Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

Statistical mechanics of warm and cold unfolding in proteins

We present a statistical mechanics treatment of the stability of globular proteins which takes explicitly into account the coupling between the protein and water degrees of freedom. This allows us to describe both the cold and the warm unfolding, thus qualitatively reproducing the known thermodynamics of proteins. Received: 19 March 1998 / Revised and Accepted: 25 May 1998     

Results on the Generic Kurepa Hypothesis

K.J. Devlin has extended Jensen's construction of a model ofZFC andCH without Souslin trees to a model without Kurepa trees either. We modify the construction again to obtain a model with these properties, but in addition, without Kurepa trees inccc-generic extensions. We use a partially defined -sequence, given by a fine structure lemma. We also show that the usual collapse of Mahlo to ₂ will give a model without Kurepa trees not only in the model itself, but also inccc-extensions.     

Structural and magnetic investigations of the mixed-valence Fe(II,III) two-dimensional layer complex, [Fe2(II) Fe2(III)(HCOO)10(C6H7N)6]n.

The structure of the complex, [Fe2(II)Fe2(III)(HCOO)10(C6H7N6)n, (1) exhibits a neutral two-dimensional layer network of alternating iron(II) and iron(III) ions, bridged equatorially by formate groups. All iron atoms are octahedrally coordinated, with iron(III) coordinating axially to one gamma-picoline and one formate group, while the iron(II) centers interact axially with two gamma-picoline groups, above and below the layer plane. The complex crystallizes in the triclinic space group P1 at all studied temperatures [at 120 K, the cell dimensions are: a = 10.228(1), b = 12.071(1), c = 12.072(1) A, alpha = 89.801(2), beta = 71.149(2), gamma = 73.371(2) degrees]. An intralayer antiferromagnetic exchange interaction of J = -2.8 cm(-1) between iron(II) and iron(III) was observed in the magnetic studies. Decreasing the temperature to close to 20 K causes a magnetic-ordering phenomenon to occur and a low-temperature phase with a long-range antiferromagnetic spin orientation appears. The magnetic phase transition was confirmed by M?ssbauer spectroscopic studies at temperatures above and below the critical temperature. Structural information of 1 from synchrotron X-ray diffraction data collected at room temperature and 16 K suggests that the antiferromagnetic ordering is caused by an enhanced pi-pi interaction between chi-picoline groups from adjacent layers.