Common Tangents to Spheres in ℝ3

We prove that four spheres in ℝ³ have infinitely many real common tangents if and only if they have aligned centers and at least one real common tangent.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.      

Early reactions of light-induced protochlorophyllide and chlorophyllide transformations analyzed in vivo at room temperature with a diode array spectrofluorometer

The steps of protochlorophyllide (Pchlide) photoreduction and subsequent chlorophyllide (Chlide) transformations which occur in the seconds to minutes time-scale were studied using a diode array spectrofluorometer in dark-grown barley leaves. The intensity of the excitation light was varied between 3 and 2,500 micromol m(-2) s(-1) and a series of fluorescence spectra were recorded at room temperature in the seconds and minutes time scales. In certain experiments, 77-K emission spectra were measured with the same equipment. The high quality of the spectra allowed us to run spectral resolution studies which proved the occurrence, at room temperature, of multiple Pchlide and Chlide forms found previously in 77-K spectra. The comparison of the 77-K and room-temperature spectra showed that the fluorescence yields of the nonphotoactive 633-nm Pchlide form and of the Chlide product emitting at 678 nm were temperature independent. The fluorescence intensity of aggregated NADPH-pigment-POR complexes (photoactive 656-nm Pchlide and 693-nm Chlide forms) were strongly increased at 77 K, while that of the NADP(+)-Chlide-POR (684-686-nm Chlide form) was much less affected by temperature. Information was obtained also about the dynamics of the transformation of pigment forms in the light at different photon densities. At low light intensities, the phototransformation of the 642-644-nm Pchlide form was faster than that of the 654-656-nm form. The relative amplitudes of Gaussian components related to different Chlide forms found after exposure to a constant amount of photons strongly depended on the light intensity used. Strong quenching of all Chlide components occurred upon prolonged exposure to high intensity light. These effects are discussed by considering the interconversion processes between different forms of the pigment-protein complexes, their relative fluorescence yields and energy migration processes.     

Ferromagnetism in a dinuclear nickel(II) complex containing triethylenetetramine and tricyanomethanide

Triethylenetetramine (L(4)) was used as a tetradentate blocking ligand that, after complexation with Ni(II), leaves two sites ready for ligation with tricyanomethanide. The formed binuclear complex [L(4)Ni(NCC(CN)CN)(2)NiL(4)](ClO(4))(2) exhibits a ferromagnetic coupling with J/hc = +0.15 cm(-1) and g(Ni) = 2.126; below 16 K, a ferromagnetic ordering is evidenced by ac magnetic susceptibility (both in-phase and out-of-phase), magnetization, field-cooled magnetization, and zero-field-cooled magnetization measurements.     

Enantioselective Preparation of 2‐Aminomethyl Carboxylic Acid Derivatives: Solving the β2‐Amino Acid Problem with the Chiral Auxiliary 4‐Isopropyl‐5,5‐diphenyloxazolidin‐2‐one (DIOZ). Preliminary Communication

Multigram amounts of suitably protected β²‐amino acids with 17 of the 20 proteinogenic side chains are prepared by diastereoselective reactions of Li, B, or Ti enolates of the corresponding 3‐acyl‐4‐isopropyl‐5,5‐diphenyloxazolidin‐2‐ones (acyl‐DIOZ; 1 ) with appropriate electrophiles (amidomethylation, hydroxyalkylation, (benzyloxycarbonyl)methylation) in yields of 55–90% and with diastereoselectivities of 80 to >97% (Scheme). The primary products 2 – 8 thus obtained are converted to protected β²‐amino acids by standard procedures (Table 1). Many of the DIOZ derivatives are highly crystalline compounds (31 X‐ray crystal structures in Table 2). The chiral auxiliary DIOZ, readily prepared in either enantiomeric form, is recovered with high yield.     

A theoretical study of the large Hg-Hg spin-spin coupling constants in Hg(2)(2+), Hg(3)(2+), and Hg(2)(2+)-crown ether complexes

Nuclear spin-spin coupling constants (1)J(Hg-Hg) in the systems Hg(2)(2+) and Hg(3)(2+) represent the largest coupling constants so far observed in NMR experiments. We have performed a computational study on these ions, on Hg(2)(2+) complexes with 18-crown-6 and 15-crown-5, and on Hg(3)(2+) with solvent molecules and counterions. The results obtained with our recently developed program for the density functional computation of heavy nucleus spin-spin coupling constants are in good agreement with experiments. The data reveal that the bare ions Hg(2)(2+) and Hg(3)(2+) would afford much larger coupling constants than those experimentally observed, with an upper limit of approximately 0.9 MHz for Hg(2)(2+). This limit is much larger than that previously estimated by Hückel theory. It is demonstrated that in solution or due to complexation the experimentally determined values are much smaller than the free ion's coupling constants. With the help of intuitive MO arguments, it is illustrated how the environment strongly reduces the coupling constants in Hg(2)(2+) and Hg(3)(2+). The two-bond coupling constant (2)J(Hg-Hg) in Hg(3)(2+) is also examined.     

OXYGEN QUENCHING OF CHLOROPHYLL FLUORESCENCE IN CHLOROPLASTS

Abstract— Three phases of chlorophyll a fluorescence quenching by O₂ are observed in green plants. The effects of various inhibitors on photosynthetic partial processes in chloroplasts were investigated in attempts to (1) localize the O₂-quenching sites and (2) assess possible physiological significance of O₂-quenching. Our results localize the most sensitive (and presumably functionally important) phase to a site between plastoquinone and the photosystem I acceptor, chlorophyll (P₇₀₀), possibly plastocyanin. It is suggested that PC may transfer electrons to oxygen in addition to P₇₀₀.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.