L p-discrepancy and statistical independence of sequences

We characterize statistical independence of sequences by the L ^p-discrepancy and the Wiener L ^p-discrepancy. Furthermore, we find asymptotic information on the distribution of the L ²-discrepancy of sequences     

Strukturwechselbeziehungen planarer und nichtplanarer Bis(1,2‐dithioquadratato)metallat‐Wirtsgittersysteme mit CuII‐Gastkomplexen – Struktur‐ und EPR‐Untersuchungen

Structural Interactions of Planar and Non‐planar Bis(1,2‐dithiosquarato)metalate Host Lattices with Cu^II Complexes – Structure and EPR Investigations 1,2‐Dithiosquaratometalates (M = Cu, Ni, Zn) are available by direct synthesis from metal salts with dipotassium‐1,2‐dithiosquarate. The structural influence of the planar and nonplanar host lattice systems (BzlEt₃N)₂[Cu/Ni(dtsq)₂] and (BzlEt₃N)₂[Cu/Zn(dtsq)₂] on the geometrical and electronic structure of the Cu^II guest complex [Cu(dtsq)₂]^2– is studied by EPR spectroscopy. The used host lattices (BzlEt₃N)₂[Ni(dtsq)₂] (planar) and (BzlEt₃N)₂[Zn(dtsq)₂] (tetrahedral) are characterized by X‐ray structure analysis. (BzlEt₃N)₂[Ni(dtsq)₂] crystallizes in the triclinic unit cell P1 with a = 9.1021(8) Å, b = 9.4190(8) Å, c = 11.0119(10) Å, α = 92.8560(10)°, β = 95.375(2)°, γ = 104.5180(10)° and Z = 1. (BzlEt₃N)₂[Zn(dtsq)₂] crystallizes in the monoclinic unit cell C2/c with a = 21.1299(14) Å, b = 16.6641(11) Å, c = 13.8324(9) Å, β = 123.9100(10)° and Z = 4. The g and A ^Cu tensors in the Cu/Ni system are nearly axial symmetric (g_|| = 2.122, g_⊥ = 2.028; A = –159.5 · 10^–4 cm^–1, A = –36.9 · 10^–4 cm^–1). The coordination geometry of the Cu^II guest complex in the tetrahedral Cu/Zn system is rather distorted, which is shown by the changed g and A ^Cu tensor parameters (g_|| = 2.143, g_⊥ = 2.042; A = –103.0 · 10^–4 cm^–1, A ≈ –5.0 · 10^–4 cm^–1). The spin density distribution is discussed using EHT molecular orbital calculations.     

Dynamics of argon in confined geometry

The role of geometrical confinement on the dynamics of argon is studied. We have investigated ³⁶Argon adsorbed in nanoporous Gelsil glass by inelastic neutron scattering. By fractional filling the `dimensionality' of the system is tuned from a two-dimensional towards the bulk state. Ab-initio calculations of plane sheets of Ar atoms and of bulk Ar are compared to the experimental results. A shift of various phonon modes to lower energies with decreasing dimensionality is observed in the results of both methods.     

Giant resonances in the doubly magic nucleus 48Ca from the (e, e'n) reaction

The 48Ca(e,e(')n) reaction has been investigated for excitation energies 11-25 MeV and momentum transfers 0.22-0.43 fm(-1) at the superconducting Darmstadt electron linear accelerator S-DALINAC. Electric dipole and quadrupole plus monopole strength distributions are extracted from a multipole decomposition of the spectra. Their fragmented structure is described by microscopic calculations allowing for coupling of the basic particle-hole excitations to more complex configurations. Comparison of the excitation spectrum of the residual nucleus 47Ca with statistical model calculations reveals a 39(5)% contribution of direct decay to the damping of the giant dipole resonance.     

Lattice dynamics of alkali cyanide crystals

The recent microscopic model of Michel and Naudts for the interaction of ionic vibrational displacements and molecular rotational displacements is combined with the lattice dynamical shell model to calculate phonon dispersion curves of KCN and NaCN. Very good agreement with the existing experimental data is obtained. In particular, the upward dispersion of the TA phonon branches, characteristic of the alkali cyanide crystals, is well reproduced.     

On statistical limit points

The set of all statistical limit points of a given sequence is characterized as an -set. It is also characterized in terms of discontinuity points of distribution functions of .

     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

Acknowledgement to our referees

Abstract

In the hydrosphere sulfates of the following origin may exist: (1) evaporitic; they come from the leaching of sulfate rocks, (2) biological, formed by sulfur-oxidizing bacteria and (3) anthropogenic, which get into water with wastes, fertilizers or acid rains. Chemical analyses may reveal sulfates in water, but their origin cannot be assessed by means of chemical analysis. The sulfates of various origin may differ in their isotopic compositions. However, sometimes we can observe the similarity of δ³⁴S of sulfates whose origin was entirely different. This similarity may be so suggestive that it could be misleading.

This paper presents patterns of completely different sulfates whose δ³⁴S are similar, though they have nothing in common. Other tables present patterns of sulfates whose origin is similar or even the same but their δ³⁴S are characterized by great variety. All of the isotopic data presented in the tables were specially chosen from some of the results of the studies of the sulfates in waters in Poland.

Isotopes techniques are becoming more popular and are useful for studies in many fields. These patterns may be a warning against drawing hasty conclusions from the results of δ-measuring.