Lifschitz tail in a magnetic field: the nonclassical regime

We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two-dimensional magnetic Schr?dinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by Brézin, Gross and Itzykson which predict that the IDS is discontinuous at the bottom of the spectrum for zero range (Dirac delta) impurities at low density. We also elucidate the reason behind this apparent controversy. Our methods involve magnetic localization techniques (both in space and energy) in addition to a modified version of the “enlargement of obstacles” method developed by A.-S. Sznitman. Received: 20 July 1997 / Revised version: 20 April 1998     

On the characteristic polynomial of supermatrices

We prove that the coefficients of the so-called right 2-characteristic polynomial of a supermatrix over a Grassmann algebraG=G ₀⊕G ₁ are in the even componentG ₀ ofG. As a consequence, we obtain that the algebra ofn×n supermatrices is integral of degreen ² overG ₀. Partially supported by OTKA of Hungary, grant no. T16432.     

Synthesis of poly(chitosan‐N‐isopropylacrylamide) complex particles with the method of soapless dispersion polymerization

Crosslinked poly(chitosan‐N‐isopropylacrylamide) [poly(NIPAAM‐chitosan)] complex particles were successfully synthesized with the method of soapless dispersion polymerization. The anionic initiator ammonium persulfate (APS) and the cationic initiator 2,2′‐azobis(2‐methylpropionamidine) dihydrochloride (AIBA) were used to initiate the copolymerization. The poly(NIPAAM‐chitosan) copolymer particles synthesized with APS as the initiator had a homogeneous morphology, whereas the copolymer particles synthesized with AIBA as the initiator showed a core–shell morphology. In addition, various variables such as the particle size, reaction rate, and ζ potential were taken into account. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2053–2063, 2003     

Algebras with transitive automorphism groups

Presented by I. Rosenberg.     

Homogeneous catalytic reduction of NO in the presence of Co(III) complexes

Several Co(III) complexes have been found to be active catalysts in the reaction of NO with n-butylamine. N₂ and N₂O were identified as gaseous products of the reduction. Isotope scrambling in N₂ and N₂O in the experiments with N-15 enriched NO suggests two types of stoichiometric processes. The catalysis is interpreted by formation of a NO-complex as intermediate.     

On the real meaning of Bell's theorem

In the last couple of years many important results have been derived showing that Bell's inequalities are nothing else but the indicator whether certain events and their probabilities can be represented or not within a Kolmogorovian probabilistic model. It has become evident that one can derive the Bell's inequalities without mentioning locality, causality hidden variable, etc. Many authors jumped to conclusion that the original content of the Bell's theorem had lost its meaning. I reconsider original problem posed by Bell and I show that the Bell's theorem is still valid.1. On leave from the Institute for Theoretical Physics, Eötvös University, Budapest.     

An anti-Ramsey theorem

An edge-coloring of a graph is a partition of the set of edges into color-classes such that no two edges in the same class are adjacent. A subsetA of the vertex set isantihomogeneous if all edges in the subgraph induced byA have different colors. We study the maximum size of antihomogeneous subsets of the complete graphK _n with respect to edge-colorings. The greedy algorithm shows that this size is always at least (2n)^1/3. On the other hand, we prove thatK _n has an edgecoloring admitting no antihomogeneous subset of size 8 (nlnn)^1/3, answering a question of V. Rödl. The proof is not constructive; it employs a probabilistic argument. Related problems concerning Sidon sets in groups are mentioned.     

Neighbourhood-Perfect Line Graphs

We show that the line graph of any balanced hypergraph is neighbourhood-perfect. This result is a hypergraphic extension of a recent theorem in [GKLM] saying that the line graphs of bipartite graphs are neighbourhood-perfect. The note contains also a graphical extension of the same theorem: the characterization of all graphs with neighbourhood-perfect line graph. The proof relies on a characterization of neighbourhood-perfect graphs among line graphs in terms of forbidden induced subgraphs.     

Statistical design of data handling in environmental analysis

In environmental analysis, owing to the huge number of analytical data, statistical evaluation is inevitable and must be carefully designed. Though the appropriate statistical test system is basically depending on the given analytical task, some general principles of the statistical design can be outlined, namely: i) before calculating mean value and standard deviation (SD), a preliminary test series must be performed for trend, distribution and outliers; ii) while the trueness of the measured mean values can be tested using appropriate certified reference materials (CRMs), even for a correct test, use of SD reference values are also necessary; iii) as the distribution may differ from the normal one, alternative non-parametric tests must be also built into the test system. The fulfillment of these requirements necessitates a flexible, adaptable statistical software, such as the DATAPRO 2.0 software recently developed.