Proton–neutron structure of the N=52 nucleus Zr

Following the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei ⁹⁴Mo and ⁹⁶Ru, we have performed a photon scattering experiment on the N=52 isotone ⁹²Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of ⁹²Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2⁺ state, while calculations and data indicate an almost pure neutron configuration for the 2⁺₁ state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1⁺ two-phonon state, were observed.     

Advanced finite element formulations for modeling thin piezoelectric structures

This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lattice points in a circle and divisors in arithmetic progressions

Let A(x) denote the number of lattice points in the circle u²+v²x and define as the infimum of all reals for which . The objective of this paper is to show that 35/108 which improves upon all previously known results. This estimate is an immediate consequence of a surprisingly easy generalization of KOLESNIK's work on Dirichlet's divisor problem to divisor functions with respect to arithmetic progressions.     

Higher order derivative tests for exponential sums incorporating the Discrete Hardy–Littlewood method

This paper provides estimates for exponential sums, combining classic tools of Van der Corput type with a deep result from the modern “discrete Hardy–Littlewood method”. As an application, an improved bound for the lattice point discrepancy of a large ellipsoid of rotation is deduced.     

Akustische wellen in Gebieten,die von zwei lokal gestorten parallelen ebenen begrenzt sind

We consider acoustic waves in domains with boundaries, coinciding with two parallel planes outside a sufficiently large sphere. Several results on spectral properties of the Laplace operator in such domains are derived and used to prove uniqueness and existence of a solution of the Dirichlet boundary value problem for the reduced wave equation under additional restrictions. In particular, a class of domains is described for which no eigenvalues are present.     

Continuous bordering of matrices and continuous matrix decompositions

Summary. Let be the set of all real -matrices of rank . We prove that for there are no continuous vector fields such that the bordered matrix is regular for all . This result has some relevance for the numerical analysis of steady state bifurcation. As a by-product we show that there is no nonvanishing continuous vector field with for all , where is the set of all matrices of rank deficiency one. This implies that there is no singular value decomposition of depending continuously on in any matrix set which contains . As another application we prove that in general there is no global analytic singular value decomposition for analytic matrix valued functions of more than one real variable. Received October 6, 1993 / Revised version received July 18, 1994     

Spectral measures and the Bade reflexivity theorem

Let $\text{B}$ be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by $\text{B}$ in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed $\text{B}$-invariant subspace of X.     

A novel methodological approach for δ18O analysis of sugars using gas chromatography-pyrolysis-isotope ratio mass spectrometry

Although the instrumental coupling of gas chromatography-pyrolysis-isotope ratio mass spectrometry (GC-Py-IRMS) for compound-specific δ¹⁸O analysis has been commercially available for more than a decade, this method has been hardly applied so far. Here we present the first GC-Py-IRMS δ¹⁸O results for trimethylsilyl-derivatives of plant sap-relevant sugars and a polyalcohol (glucose, fructose, sucrose, raffinose and pinitol). Particularly, we focus on sucrose, which is assimilated in leaves and which is the most important transport sugar in plants and hence of utmost relevance in plant physiology and paleoclimate studies. Replication measurements of sucrose standards and concentration series indicate that the GC-Py-IRMS δ¹⁸O measurements are not stable over time and that they are amount (area) dependent. We, therefore, suggest running sample batch replication measurements in alternation with standard concentration series of reference material. This allows for carrying out (i) a drift correction, (ii) a calibration against reference material and (iii) an amount (area) correction. Tests with ¹⁸O-enriched water do not provide any evidence for oxygen isotope exchange reactions affecting sucrose and raffinose. We present the first application of GC-Py-IRMS δ¹⁸O analysis for sucrose from needle extract (soluble carbohydrate) samples. The obtained δ¹⁸O_{sucrose/ Vienna Standard Mean Ocean Water (VSMOW)} values are more positive and vary in a wider range (32.1–40.1 ‰) than the δ¹⁸O_{bulk/ VSMOW} values (24.6–27.2 ‰). Furthermore, they are shown to depend on the climate parameters maximum day temperature, relative air humidity and cloud cover. These findings suggest that δ¹⁸O_sucrose of the investigated needles very sensitively reflects the climatically controlled evaporative ¹⁸O enrichment of leaf water and thus highlights the great potential of GC-Py-IRMS δ¹⁸O_sucrose analysis for plant physiology and paleoclimate studies.     

Tunneling Times with Covariant Measurements

We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems to cross the tunnel region instantaneously. An obstacle to the utilization of this effect for getting faster signals is the exponential damping by the tunnel, so there seems to be a trade-off between speedup and intensity. In this paper we prove that this trade-off is never in favor of faster signals: the probability for a signal to reach its destination before some deadline is always reduced by the tunnel, for arbitrary incoming states, arbitrary positive and compactly supported tunnel potentials, and arbitrary detectors. More specifically, we show this for several different ways to define “the same incoming state” and “the same detector” when comparing the settings with and without tunnel potential. The arrival time measurements are expressed in the time-covariant approach, but we also allow the detection to be a localization measurement at a later time. Dedicated to Pekka Lahti on the occasion of his 60th birthday.