Zur Untersuchung von Zuckersirup

Ohne Zusammenfassung     

An extended Heath–Jarrow–Morton risk-neutral drift

Using a finite dimensional Hilbert space framework, this work proposes a new derivation of the HJM [D. Heath, R. Jarrow, A. Morton, Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation, Econometrica 60 (1992) 77–105] risk-neutral drift that takes into account nonzero instantaneous correlations between factors. The results obtained generalize the original HJM risk-neutral drift and provide an approach by which interest rate derivatives can be priced using functions of directly observable factors.     

A Computationally Motivated Definition Of Parametric Estimation And Its Applications To The Gaussian Distribution

We introduce a treatment of parametric estimation in which optimality of an estimator is measured in probability rather than in variance (the measure for which the strongest general results are known in statistics). Our motivation is that the quality of an approximation algorithm is measured by the probability that it fails to approximate the desired quantity within a set tolerance. We concentrate on the Gaussian distribution and show that the sample mean is the unique “best” estimator, in probability, for the mean of a Gaussian distribution. We also extend this method to general penalty functions and to multidimensional spherically symmetric Gaussians. The algorithmic significance of studying the Gaussian distribution is established by showing that determining the average matching size in a graph is #P-hard, and moreover approximating it reduces to estimating the mean of a random variable that (under some mild conditions) has a distribution closely approximating a Gaussian. This random variable is (essentially) polynomial time samplable, thereby yielding an FPRAS for the problem.     

Preparation and characterization of copper(II) tetrasulfonated phthalocyanine nanoparticles formed by laser ablation in poor solvents

Laser irradiation of copper(II) tetrasulfonated phthalocyanine (CuTsPc) microcrystals in poor organic solvents such as methanol, 2-methyl-2-propanol, ethanol, tetrahydrofuran, and acetone has produced CuTsPc nanoparticles with 15–112 nm in diameter. Field emission scanning electron microscopy (FESEM) images have shown the formation of CuTsPc nanoparticles in poor organic solvents used in this work. The mean diameters of CuTsPc nanoparticles obtained from transmission electron microscopy (TEM) images in methanol, 2-methyl-2-propanol, ethanol, tetrahydrofuran, and acetone were determined to be 26, 36, 35, 86, and 78 nm, respectively. A correlation between the size of CuTsPc nanoparticles and a solvent polarity could be found in this work.     

Examination of Selectivities of Thermally Stable Geminal Dicationic Ionic Liquids by Structural Modification

Dicationic ionic liquids (ILs) are widely used as gas chromatography (GC) stationary phases as they show higher thermal stabilities, variety of polarities, and unique selectivities towards certain compounds. An important aspect contributing to them is that they show multiple solvation interactions compared to the traditional GC stationary phases. Dicationic ILs are considered as combination of three structural moieties: (1) cationic head groups; (2) a linkage chain; and (3) the counter anions. Modifications in these structural moieties can alter the chromatographic properties of IL stationary phases. In this study, a series of nine thermally stable IL stationary phases were synthesized by the combination of five different cations, two different linkage chains, and two different anions. Different test mixtures composed of a variety of compounds having different functional groups and polarities were analyzed on these columns. A comparison of the separation patterns of these different compounds on nine different IL columns provided some insights about the effects of structural modifications on the selectivities and polarities of dicationic ILs.     

Are there reliable DFT approaches for 13C NMR chemical shift predictions of fullerene C60 derivatives?

The relationships between experimental and theoretical ¹³C NMR chemical shifts of a pristine fullerene C₆₀, monoadducts from [2 + n] cycloaddition (n = 1–3), and one [2 + 1] bis‐adduct are systematically analyzed for the first time by using diverse quantum‐chemical levels of theory. These levels involved B3LYP, B3PW91, B97‐2, mPW1PW91, PBE1PBE, and X3LYP hybrid functionals combined with 3‐21G, 6‐31G, 6‐31G(d), 6‐31G(d,p), 6‐31G(d,2p), LanL2DZ, and SDDAll basis sets. X3LYP/6‐31G approach is determined to have the lowest deviations from the ¹³C NMR experimental data compared to the other methods for all the fullerene compounds (mean absolute error value is 0.856 ppm and root mean squared error value is 1.197 ppm). The highest deviations are characteristic for α (sp² C2/C5/C8/C10) and β (sp² C6/C7/C11/C12) carbon atoms relative to a functionalization site and for those (sp³ C1/C9) directly attached with a side fragment in the [2 + n] monoadducts (n = 1–3). A probable reason of such deviation is that the approaches do not take into account a contribution of paramagnetic ring currents to ¹³C NMR chemical shifts. The results will be useful in design of novel fullerene derivatives and in performing unambiguous ¹³C NMR chemical shift assignments with modern quantum chemistry calculations.     

Stimulated creation of quanta during inflation and the observable universe

Inflation provides a natural mechanism to account for the origin of cosmic structures. The generation of primordial inhomogeneities during inflation can be understood via the spontaneous creation of quanta from the vacuum. We show that when the corresponding stimulated creation of quanta is considered, the characteristics of the state of the universe at the onset of inflation are not diluted by the inflationary expansion and can be imprinted in the spectrum of primordial inhomogeneities. The non-gaussianities (particularly in the so-called squeezed configuration) in the cosmic microwave background and galaxy distribution can then tell us about the state of the universe that existed at the time when quantum field theory in curved spacetime first emerged as a plausible effective theory.     

Theoretical studies on aromaticity of selected hydroxypyrones. Part 3#. Chelatoaromaticity phenomenon in metalcomplexes of hydroxypyrones

The aim of this project is to study the aromatic properties of various forms (neutral, cationic, and anionic) of selected hydroxypyrones (pyromeconic acid, maltol, and ethylmaltol) and their metalcomplexes with aluminum, gallium, and indium ions. Aromaticity of hydroxypyrone metalcomplexes is important because it can influence the stability of such complexes, which is crucial for their applications in medicinal and environmental chemistry. Results from ten different indices of aromaticity (HOMA, NICS(0), NICS(1), NICS_scan, ASE_iso, PDI, FLU, I_ring, MCI, and KMCI) show that aromaticity in hydroxypyrones decreases in the order cations > neutral molecules > anions. Performed calculations situate the aromaticities of ligands in metalcomplexes close to their respective cations. This means that complexation causes a significant increase of the aromaticity of ligands, which stabilizes formed chelatocomplexes. On the other hand, we clearly show that rings that are involved in binding metal ions are not aromatic. Copyright © 2010 John Wiley & Sons, Ltd.     

A supramolecular assembly containing an unusually short n‐h…n hydrogen bond ‐ an x‐ray and neutron diffraction study

A supramolecular assembly formed between phthalimide and 2‐guanidinobenzimidazole, containing a short 2.692(4)AR N‐H…N hydrogen bond, is reported. The crystal structure of this species was determined by both X‐ray and neutron diffraction. The diffraction data reveal that the proton involved in the short hydrogen bond has been transferred from the phthalimide to the guanidinobenzimidazole to form an ion pair. There is also an interesting stacking interaction between the atoms involved in the short hydrogen bond and the π system of a phthalimide molecule that is approximately 3.3 Å away. The structure is compared with the structure of a similar assembly formed between 4‐nitrophthalimide and 2‐guanidinobenzimidazole.