Boundedness of Convolution Operators and Input–Output Maps between Weighted Spaces

We ask when convolution operators with scalar- or operator-valued kernel functions map between weighted L² spaces of Hilbert space-valued functions. For a certain class of decreasing weights, including negative powers (t + a)^−m for example, we solve the one-weight problem completely by using Laplace transforms and Bergman-type spaces of vector-valued analytic functions. For a much more general class of decreasing weights, we solve the one-weight problem for all positive real kernels (also for L^p(w) with p > 1), by results on Steklov operators which generalise the weighted Hardy inequality. When the kernel function is a strongly continuous semigroup of bounded linear Hilbert space operators, which arises from input–output maps of certain linear systems, then the most obvious sufficient condition for boundedness, obtained by taking norm signs inside the integrals, is also necessary in many cases, but not in general. Submitted: July 15, 2007.,Revised: November 19, 2007.,Accepted: December 14, 2007.     

Ring current effects in crystals. Evidence from 13C chemical shift tensors for intermolecular shielding in 4,7-di-t-butylacenaphthene versus 4,7-di-t-butylacenaphthylene

13C chemical shift tensor data from 2D FIREMAT spectra are reported for 4,7-di-t-butylacenaphthene and 4,7-di-t-butylacenaphthylene. In addition, calculations of the chemical shielding tensors were completed at the B3LYP/6-311G** level of theory. While the experimental tensor data on 4,7-di-t-butylacenaphthylene are in agreement with theory and with previous data on polycyclic aromatic hydrocarbons, the experimental and theoretical data on 4,7-di-t-butylacenaphthene lack agreement. Instead, larger than usual differences are observed between the experimental chemical shift components and the chemical shielding tensor components calculated on a single molecule of 4,7-di-t-butylacenaphthene, with a root mean square (rms) error of +/-7.0 ppm. The greatest deviation is concentrated in the component perpendicular to the aromatic plane, with the largest value being a 23 ppm difference between experiment and theory for the 13CH2 carbon delta11 component. These differences are attributed to an intermolecular chemical shift that arises from the graphitelike, stacked arrangement of molecules found in the crystal structure of 4,7-di-t-butylacenaphthene. This conclusion is supported by a calculation on a trimer of molecules, which improves the agreement between experiment and theory for this component by 14 ppm and reduces the overall rms error between experiment and theory to 4.0 ppm. This intermolecular effect may be modeled with the use of nuclei independent chemical shieldings (NICS) calculations and is also observed in the isotropic 1H chemical shift of the CH2 protons as a 4.2 ppm difference between the solution value and the solid-state chemical shift measured via a 13C-1H heteronuclear correlation experiment.     

Vitamin B12 as an allosteric cofactor; dual fluorescence, hysteresis, oscillations and the selection of corrin over porphyrin

Studies of the emission spectra of four Co(III) cobinamides (diaquo-, aquohydroxo-, dihydroxo- and dicyano-) show (1) that the excited states corresponding to the alphabeta and epsilon absorption bands behave like the S(1) and S(2) levels in the non-alternant hydrocarbon azulene (with emission from S(2)> S(1) in violation of Kasha's rule) and (2) that the excited states include a TICT (twisted intramolecular charge transfer) mechanism, as in the simpler cyanines, but where the TICT state gives rise to dual fluorescence instead of cis-trans isomerisation. Combined with the previously reported dual fluorescence from the S(1) level in synthetic metal corrinoids and in the naturally-occurring metal-free corrin, this provides evidence that the existence of an additional (metastable) ground state with a significantly different vibronic splitting and nuclear configuration is an intrinsic property of the basic corrin ligand (irrespective of the nature of the side-chains and the metal ion or even the absence of a metal) which distinguishes it from porphyrin. The occurrence of hysteresis (and its associated oscillations) in redox reactions of the cobinamides involving both the Co(III/II) and Co(II/I) couples indicates that the corrin ligand also has an intrinsic ability to exist in different conformations or "allosteric" forms with differing redox potential, which further distinguishes it from the porphyrin ligand. Possible links between the existence of an additional metastable ground state and of allosteric changes and the likely reasons for the selection of corrin over a porphyrin for the vitamin B(12)-dependent enzymes are discussed.     

Experimental studies of the dynamics of the bond-forming reactions of CF2(2+) with H2O using position-sensitive coincidence spectroscopy

The dynamics of the product channels forming OCF(+)+H(+)+HF and HCF(2) (+)+H(+)+O following the collisions of CF(2) (2+) with H(2)O have been investigated with a new position-sensitive coincidence experiment at a center-of-mass collision energy of 5.6 eV. The results show the formation of OCF(+) occurs via the formation of a doubly charged collision complex [H(2)O-CF(2)](2+) which subsequently undergoes a charge separating dissociation to form H(+) and HOCF(2) (+). The HOCF(2) (+) monocation subsequently fragments to form HF+OCF(+). The lifetimes of the collision complex and the HOCF(2) (+) ion are at least of the order of their rotational period. The kinetic energy release in this reaction indicates that it involves the ground state of CF(2) (2+) and forms the ground electronic states of OCF(+) and HF. The mechanism for forming HCF(2) (+) involves the direct and rapid abstraction of a hydride ion from H(2)O by CF(2) (2+). The resulting OH(+) ion subsequently fragments to H(+)+O, on a time scale at least comparable with its rotational period.     

Competition between DPPC and SDS at the air-aqueous interface

Vibrational sum frequency generation spectroscopy is used to study the interactions of the charged soluble organic surfactant sodium dodecyl sulfate (SDS) with an insoluble 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) monolayer at the air-aqueous interface. Results indicate that the surfactant species compete for surface sites in the mixed system, with a lower monolayer number density of DPPC molecules being observed in the presence of dodecyl sulfate anions at the interface. Spectroscopic results also indicate that fewer dodecyl sulfate chains reside at the interface when the insoluble DPPC film is present. Increased conformational ordering of the acyl chains of both the DPPC molecules and the interfacial dodecyl sulfate anions is observed in the mixed system. Additionally, charged surfactant SDS promotes the alignment of the interfacial water molecules even in the presence of a DPPC monolayer.     

Using stable isotope analyses to identify allochthonous inputs to Lake Naivasha mediated via the hippopotamus gut

The hippopotamus grazes nocturnally on land and resides in water during the day. Much of the ingested material must therefore be defecated directly into the aquatic system and can thus be considered an allochthonous resource available to aquatic consumers. The utility of stable isotope analyses of carbon and nitrogen to distinguish hippo faecal matter from other potential basal resources was tested at Lake Naivasha, Kenya. Hippopotami proved faithful to a short grass diet although supplementary grazing of aquatic macrophytes was observed. The typical isotopic ratios of C4 grasses ingested were not altered substantially by gut processes, and were clearly distinct from algal and aquatic macrophyte isotopic ratios. However, marginal plants such as Cyperus papyrus exhibit C4 ratios, and so the technique is suitable only for use in localities where 'contamination' from such sources is negligible.     

A device for feline head positioning and stabilization during magnetic resonance imaging

Minimization of head movement and reproduction of standard head positions are essential for reliable brain functional magnetic resonance imaging. Devices for stabilization and alignment of feline preparations are not available currently. We describe a system that involves minimal surgery, allows for both acute and chronic atraumatic positioning, and has the potential to be used for unanesthetized animals. The device uses non-metallic materials and stabilizes the head by means of an apparatus that fixes the head with nylon screws and dental cement in the frontal sinuses. Application of the head-stabilizing device decreases head movements by more than a factor of ten. Anatomical images show that this device provides 3 dimensional head placement at a precision comparable to that of a stereotactic frame, i.e. within 1 mm.     

Origin of antimony segregation in GaInSb/InAs strained-layer superlattices

We show how cross-sectional scanning tunneling microscopy may be used to reconstruct the Sb segregation profiles in GaInSb /InAs strained-layer superlattices. These profiles are accurately described by a one-dimensional model parametrizing the spatial evolution of an Sb seed at the InAs-on-GaInSb interface in terms of two-anion-layer exchange. We argue that the segregation seed, which decreases from 2 / 3 to 1 / 2 monolayer when growth conditions are made less anion rich, has its origin in the Sb-bilayer reconstruction maintained during GaInSb epitaxy.