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.     

Simultaneous determination of 1H-1H and 1H-13C residual dipolar couplings in a chiral liquid crystal solvent using a natural abundance HSQC experiment

A high-resolution, phase-sensitive, natural abundance F2-coupled 1H-13C HSQC (F2HSQC) NMR experiment was developed to measure simultaneously both (n)D(HH) and 1D(CH) residual dipolar couplings (RDCs) of small molecules present in a chiral polypeptide liquid crystal solvent system composed of poly-gamma-benzyl-L-glutamate (PBLG) in CDCl3. Because this is an indirect-detection NMR experiment, the relatively small amount of sample (7.5 mg in this study) and short acquisition times (5 h) that are required make this HSQC experiment well suited for samples that are either limited in solubility or in quantity or require short analysis times. The F2HSQC experiment can be performed without any specialized equipment or sample modification and can enhance our ability to measure RDCs accurately and rapidly in polypeptide liquid crystal solvents.     

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.     

A numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin's Form II gradient elastic theory

Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlin's Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlin's elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.     

Ab initio and density functional study of substituent effects in halogenated cations of alkenes

A theoretical study of the halogenated cations of mono-, di-, tri- and tetramethyl-substituted ethylenes, C₃H₆X⁺, C₄H₈X⁺, C₅H₁₀X⁺ and C₆H₁₂X⁺, X=F, Cl, Br, have been studied at the ab initio MP2 and density functional B3LYP levels of theory implementing 6-311++G(d,p) basis set. The potential energy surfaces of all molecules under investigation have been scanned and the ¹³C and ¹H NMR chemical shifts for all the bridged halonium ions studied have been calculated using the GIAO method at the B3LYP level. The calculated halogen binding energies in the halonium ions have been correlated with the experimental rates of chlorination and bromination of the corresponding alkenes. The computed hydride affinities and the NICS values for the bridged cations show that the bromo cations are more stable than the analogous chloro and fluoro cations.     

Reaction of graphite fluoride with NaOH-KOH eutectic

Graphite fluoride has been generally considered chemically inert against strong alkalis under ambient conditions. In the present study we demonstrate that treatment of graphite fluoride with eutectic NaOH-KOH mixture at 250 °C induces dramatic structural and textural changes in the solid as evidenced by XRD, FT-IR, Raman, UV-vis absorption and fluorescence and microscopy techniques (TEM, AFM). The reaction proceeds in the molten state leading to water-soluble, graphitized carbon particles which unlike graphite fluoride, adopt a variety of morphologies, like platy, tetragonal, triangular, discoid and spherical. The resulting carbon particles are dispersible in water and fluoresce under UV excitation.     

Representations and properties of the W-Weighted Drazin inverse

Several new representations of the W-weighted Drazin inverse are introduced. These representations are expressed in terms of various matrix powers as well as in terms of matrix products involving the Moore–Penrose inverse and the usual matrix inverse. Also, the properties of various generalized inverses which arise from derived representations are investigated. The computational complexity and efficiency of the proposed representations are considered. Representations are tested and compared among themselves in a substantial number of randomly generated test examples.     

On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope

In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope. Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints, a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means of an example from the literature.