Special vekua equations with singular coefficients

Special equations of Vekua-type with singular coefficients are considered. As a first step we study the influence of the coefficients of model equations on the choice of the function spaces for its solutions and on the boundary conditions. As an application we sketch the consideration of boundary value problems for Vekua equations with variable coefficients having a strong singularity at z =0     

Structural and orientational properties of the ferro, antiferroelectric, and re-entrant smectic C phases of ZLL7/ by deuterium NMR and other experimental techniques

In this work, two selectively deuterium-labeled isotopomers of the (S)-2-methylbutyl- [4'-(4' '-heptyloxyphenyl)-benzoyl-4-oxy-(S)-2-((S)-2')-benzoyl)-propionyl)]-propionate (ZLL 7/), one labeled on the phenyl ring (ZLL 7/-phe-D2) and the other one on the biphenyl fragment (ZLL 7/-biphe-D2), have been investigated by deuterium NMR (DNMR) spectroscopy and other experimental techniques. These compounds possess the paraelectric SmA, the ferroelectric SmC, the antiferroelectric SmC(A), the re-entrant ferroelectric SmC(re), and the ferroelectric hexatic phases down to room temperature. The orientational ordering properties of the two labeled fragments have been determined by means of DNMR, and the mesophase behavior at two magnetic fields is discussed. In particular, the effect of the magnetic field on the supramolecular structure of the SmC and SmC(re) phases is commented. This study revealed to be useful to understand the structural and conformational properties of the ferroelectric/antiferroelectric/re-entrant/hexatic smectic phases. Mesomorphic properties, spontaneous tilt angle, polarization, and layer spacing have been studied for the labeled materials and compared with those obtained for the nonlabeled compound. The two self-consistent set of data, from optical and DNMR measurements and X-ray results, allow us to associate at the transition from the SmC to the SmC(A) phase a change of the molecular conformation.     

Selective detection of ordered sodium signals via the central transition

Given the correlation between the concentrations of ordered (23)Na and the onset of tissue disorders, the ability to select the signal from ordered (23)Na over that of free (23)Na is of particular importance and can greatly enhance the potential of (23)Na-MRI as a diagnostic tool. Here, we describe a simple method that selectively detects the central transition of ordered sodium while minimizing the signal from free sodium. Our method relies upon the influence of the quadrupolar interaction on nutation frequencies and may also benefit solid-state imaging experiments. Both a liquid crystalline environment and a cartilage sample are used to demonstrate a clean separation between anisotropic and isotropic regions in the experiments.     

Subquasivarieties of implicative locally‐finite quasivarieties

A quasivariety is said to be implicative if it is generated by a class of algebras with equationally‐definable implication of equalities. Implicative finitely‐generated quasivarieties appear naturally within logic, for instance, as equivalent quasivarieties of Gentzen‐style calculi for finitely‐valued propositional logics with equality determinant (cf. [17], [18, Subsection 7.5] and Section A). Furthermore, any discriminator quasivariety is implicative. We prove that, for any implicative locally‐finite quasivariety ? and any skeleton S of the class of all finite ?‐simple members of ?, the image of the first component of a natural Galois connection between the dual poset of subquasivarieties of ? and the poset of all sets of finite subsets of S is the closure system of all U_S‐ideals of the poset 〈S, ?〉, where ? is the embeddability relation and U_S is the up‐set on S constituted by all members of S having a one‐element subalgebra, with closure basis determined by the sets of all principal and non‐empty finitely‐generated up‐sets on S. It is also shown that the first component of the Galois connection under consideration is injective if and only if, for each finite sequence

     

Hydrothermal Synthesis and Crystal Structure of Novel Alkali Trimolybdates

Novel alkali trimolybdates of the triclinic (M, M′)₂Mo₃O₁₀ (M = Rb; M′ = K, Cs) type were obtained through a systematic hydrothermal approach based on the reaction of MoO₃ with alkali halide solutions at 180 °C. The crystal structures were determined from X‐ray single crystal data. The alkali trimolybdates extend the family of known alkali trimolybdates in an unexpected fashion, because they contain a distorted variation of [Mo₃O₁₀]^2? chains as a key structural motif that has only been found in a single compound before, namely ethylenediammonium trimolybdate, (C₂H₁₀N₂)[Mo₃O₁₀]. The applied hydrothermal strategy is discussed in the general context of systematic pathways to polyoxomolybdates. Furthermore, the templating role of the alkali cations and their interaction with the polyoxomolybdate surroundings is compared to (C₂H₁₀N₂)[Mo₃O₁₀] in terms of electrostatic calculations.     

GC-FTIR and GC-MS in odour analysis of essential oils

The analysis of odour components in East Indian Sandalwood Oil (Santalum album L.) and in Patchouli Oil (Pogostemon cablin Benth.) based on GC-, GC-FTIR- and GC-MS-data resulted in the identification of-santalene,-santalal,-santalal, epi--santalal,-santalol,-santalol, (E)--santalol,-bergamotol and spirosantalol in Sandalwood Oil and of (–)-patchoulol,-guaiene,-patchoulene, seychellene,-bulnesene, norpatchoulenol and pogostol in Patchouli Oil as the most intense aroma compounds of these oils.     

Cis-Cycloprolylprolin-Anion-ein konfigurationsstabiles Carbanion

The racemisation ofcyclo-(l-Pro?l-Pro) (2) with metal amides in liq. ammonia was examined. The K-kation causes more extensive racemisation than Na-kation, which in turn is more effective than Li⁺. This, the racemisation of2 int-butyl alcohol with K⁺C₆H₅O^? and the data gained from corresponding deuterated medium show that the racemisation of2 proceeds in two steps: in the first, the less stabletrans-cyclo-(l-Pro?d-Pro) (3) is formed, followed by the rapid conversion of3 to a mixture ofcyclo-(l-Pro?l-Pro) andcyclo-(d-Pro?d-Pro) in the second step.     

Novel lithocholaphanes: Syntheses, NMR, MS, and molecular modeling studies

Novel head-to-head lithocholaphanes 6 and 11 have been synthesized via precursors 1–5 and 7–10 with overall good yields, and characterized by ¹H, ¹³C, and ¹⁵N NMR spectroscopy, ESI-TOF mass spectrometry, thermal analysis, and molecular modeling. In addition, the binding abilities of 6 and 11 towards alkali metal cations have been investigated via competitive complexation studies using equimolar mixtures of Li⁺, Na⁺, K⁺, and Rb⁺-cations, and cholaphanes 6 and 11. The formation of cation–cholaphane adducts was detected by ESI-TOF mass spectrometry. The trends in these comparative binding studies are nicely reproduced theoretically with PM3 energetically optimized structures of 6 and 11 and their interaction energies with alkali metal cations calculated by molecular mechanics. Cholaphane 11 possessing a peptoid type structural fragment, –(CH₂CONHCH₂CH₂)₂O–, as a coordination sphere, shows binding tendency towards lithium and sodium cations, whereas 6 possessing an ester type, –(CH₂OCOCH₂)₂O–, moiety and a bigger cavity size than 11, shows merely a tendency towards bigger alkali metal cations, potassium and rubidium.     

Intra-dot relaxation and dephasing rates from time-resolved photoluminescence from InAs quantum dot ensembles

An ensemble of InAs quantum dots with ground state transition energies centered at 1.216 eV and density 10¹¹dots/cm² has been studied by time-resolved photoluminescence (PL). The wavelength of the 100-fs excitation pulse was tuned through the ground (excited) state transitions, resulting in resonant (optical phonon sideband) PL. The decay of the PL was time resolved with a streak camera in the interval 1.5–3 ns to avoid scattered laser light. The intensity of the PL was recorded with its polarization both parallel with and perpendicular to the excitation polarization (along one of the crystal’s cleave axes); the ratio is 2.22 at low temperatures and low excitation. A phenomenological rate equation analysis is made, separating the excitations into two classes, one polarized along the excitation polarization and the other unpolarized (either that way immediately after the excitation pulse or scattered from the first class). Excellent fits to the data lead to the conclusion that both classes decay radiatively with a lifetime of 1 ns, and a transfer from the polarized to the unpolarized species takes place with a distribution time of 12 ns at low temperatures and low excitation, dropping rapidly toward zero for temperatures above 30 K and for intense excitation levels. The polarization of a coherently excited ground state exciton should dephase with a rate equal to the sum of the radiative rate plus the inverse of this distribution time.