Trace cocharacters and the Kronecker products of Schur functions

It follows from the theory of trace identities developed by Procesi and Razmyslov that the trace cocharacters arising from the trace identities of the algebra M_r(F) of r×r matrices over a field F of characteristic zero are given by TC_r,n=∑_λΛr(n)χ^λχ^λ where χ^λχ^λ denotes the Kronecker product of the irreducible characters of the symmetric group associated with the partition λ with itself and Λ_r(n) denotes the set of partitions of n with r or fewer parts, i.e. the set of partitions λ=(λ₁λ_k) with kr. We study the behavior of the sequence of trace cocharacters TC_r,n. In particular, we study the behavior of the coefficient of χ^(ν,n−m) in TC_r,n as a function of n where ν=(ν₁ν_k) is some fixed partition of m and n−mν_k. Our main result shows that such coefficients always grow as a polynomial in n of degree r−1.     

A chemoenzymatic synthesis of the linear triquinane (−)-hirsutene and identification of possible precursors to the naturally occurring (+)-enantiomer

An enantiomerically pure cis-1,2-dihydrocatechol, which is readily obtained via a toluene dioxygenase-mediated dihydroxylation of toluene in a whole-cell biotransformation process, has been converted over 17 steps into the linear triquinane (−)-hirsutene. Since the enantiomer of the starting material is also available this work constitutes a formal total synthesis of the naturally occurring (+)-form of hirsutene. Furthermore, minor modifications of the route used here offer the possibility of accessing (+)-hirsutene from the original starting material.     

Conformational and photophysical studies on porphyrin-containing donor-bridge-acceptor compounds. Charge separation in micellar nanoreactors

Photophysical studies with semi-rigid, 1, and flexible, 2, donor-bridge-acceptor (D-b-A2+) molecules with D a porphyrin and A2+ a methyl viologen moiety, were performed in neat polar solvents as well as included in surfactant (DTAB) aqueous and in reverse AOT/n-alkane micelles. The micelles acted as nanoreactors for the photoinduced electron transfer reaction upon laser excitation. In spite of the longer lifetime of the charge separated (CS) state in the semi-rigid tetrad 1(ca. 200 ns vs. ca. 100 ns for the flexible dyad 2), the CS formation quantum yield, for example in acetonitrile, was lower for the former (phi(CS) = 0.13) than for the latter (0.58). Comparison of the time-resolved fluorescence data in neat solvent and in the micelles yielded the phi(CS) values in the dilute micellar solutions. Application of laser-induced optoacoustic spectroscopy at various temperatures to 1 dissolved in a polar organic solvent (benzonitrile, BZN) included in aqueous DTAB nanoreactors afforded structural volume changes for the production in hundreds of ps of the CS state upon excitation of a polar molecule. The contraction during CS formation upon excitation of the collapsed conformer in BZN is attributed to the entering of solvent into the open molecular cavity. The opening upon formation of the CS state due to photoinduced electron transfer in the 1 collapsed conformation arises from the repulsion of the two positively charged ends in this state, as previously calculated. Inclusion of 1 in reverse AOT micelles in various n-alkanes also led to a contraction upon excitation, but the data had much more error due to the limited range of variability of the ratio of thermoelastic parameters. The data obtained with the more flexible "supermolecule" 2 showed the predicted large conformation flexibility of these molecules.     

Thermodynamik und Struktur von Ni1−xTe*

Zusammenfassung DurchEMK-Messungen und Röntgenbeugungsaufnahmen wurden die thermodynamischen und strukturellen Eigenschaften von Ni₁–xTe untersucht. Die Phase Ni₁–xTe reicht von NiTe (x=0) mit dem Strukturtype des NiAs bis zu Ni_0,5Te mit dem Strukturtyp des CdJ₂. Das Phasenfeld zwischen den beiden Verbindungen ist homogen und zeigt umx=0,25 einen Übergang zweiter Ordnung. Bei dieser Zusammensetzung ändert sich der Anstieg der Kurve Ni-Aktivität gegen Zusammensetzung. Auch der Gitterparameterc ₀ ändert sich drastisch, und Beugungslinien der geordneten CdJ₂-Struktur beginnen aufzutreten. Die Intensität der Beugungslinien ändert sich von der NiAs-Struktur bis zur CdJ₂-Struktur gleichmäßig. Istx<0,2, so stimmen die Intensitäten mit denen überein, die man für die NiAs-Struktur berechnet, fürx>0,4 mit denen der CdJ₂-Struktur. Aus den Aktivitätsmessungen wurde die Fehlstellenwechselwirkungsenergie berechnet. In dem Strukturtyp NiAs ist die Wechselwirkungsenergie zwischen zwei Leerstellen gleich Null. Die Leerstellen stoßen einander also weder ab noch ziehen sie einander an, sie sind also statistisch verteilt. Im Bereich der CdJ₂-Struktur ist die Wechselwirkungsenergie zwischen zwei Leerstellen positiv, und zwarE ₁₁=26,5 kcal/Mol. Die Leerstellen stoßen einander ab, und dac ₀/2 kleiner ist alsa ₀, trachten die Leerstellen, benachbarte Schichten zu vermeiden, und bilden so die CdJ₂-Struktur.

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Thermodynamics and Structure of Ni_1–xTe

The thermodynamic properties and structural properties of Ni_1–xTe have been studied using galvanic cell and X-ray diffraction techniques. The Ni_1–xTe phase extends from NiTe (x=0) which has a NiAs type structure to Ni_0.5Te (x=0.5) which has the CdI₂ structure. The phase field between the two compounds is continuous and a second order type transition is taking place aroundx=0.25. At that composition the Ni-activity vs. composition curve changes slope. Thec _o lattice parameter also changes drastically and diffraction lines due to the ordered CdI₂ structure start to appear. The intensity of diffraction lines varies smoothly from the NiAs structure to the CdI₂ structure. The intensities agree with that calculated for NiAs whenx<0.2, it agrees with the CdI₂ intensity whenx>0.4. From the activity measurement, the defect interaction energy was calculated. In the NiAs type structure, the vacancyvacancy interaction energy is zero, the vacancies do not repel or attract each other and thus are random. In the CdI₂ structure region the vacancy-vacancy interaction energy is positiveE ₁₁=26.5 kcal/mole. The vacancies repel each other and asc ₀/2 is smaller thana ₀ the vacancies tend to avoid adjacent layers and thus form the CdI₂ structure.

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Mit 9 Abbildungen

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Herrn Prof. Dr.H. Nowotny gewidmet.

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Diese Arbeit wurde zum Teil durch die National Aeronautics and Space Administration mit dem Grant NSG (T) 43 1101-020 unterstützt.     

The Preparation of Substituted Hydroxyphenyl-pyridyl-ethanols and α-Hydroxyphenyl-α-methylpyridineethanols by the Condensation of 2-, 3-, or 4-Picolyllithium with Select Hydroxy-benzaldehydes and 4-Hydroxyacetophenone

2-, 3-, or 4-Picolyllithium was prepared in excess lithium diiso-propylamide and condensed with several hydroxy-benzaldehydes and 4-hydroxy-acetophenone to afford substituted hydroxyphenyl-pyridyl-ethanols and α-hydroxyphenyl-α-methylpyridineethanols. In two instances. 3-picolyllithium condensed with aldehydes to presumably form the hydroxyphenyl-pyridyl-ethanol, which underwent linear dehydration to the substituted pyridyl-ethylenyl-phenol.     

Automated,high performance,flow-through chemiluminescence microarray for the multiplexed detection of phycotoxins

A novel multiplexed immunoassay for the analysis of phycotoxins in shellfish samples has been developed. Therefore, a regenerable chemiluminescence (CL) microarray was established which is able to analyze automatically three different phycotoxins (domoic acid (DA), okadaic acid (OA) and saxitoxin (STX)) in parallel on the analysis platform MCR3. As a test format an indirect competitive immunoassay format was applied. These phycotoxins were directly immobilized on an epoxy-activated PEG chip surface. The parallel analysis was enabled by the simultaneous addition of all analytes and specific antibodies on one microarray chip. After the competitive reaction, the CL signal was recorded by a CCD camera. Due to the ability to regenerate the toxin microarray, internal calibrations of phycotoxins in parallel were performed using the same microarray chip, which was suitable for 25 consecutive measurements. For the three target phycotoxins multi-analyte calibration curves were generated. In extracted shellfish matrix, the determined LODs for DA, OA and STX with values of 0.5 ± 0.3 μg L⁻¹, 1.0 ± 0.6 μg L⁻¹, and 0.4 ± 0.2 μg L⁻¹ were slightly lower than in PBS buffer. For determination of toxin recoveries, the observed signal loss in the regeneration was corrected. After applying mathematical corrections spiked shellfish samples were quantified with recoveries for DA, OA, and STX of 86.2%, 102.5%, and 61.6%, respectively, in 20 min. This is the first demonstration of an antibody based phycotoxin microarray.     

Water‐Soluble and pH‐Responsive Polymeric Nanotubes from Cyclic Peptide Templates

Water‐soluble organic nanotubes were prepared by convergently conjugating polymers of hydroxyethyl acrylate (HEA) and acrylic acid (AA) to self‐assembling cyclic octapeptides of alternating D and L chirality. The structure of the self‐assembled tubes was characterised in a number of polar solvents, and notably water, by using light scattering, TEM and small angle neutron scattering (SANS) techniques. In addition, the self‐assembly into tubes could be controlled by exploiting the pH responsiveness of acrylic acid polymers.     

A new high: Cannabis as a budding source of carbon-based materials for electrochemical power sources

Cannabis sativa L., a low-cost, fast-growing herbaceous plant, is seeing a resurgence in widespread cultivation as a result of new policies and product drive. Its biodegradable and environmentally benign nature coupled with its high specific surface area and three-dimensional hierarchal structure makes it an excellent candidate for use as a biomass-derived carbon material for electrochemical power sources. It is proposed that this ‘wonder crop’ could have an important role in the energy transition by providing high-functioning carbon-based materials for electrochemistry. In this article, all instances of C. sativa usage in batteries, fuel cells and supercapacitors are discussed with a focus on highlighting the high capacity, rate capability, capacitance, current density and half-wave potential that can be achieved with its utilisation in the field.     

Oxidation of tertiary polycycl1c amines by RuO4

The reactions of certain tertiary polycyclic amines such as N-benzyl-9-azabicy-clo- [3,3,1]-nonane, N-benzyl-5, 6-dihydro-11H-dibenz [b,e] azepine, and N-benzyl-1,2,3,4-tetrahydroisoquinoline with ruthenium tetroxide, taking place in both heterogeneous and homogeneous systems, have made it possible to establish the order of reactivity of the various methylene groups adjacent to the nitrogen with respect to this oxidizing agent.     

Carbaporphyrinoid chemistry has a silver lining! silver(III) oxybenzi-, oxynaphthi-, tropi-, and benzocarbaporphyrins

[structure: see text] Carbaporphyrinoid systems with semiquinone, cycloheptatriene, or indene subunits react under mild conditions with silver(I) acetate to give stable silver(III) organometallic derivatives.