Indoor radon and lung cancer: a case-control study

Lung-cancer risk to the general population from indoor radon remains controversial, although studies of radon exposure have established that radon decay products have been a cause of lung cancer among miners.

For the case group of patients, suffering from lung cancer, and the control group distributions of the number of homes with high indoor levels of radon were compared with the log-normal distribution, the empirical frequency distribution of the control group obeyed the theoretical log-normal distribution.

Using the ratio of frequencies of the case group to the control groups, or the relative frequencies, an association between the relative frequencies and indoor radon concentrations was found, and a positive correlation coefficient was obtained, thus enabling the rate of lung cancer to be estimated for certain indoor radon concentrations.

The significant difference between the mean radon levels for the case sample and the control led to the conclusion that patients with lung cancer lived in homes with radon concentrations which were significantly higher than those of Osijek’s inhabitants for the control sample.     

A simple metal-free synthesis of 2-substituted pyridine-4,5-dicarboxylates and their N-oxides

Herein a simple, metal-free synthesis of 2-alkyl-, 2-cycloalkyl-, 2-aryl-, and 2-heteroaryl-substituted pyridine 3,4-dicarboxylates and their N-oxides from the corresponding methyl ketones in good to excellent yield, demonstrated with 22 examples in each case, is described. The method complements the current coupling reactions of 2-heterocyclic organometallic reagents.     

Vacuum fluctuations of the supersymmetric field in curved background

We study a supersymmetric model in curved background spacetime. We calculate the effective action and the vacuum expectation value of the energy momentum tensor using a covariant regularization procedure. A soft supersymmetry breaking induces a nonzero contribution to the vacuum energy density and pressure. Assuming the presence of a cosmic fluid in addition to the vacuum fluctuations of the supersymmetric field an effective equation of state is derived in a self-consistent approach at one loop order. The net effect of the vacuum fluctuations of the supersymmetric fields in the leading adiabatic order is a renormalization of the Newton and cosmological constants.     

Spectral Theory of the Klein–Gordon Equation in Pontryagin Spaces

In this paper we investigate an abstract Klein–Gordon equation by means of indefinite inner product methods. We show that, under certain assumptions on the potential which are more general than in previous works, the corresponding linear operator A is self-adjoint in the Pontryagin space induced by the so-called energy inner product. The operator A possesses a spectral function with critical points, the essential spectrum of A is real with a gap around 0, and the non-real spectrum consists of at most finitely many pairs of complex conjugate eigenvalues of finite algebraic multiplicity; the number of these pairs is related to the ‘size’ of the potential. Moreover, A generates a group of bounded unitary operators in the Pontryagin space . Finally, the conditions on the potential required in the paper are illustrated for the Klein–Gordon equation in ; they include potentials consisting of a Coulomb part and an L _p -part with n ≤ p < ∞.Branko Najman: Deceased     

Formulae of partial reduction for linear systems of first order operator equations

This paper deals with the reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and first order linear operator equations in two variables, is obtained by using the rational canonical form.     

Equipartite polytopes

A polytope P with 2n vertices is called equipartite if for any partition of its vertex set into two equal-size sets V ₁ and V ₂, there is an isometry of the polytope P that maps V ₁ onto V ₂. We prove that an equipartite polytope in ℝ ^d can have at most 2d+2 vertices. We show that this bound is sharp and identify all known equipartite polytopes in ℝ ^d . We conjecture that the list is complete.     

Metrically homogeneous sets: Corrigendum

A flaw in Lemma 2 is corrected and other parts of the paper changed a accordingly so as to preserve all the theorems. We are indebted to Professor Rigby for kindly bringing these facts to our attention.     

Über den Verlauf der Bindung der Stickstoffoxyde an Calciumoxyd

Zusammenfassung Die Resultate isothermer Messungen der Sorption der Stickoxyde an CaO bei verschiedenen Drücken (0,05 bis 1 Atm) und bei Temperaturen von 20 bis 650°C werden wiedergegeben. Im untersuchten Temperaturintervall verläuft die Reaktion unter Bildung von Calciumnitrat mit kleinen Nitritbeimengungen. In bezug auf die Kinetik der Bildung kann man das untersuchte Temperaturintervall für 1 Atm Stickoxyde-Druck in drei Bereiche einteilen: unter 50°C, von 50 bis 400°C und von 450 bis 610°C. In den ersten zwei Bereichen findet die Reaktion im System fest—gasförmig statt, während im dritten die Gasphase mit einer mehr oder weniger ausgeprägten Schmelze reagiert.     

Metrically homogeneous sets

A subset of a metric space is called metrically homogeneous if the set of distances from a chosen point of the subset to all the other points of the subset is independent of the chosen point. The main result of the paper is a complete characterization of the compact, metrically homogeneous subsets of the Euclidean plane.     

Rhodium(I)-catalyzed ene-allene carbocyclization strategy for the formation of azepines and oxepines

[reaction: see text] A novel strategy for the preparation of seven-membered heterocyclic compounds has been realized. Treatment of ene-allene 1 with a catalytic quantity of rhodium biscarbonyl chloride dimer affords the cyclization product 2 in moderate to high yields. The scope and limitations of this new method are currently under investigation, and the results obtained to date are discussed within.