Isotope shifts in dysprosium measured by high resolution laser spectroscopy

Using a pulsed dye laser, acting on a collimated atomic beam, the isotope shifts between the dysprosium isotopes 164, 162, and 160 were measured with high precision in three lines, $\text{λ=5547}\text{A}\text{?}$, $\text{λ=5640}\text{A}\text{?}$ and 5652 Å.     

Uniaxial magnetocrystalline anisotropy of metal/semiconductor interfaces: Fe/ZnSe(001)

A theoretical study of the magnetic moments and the in-plane magnetic anisotropy of an interface between a cubic ferromagnet and a cubic semiconductor, Fe/ZnSe(001), is presented. Theory confirms the observed, much debated, uniaxial anisotropy of the iron film. This result is important since the calculations are for perfect interfaces with squarelike environments, proving that the fourfolded symmetry of the interface Fe atoms is broken beyond the nearest neighboring semiconducting layer, effects that are usually assumed small. It is demonstrated how the uniaxial anisotropy is produced by the directional covalent bonds at the interface, even without atomic relaxations.     

Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type

In this paper we study the system $$\begin{aligned}&\min \biggl \{-\mathcal H u_i(x,t)-\psi _i(x,t),u_i(x,t)-\max _{j\ne i}(-c_{i,j}(x,t)+u_j(x,t))\biggr \}=0,\\&u_i(x,T)=g_i(x),\ i\in \{1,\ldots ,d\}, \end{aligned}$$ where \((x,t)\in \mathbb R ^{N}\times [0,T]\) . A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth, and structural assumptions on the data, i.e., on the operator \(\mathcal H \) and on continuous functions \(\psi _i\) , \(c_{i,j}\) , and \(g_i\) . A key aspect is that we make no sign assumption on the switching costs \(\{c_{i,j}\}\) and that \(c_{i,j}\) is allowed to depend on \(x\) as well as \(t\) . Using the comparison principle, the existence of a unique viscosity solution \((u_1,\ldots ,u_d)\) to the system is constructed as the limit of an increasing sequence of solutions to associated obstacle problems. Having settled the existence and uniqueness, we subsequently focus on regularity of \((u_1,\ldots ,u_d)\) beyond continuity. In this context, in particular, we assume that \(\mathcal H \) belongs to a class of second-order differential operators of Kolmogorov type of the form: $$\begin{aligned} \mathcal H =\sum _{i,j=1}^m a_{i,j}(x,t)\partial _{x_i x_j}+\sum _{i=1}^m a_i(x,t)\partial _{x_i} +\sum _{i,j=1}^N b_{i,j}x_i\partial _{x_j}+\partial _t, \end{aligned}$$ where \(1\le m\le N\) . The matrix \(\{a_{i,j}(x,t)\}_{i,j=1,\ldots ,m}\) is assumed to be symmetric and uniformly positive definite in \(\mathbb R ^m\) . In particular, uniform ellipticity is only assumed in the first \(m\) coordinate directions, and hence, \(\mathcal H \) may be degenerate.     

The power of bootstrap tests of cointegration rank

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of asymptotic tests. The effect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymptotic test. The bootstrap test therefore estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.     

On two-scale convergence and related sequential compactness topics

A general concept of two-scale convergence is introduced and two-scale compactness theorems are stated and proved for some classes of sequences of bounded functions in L ²(Ω) involving no periodicity assumptions. Further, the relation to the classical notion of compensated compactness and the recent concepts of two-scale compensated compactness and unfolding is discussed and a defect measure for two-scale convergence is introduced.