Parabolic Differential Equations in Ordered Banach Spaces of Bounded Functions

Let A be a set, and let E be the Banach space of bounded functions : A R, equipped with its natural order. With a rectangle R = (a,b) × (0,T] let F(x,t,) : R × E E be a bounded, continuous function satisfying a local Hölder condition and being quasimonotone increasing with respect to . Then there exists a solution u: [a,b] × [0,T] E of the problem ut(x,t) – uxx(x,t) = F(x,t,u(x,t)) ((x,t) R), u(x,t) = 0 ((x,t) R R).     

Analysis of the major chiral compounds of Artemisia herba-alba essential oils (EOs) using reconstructed vibrational circular dichroism (VCD) spectra: En route to a VCD chiral signature of EOs

An unprecedented methodology was developed to simultaneously assign the relative percentages of the major chiral compounds and their prevailing enantiomeric form in crude essential oils (EOs). In a first step the infrared (IR) and vibrational circular dichroism (VCD) spectra of the crude essential oils were recorded and in a second step they were modelized as a linear weighted combination of the IR and VCD spectra of the individual spectra of pure enantiomer of the major chiral compounds present in the EOs. The VCD spectra of enantiomer of known enantiomeric excess shall be recorded if they are not yet available in a library of VCD spectra. For IR, the spectra of pure enantiomer or racemic mixture can be used. The full spectra modelizations were performed using a well known and powerful mathematical model (least square estimation: LSE) which resulted in a weighting of each contributing compound. For VCD modelization, the absolute value of each weighting represented the percentage of the associate compound while the attached sign addressed the correctness of the enantiomeric form used to build the model. As an example, a model built with the non-prevailing enantiomer will show a negative sign of the weighting value. For IR spectra modelization, the absolute value of each weighting represented the percentage of the compounds without of course accounting for the chirality of the prevailing enantiomers. Comparison of the weighting values issuing from IR and VCD spectra modelizations is a valuable source of information: if they are identical, the EOs are composed of nearly pure enantiomers, if they are different the chiral compounds of the EOs are not in an optically pure form. The method was applied on four samples of essential oil of Artemisia herba-alba in which the three major compounds namely (−)-α-thujone, (+)-β-thujone and (−)-camphor were found in different proportions as determined by GC–MS and chiral HPLC using polarimetric detector. In order to validate the methodology, the modelization of the VCD spectra was performed on purpose using the individual VCD spectra of (−)-α-thujone, (+)-β-thujone and (+)-camphor instead of (−)-camphor. During this work, the absolute configurations of (−)-α-thujone and (+)-β-thujone were confirmed by comparison of experimental and calculated VCD spectra as being (1S,4R,5R) and (1S,4S,5R) respectively.     

Multilayer Laue Lens: A Brief History and Current Status

X-rays are intrinsically capable of being used for the study of non-periodic objects with atomic resolution, with high penetration, in applied electromagnetic fields, and in fluids and gases. For direct imaging via nanofocused X-ray beams, reflective [1 K. Yamauchi, Journal of Physics: Condensed Matter 23(39), 394206 (2011).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], refractive [2 C.G. Schroer, Applied Physics Letters 87(12), 124103–3 (2005).[Crossref], [Web of Science ®] , [Google Scholar]], and diffractive [3 K. Burkhard, Journal of Physics: Condensed Matter 23(8), 083002 (2011).[Crossref], [Web of Science ®] , [Google Scholar], 4 J. Kirz, C. Jacobsen, and M. Howells, Quarterly Reviews of Biophysics 28(01), 33–130 (1995).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] optics are used in various approaches for high-resolution imaging. Diffractive X-ray optics are endowed with the highest numerical aperture, in principle allowing focusing of X-rays to sub-nanometer dimensions. Lithographically produced Fresnel zone plates (FZP) find broad deployment around the globe, in both nanofocusing and full-field imaging approaches, and have, for many years, been workhorse optics in both synchrotron-based and laboratory-based X-ray imaging systems [4 J. Kirz, C. Jacobsen, and M. Howells, Quarterly Reviews of Biophysics 28(01), 33–130 (1995).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. A FZP consists of a series of radially symmetric rings, which are known as Fresnel zones, which alternate between transparent and opaque. Radiation traversing into the FZP diffracts around the opaque zones, which are placed in an arrangement where light constructively interferes at the focal plane.     

A Stable Crystalline Triarylphosphine Oxide Radical Anion

Triarylphosphine oxides (Ar₃P=O) are being intensely studied as electron‐accepting (n‐type) materials. Despite the widespread application of these compounds as electron conductors, experimental data regarding the structural and electronic properties of their negatively charged states remain scarce owing to their propensity for follow‐up chemistry. Herein, a carefully designed triarylphosphine oxide scaffold is disclosed that comprises sterically demanding spirofluorenyl moieties to shield the central phosphoryl (P=O) moiety. This compound undergoes chemical one‐electron reduction to afford an exceptionally stable radical anion, which was isolated and characterized by X‐ray crystallography for the very first time. The experimental data, corroborated by computational studies, shall allow for the construction of phosphine oxide materials with enhanced stability.     

DNA‐Accelerated Catalysis of Carbene‐Transfer Reactions by a DNA/Cationic Iron Porphyrin Hybrid

A novel DNA‐based hybrid catalyst comprised of salmon testes DNA and an iron(III) complex of a cationic meso‐tetrakis(N‐alkylpyridyl)porphyrin was developed. When the N‐methyl substituents were placed at the ortho position with respect to the porphyrin ring, high reactivity in catalytic carbene‐transfer reactions was observed under mild conditions, as demonstrated in the catalytic enantioselective cyclopropanation of styrene derivatives with ethyl diazoacetate (EDA) as the carbene precursor. A remarkable feature of this catalytic system is the large DNA‐induced rate acceleration observed in this reaction and the related dimerization of EDA. It is proposed that high effective molarity of all components of the reaction in or near the DNA is one of the key contributors to this unique reactivity. This study demonstrates that the concept of DNA‐based asymmetric catalysis can be expanded into the realm of organometallic chemistry.     

Site‐Specific Substitution Preferences in the Solid Solutions Li12Si7–xGex,Li12–yNaySi7, Na7LiSi8–zGez,and Li3NaSi6–vGev

The mixed silicide‐germanides Li₁₂Si_7–xGe_x, Na₇LiSi_8–zGe_z, and Li₃NaSi_6–vGe_v which could serve as potential precursors for Si_1–xGe_x materials were synthesized and characterized by X‐ray diffraction methods. The full solid solution series Li₁₂Si_7–xGe_x (0 ≤ x ≤ 7) is easily accessible from the elements and features preferential occupation of the more negatively charged crystallographic tetrel positions by Ge, which is the more electronegative element. In case of Na₇LiSi_8–zGe_z a broad solid solution range of 1.3 ≤ x ≤ 8 is available but the ternary silicide Na₇LiSi₈ could not be obtained by the tested methods of synthesis. The solubility of Ge in Li₃NaSi_6–vGe_v is highly limited to a maximum of v ≈ 0.5, and again the formally more negatively charged tetrel positions are preferred by Ge. Additionally, the two crystallographic Li positions in Li₁₂Si₇ with unusually large displacement parameters can be partially substituted by Na in Li_12–yNa_ySi₇ with 0 ≤ y ≤ 0.6. The statistical mixing of Li and Na in this solid solution contrasts the typical ordering of Li and Na in most ternary tetrelides.     

Solid-state conformational heterogeneity of the 2,2,5,5-tetramethyl-3,4-hexandione monohydrazone: X-ray diffraction and MAS NMR experiments

The X-ray diffraction study of the 2,2,5,5-tetramethyl-3,4-hexandione mono-hydrazone 1 shows a solid solution of two screwed conformers in the crystal. In each of these conformers, the conjugated C=O and C=N double bonds have an approximately perpendicular orientation with = 101.1°(2) and –93.4°(2), respectively. AM1 theoretical calculations give the same result for the isolated molecule. The calculated rotational barrier around the central single bond of the conjugated moiety is about 45.98 kJ mol^–1 which is higher than the classical values observed for 1,3 conjugated systems (28.42 kJ mol^–1 in the 1,3-butadiene). Variable temperature ¹³C CPMAS NMR experiments show hindered rotation around the COC(CH₃)₃ tert-butyl group in the solid state. 1 crystallizes in the triclinic space group P ₁ with a = 10.106(1)Å, b = 11.698(1)Å, c = 12.313(1)Å, = 62.108(1)° = 70.517(1)° = 66.052(1), V = 1157.0(3)ų, D _calc = 1.06 with Z = 4.     

CrAsH-quantum dot nanohybrids for smart targeting of proteins

Smart nanohybrids were prepared by conjugation of CrAsH to hydrosoluble and biocompatible quantum dots (QDs). The resulting probes were shown to bind efficiently and selectively to Cys-tagged proteins. The interaction with the protein was detected by an increase of the fluorescence emission of CrAsH. While the latter faded rapidly under continuous excitation, emission of the QD remained unaffected. The persistent fluorescence of the QD should thus allow extended monitoring of the target protein.