual of Hausdorff measure in that it is defined in terms of packings rather than coverings. However, in contrast to Hausdorff measure, the usual definition of packing measure requires two limiting procedures, first the construction of a premeasure and then a second standard limiting process to obtain the measure. This makes packing measure somewhat delicate to deal with. The question arises as to whe…
A note on the distance set problem in the plane
2001
We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.
Symplectic automorphisms of prime order on K3 surfaces
2006
The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.
On the conical density properties of measures on $\mathbb{R}^n$
2005
We compare conical density properties and spherical density properties for general Borel measures on $\mathbb{R}^n$ . As a consequence, we obtain results for packing and Hausdorff measures $\mathcal{P}_h$ and $\mathcal{H}_h$ provided that the gauge function $h$ satisfies certain conditions. One consequence of our general results is the following: let $m, n\,{\in}\,\mathbb{N}, 0\,{\lt}\,s\,{\lt}\,m\,{\leq}\,n$ , $0\,{\lt}\,\eta\,{\lt}\,1$ , and suppose that $V$ is an $m$ -dimensional linear subspace of $\mathbb{R}^n$ . Let $\mu$ be either the $s$ -dimensional Hausdorff measure or the $s$ -dimensional packing measure restricted to a set $A$ with $\mu(A)\,{\lt}\,\infty$ . Then for $\mu$ -almos…
Adiabatic versus Non-Adiabatic Electron Transfer at 2D Electrode Materials
2021
<div><div><div><p>Outer-sphere electron transfer (OS-ET) is a cornerstone elementary electrochemical reaction, yet microscopic understanding is largely based on idealized theories, developed in isolation from experiments that themselves are often close to the kinetic (diffusion) limit. Focusing on graphene as-grown on a copper substrate as a model 2D material/metal-supported electrode system, this study resolves the key electronic interactions in OS-ET, and identifies the role of graphene in modulating the electronic properties of the electrode/electrolyte interface. An integrated experimental-theoretical approach combining co-located multi-microscopy, centered on sc…
Jurisdiction and applicable law in cases of damage from space in Europe—The advent of the most suitable choice—Rome II
2010
Liability for space activities is a much discussed subject and the advent of commercial space operations has only added to its importance. Articles VI and VII Outer Space Treaty, together with Articles II and III Liability Convention, remain the main entry level for state liability for damage arising from private space activities. Few space-faring nations have introduced national space statutes that include a flow down of their international obligations. The European Union (EU) Regulation on the law applicable to non-contractual obligations—hereinafter Rome II Regulation—could harbour developments for liability law in the context of damage resulting from space operations. Space activities w…
Enzyme-linked immunosorbent assay for detection of Aeromonas hydrophila serogroup O:19
2006
An enzyme-linked immunosorbent assay has been developed for the detection of Aeromonas hydrophila serogroup O:19 isolated from epizootics in eels. The enzyme-linked immunosorbent assay specificity was confirmed after testing A. hydrophila O:19 and non-O:19 strains from different origins, as well as other Aeromonas species and other fish pathogens such as Vibrio vulnificus biotype 2, V. furnisii, V. damsela, Yersinia ruckerii and Edwardsiella tarda. The detection limits for A. hydrophila O:19 cells were around 10(4)-10(5) cells/well. Artificially infected eels were analyzed and the immunodetection was confirmed by cultural methods. With this methodology A. hydrophila O:19 was successfully de…