Jahn-teller chromium ions in CdF<Subscript>2</Subscript> and CaF<Subscript>2</Subscript> crystals: An EPR spectroscopic study in the frequency range 9.3–300 GHz

The bivalent chromium impurity centers in CdF₂ and CaF₂ crystals are investigated using electron paramagnetic resonance (EPR) in the frequency range 9.3–300 GHz. It is found that Cr²⁺ ions in the lattices of these crystals occupy cation positions and form [CrF₄F₄]^6? clusters whose magnetic properties at low temperatures are characterized by orthorhombic symmetry. The parameters of the electron Zeeman and ligand interactions of the Cr²⁺ ion with four fluorine ions in the nearest environment are determined. The initial splittings in the system of spin energy levels of the cluster are measured.     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Synthesis of ladder-type filters based on SAW resonators

A synthesis method for ladder-type filters based on SAW resonators is described. SAW devices are designed with modified equations for coupled waves. Nomograms for choosing the geometry of the filters on ST, X-cut quartz and on 36° Y, X-cut LiTaO₃ substrates are presented. Theoretical results are compared with experimental data.     

Activation profiles of opioid ligands in HEK cells expressing δ opioid receptors

Background  

The aim of the present study was to characterize the activation profiles of 15 opioid ligands in transfected human embryonic kidney cells expressing only δ opioid receptors. Activation profiles of most of these ligands at δ opioid receptors had not been previously characterized in vitro. Receptor activation was assessed by measuring the inhibition of forskolin-stimulated cAMP production.     

Generating solutions of Einstein's field equations by typing mistakes

A solution to Einstein's field equations is presented that represents a Petrov type II electromagnetic null field with one Killing vector. This solution generalizes a vacuum solution previously discovered by Hoenselaers. The solution was found by the peculiar method of generalizing a member of this class inadvertently discovered by making a typing error when checking the vacuum solution with the computer algebra system SHEEP.     

On Λ(p)-subsets of squares

This paper is a follow up of [B₁]. It is shown that the sequence of squares {n ²|n=1, 2, ...} contains Λ(p)-subsets of “maximal density”, for any givenp>4. The proof is based on the probabilistic method developed in [B₁] and a precise estimate of the Λ(p)-constant for the sequence of squares itself. Analogues of this phenomenon are obtained for other arithmetic sets, such as the sequence ofkth powers {n ^k |n=1, 2, ...} or the sequence of prime numbers. Sections 2 and 3 of the paper are of independent interest to orthogonal system theory.     

A characterization of cardinalsκ such that 2λ = 2κ wheneverκ ≦λ < 2κ

We characterize cardinalsκ such that 2^λ = 2^κ wheneverκ ≦λ < 2^κ using ideals in small algebras of sets satisfying certain completeness and saturation conditions. Research of this author was supported by an NSF Grant.