Ab initio investigation of the ground and low-lying states of the diatomic fluorides TiF, VF, CrF, and MnF

The electronic structure of the ground and low-lying states of the diatomic fluorides TiF, VF, CrF, and MnF was examined by multireference and coupled cluster methods in conjunction with extended basis sets. For a total of 34 states we report binding energies, spectroscopic constants, dipole moments, separation energies, and charge distributions. In addition, for all states we have constructed full potential curves. The suggested ground state binding energies of TiF(X (4)Phi), VF(X (5)Pi), CrF(X (6)Sigma(+)), and MnF(X (7)Sigma(+)) are 135, 130, 110, and 108 kcal/mol, respectively, with first excited states A (4)Sigma(-), A (5)Delta, A (6)Pi, and a (5)Sigma(+) about 2, 3, 23, and 19 kcal/mol higher. In essence all our numerical findings are in harmony with experimental results. For all molecules and states studied it is clear that the in situ metal atom (M) shows highly ionic character, therefore the binding is described realistically by M(+)F(-).     

Soft- and hard-agglomerate aerosols made at high temperatures

Criteria for aerosol synthesis of soft-agglomerate, hard-agglomerate, or even nonagglomerate particles are developed on the basis of particle sintering and coalescence. Agglomerate (or aggregate) particles are held together by weak, physical van der Waals forces (soft agglomerates) or by stronger chemical or sintering bonds (hard agglomerates). Accounting for simultaneous gas phase chemical reaction, coagulation, and sintering during the formation and growth of silica (SiO2) nanoparticles by silicon tetrachloride (SiCl4) oxidation and neglecting the spread of particle size distribution, the onset of hard-agglomerate formation is identified at the end of full coalescence, while the onset of soft-agglomerate formation is identified at the end of sintering. Process conditions such as the precursor initial volume fraction, maximum temperature, residence time, and cooling rate are explored, identifying regions for the synthesis of particles with a controlled degree of agglomeration (ratio of collision to primary particle diameters).     

Unravelling the Photoprotection Properties of Garden Cress Sprout Extract

Plants, as with humans, require photoprotection against the potentially damaging effects of overexposure to ultraviolet (UV) radiation. Previously, sinapoyl malate (SM) was identified as the photoprotective agent in thale cress. Here, we seek to identify the photoprotective agent in a similar plant, garden cress, which is currently used in the skincare product Detoxophane nc. To achieve this, we explore the photodynamics of both the garden cress sprout extract and Detoxophane nc with femtosecond transient electronic absorption spectroscopy. With the assistance of liquid chromatography-mass spectrometry, we determine that the main UV-absorbing compound in garden cress sprout extract is SM. Importantly, our studies reveal that the photoprotection properties of the SM in the garden cress sprout extract present in Detoxophane nc are not compromised by the formulation environment. The result suggests that Detoxophane nc containing the garden cress sprout extract may offer additional photoprotection to the end user in the form of a UV filter booster.     

Wheels, wheeling, and the Kontsevich integral of the Unknot

We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne [De]) for the relation between the two natural products on the space of uni-trivalent diagrams. The two formulas use the related notions of “Wheels” and “Wheeing”. We prove these formulas ‘on the level of Lie algebras’ using standard techniques from the theory of Vassiliev invariants and the theory of Lie algebras. In a brief epilogue we report on recent proofs of our full conjectures, by Kontsevich [Ko2] and by DBN, DPT, and T. Q. T. Le, [BLT]. This paper is available electronically     

Investigating the Ultrafast Dynamics and Long-Term Photostability of an Isomer Pair,Usujirene and Palythene,from the Mycosporine-like Amino Acid Family

Mycosporine-like amino acids are a prevalent form of photoprotection in micro- and macro-organisms. Using a combination of natural product extraction/purification and femtosecond transient absorption spectroscopy, we studied the relaxation pathway for a common mycosporine-like amino acid pair, usujirene and its geometric isomer palythene, in the first few nanoseconds following photoexcitation. Our studies show that the electronic excited state lifetimes of these molecules persist for only a few hundred femtoseconds before the excited state population is funneled through an energetically accessible conical intersection with subsequent vibrational energy transfer to the solvent. We found that a minor portion of the isomer pair did not recover to their original state within 3 ns after photoexcitation. We investigated the long-term photostability using continuous irradiation at a single wavelength and with a solar simulator to mimic a more real-life environment; high levels of photostability were observed in both experiments. Finally, we employed computational methods to elucidate the photochemical and photophysical properties of usujirene and palythene as well as to reconcile the photoprotective mechanism.     

Universal elements in some classes of mappings and classes of G-spaces

In the present paper it is proved the existence of topologically universal elements in some classes of mappings and classes of G-spaces generalizing some results from [S.D. Iliadis, Universal Spaces and Mappings, North-Holland Math. Stud., vol. 198, Elsevier, 2005] and [S.D. Iliadis, Universal Borel mappings and Borel actions of groups, Topology Appl., in press, doi:10.1016/j.topol.2007.05.029].     

Nonlinear optical absorption in laser modified regions of fused silica substrates

The presence of strong nonlinear absorption has been observed in laser modified fused silica. Intensity-dependent transmission measurements using 355, 532 and 1064 nm laser pulses were performed in pristine polished regions in fused silica substrates and in locations that were exposed to dielectric breakdown. The experimental results suggest that multiphoton absorption is considerably stronger in the modified regions compared to pristine sites and is strongly dependent on the excitation wavelength.     

Emulation of the evolution of a Bose–Einstein condensate in a time-dependent harmonic trap

We emulate the ground state of a Bose–Einstein condensate in a time-dependent isotropic harmonic trap by constructing analytic simulacra of a transformed wavefunction in the regions around the origin and far from the origin. This transformed wavefunction is obtained through a pseudoconformal transformation and is a function of new spatial and temporal variables, while the simulacra are generalisations of asymptotic solutions of the nonlinear Schrödinger equation and they are matched by requiring continuity not only of the wavefunction and of its slope, but of its curvature as well. The resulting piecewise analytic simulacra coincide almost perfectly with the numerically obtained solutions of the time-dependent nonlinear Schrödinger equation and constitute an easy and accurate analytic method for describing fully the condensate ground state.     

Estimation of an Exponential Quantile under a General Loss and an Alternative Estimator under Quadratic Loss

Estimation of the quantile + of an exponential distribution with parameters (, ) is considered under an arbitrary strictly convex loss function. For obeying a certain condition, the inadmissibility of the best affine equivariant procedure is established by exhibiting a better estimator. The LINEX loss is studied in detail. For quadratic loss, sufficient conditions are given for a scale equivariant estimator to dominate the best affine equivariant one and, when exceeds a lower bound specified below, a new minimax estimator is identified.