Noetherian Automorphisms of Groups

An automorphism α of a group G is called a noetherian automorphism if for each ascending chain

Competition and adaptation in an Internet evolution model

We model the evolution of the Internet at the autonomous system level as a process of competition for users and adaptation of bandwidth capability. From a weighted network formalism, where both nodes and links are weighted, we find the exponent of the degree distribution as a simple function of the growth rates of the number of autonomous systems and connections in the Internet, both empirically measurable quantities. Our approach also accounts for a high level of clustering as well as degree-degree correlations, both with the same hierarchical structure present in the real Internet. Further, it also highlights the interplay between bandwidth, connectivity, and traffic of the network.     

A Banach space admits a locally uniformly rotund norm if its dual is a Vašák space

LetV be a Banach space whose dualV ^* is Va?ák, that is, weakly countably determined. Then an equivalent locally uniformly rotund norm onV is constructed. According to a recent example of Mercourakis, this is a real extension of an earlier result of Godefroy Troyanski, Whitfield and Zizler, whereV ^* has been a subspace of a weakly compactly generated Banach space.     

Mimics of ganglioside GM1 as cholera toxin ligands: replacement of the GalNAc residue

Two new cholera toxin (CT) ligands (4 and 5) are described. The new ligands were designed starting from the known GM1 mimics 2 and 3 by replacement of their GalNAc residue with the C4 isomer GlcNAc. As predicted by molecular modelling, the conformational properties of the equivalent pairs 2-4 and 3-5 are very similar and their affinity for CT is of the same order of magnitude. NMR experiments have also proved that 5 occupies the GM1-binding site of the toxin and have revealed its bound conformation.     

Effective Radius and Underpressure of an Air Extraction Well in a Heterogeneous Porous Medium

We consider the compressible steady state air flow in a porous medium caused by an extraction well and governed by Darcy's law. For a homogeneous soil matrix we have derived formulas (in 2-D and 3-D) to determine the effective radius of a single well depending on the well position and the depth of the domain. For inhomogeneous case (in 2-D) the influence of the heterogeneity, well position and the depth of the water table on the effective radius and on the pressure at the well is studied.     

Mathematical Treatment of Point Sources in a Flow Through Porous Media Governed by Darcy's Law

We consider stationary air flow in a porous medium caused by extraction wells and governed by Darcy's law. Point sinks are described by Dirac functions. We distinguish two different situations: locally continuous and discontinuous conductivity near the wells. In both cases, well-posedness is proved. We propose a finite-element scheme in the general case and show the convergence of the approximated solution to the exact one.     

On the use of realistic wave functions in the coherent pion photoproduction on 3He nuclei

We analyze the influence of the nuclear wave functions generated from a set of different realistic soft-core two-body potentials on the coherent charged pion photoproduction on ³He nuclei at threshold and for small momentum transfers. This process is calculated in the framework of the impulse approximation including the Fermi motion. At threshold and below the resonance, our results reproduce fairly well the experimental data. At the first γN resonance region, the agreement with experiments varies with the momentum transfer.     

Joint probabilities of noncommuting operators and incompleteness of quantum mechanics

We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.⁽¹⁾ The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond it, by a more general theory of single events, using hidden variables, for example.