Achievable accuracy of parameter estimation for multidimensional NMR experiments

A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer-Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer-Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data.     

A trace formula for Hankel operators

We show that if is an operator valued analytic function in the open right half plane such that the Hankel operator with symbol is of trace-class, then has continuous extension to the imaginary axis,

exists in the trace-class norm, and .

     

Sulfur analysis of conifer needles by inductively coupled plasma atomic emission spectrometry

Zusammenfassung Nadelproben werden in einem Druckaufschlu\gefÄ\ mit SalpetersÄure aufgeschlossen und die erhaltenen Lösungen mittels ICP-AES auf Schwefel analysiert. Die Messung erfolgt bei 182,04 nm in einem mit Stickstoff gespülten Spektrometer. Die Ergebnisse korrelieren gut mit unabhÄngigen Bestimmungen durch Wickbold-Aufschlu\ und Ionen-Chromatographie. Das Verfahren hat den Vorteil, da\ keine Verluste des Analysenelements auftreten und da\ die Aufschlu\lösung auch für die simultane Bestimmung von Spurenmetallen mit der ICP-AES geeignet ist.     

Study of double pomeron exchange in pp collisions at √s=31GeV

The reaction pp→ppπ⁺π^? at √s=31GeV was studied at the Split Field Magnet Facility of the CERN-ISR. Selecting events with two leading protons of x>0.9 and a rapidity gap Δy>2 between the protons and both pions a sample of 720 events is obtained representing a cross section of 25±10μb. The mass distribution of the dipion system, x and p_T distributions for the protons are presented and analyzed for the presence of double pomeron exchange.     

Predicting thermal displacements in modular tool systems

In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite element spindle model. We find that our approach is a powerful tool to describe the relation between temperatures and displacements for simulated data. Next, we analyze the temperature-displacement relationship in a silent real experimental setup, where the tool system is thermally forced. Again, the ACE algorithm is powerful to estimate the deformation with high precision. The corresponding errors obtained by using the nonlinear regression approach are 10-fold lower in comparison to multiple linear regression analysis. Finally, we investigate the thermal behavior of a modular tool system in a working milling machine and again get promising results. The thermally induced errors can be estimated with 1-2 microm accuracy using this nonlinear regression analysis. Therefore, this approach seems to be very useful for the development of new modular tool systems.     

Signatures of carrier-wave Rabi flopping in GaAs

For excitation of the model semiconductor GaAs with optical pulses which are both extremely short ( 5 fs) and extremely intense ( approximately 10(12) W cm(-2)), we can meet the condition that the Rabi frequency becomes comparable to the band gap frequency-a highly unusual and previously inaccessible situation. Specifically, in this regime, we observe carrier-wave Rabi flopping, a novel effect of nonlinear optics which has been predicted theoretically and which is related to the failure of the area theorem.     

The effect of external modulation of the incident intensity on the self-oscillations of an induced absorber (CdS) in a (hybrid-)ring-cavity

In contrast to a dispersive nonlinearity, induced absorption may without a cavity lead to intrinsic optical bistability. If however such an absorber is placed in a ring-cavity with a round trip time larger than the relaxation time constant of the medium, oscillatory instabilities have been (theoretically) predicted. We investigate CdS at room temperature (photo-thermal effects) in a hybrid ring-cavity. A Farey-tree structure of the oscillation period as a function of the incident intensity is observed. In the present paper we discuss the influence an external modulation of the incident intensity has on the oscillation modes both, experimentally and with simple model calculations. Again a Farey-tree structure of the average period of the oscillation modes in multiples of the modulation period is obtained both as a function of the modulation frequency and the modulation amplitude.     

Short‐term dynamics of isotopic composition of leaf‐respired CO2 upon darkening: measurements and implications

Recent advances in understanding the metabolic origin and the temporal dynamics in δ¹³C of dark‐respired CO₂ (δ¹³C_res) have led to an increasing awareness of the importance of plant isotopic fractionation in respiratory processes. Pronounced dynamics in δ¹³C_res have been observed in a number of species and three main hypotheses have been proposed: first, diurnal changes in δ¹³C of respiratory substrates; second, post‐photosynthetic discrimination in respiratory pathways; and third, dynamic decarboxylation of enriched carbon pools during the post‐illumination respiration period. Since different functional groups exhibit distinct diurnal patterns in δ¹³C_res (ranging from 0 to 10‰ diurnal increase), we explored these hypotheses for different ecotypes and environmental (i.e. growth light) conditions. Mass balance calculations revealed that the effect of respiratory substrates on diurnal changes in δ¹³C_res was negligible in all investigated species. Further, rapid post‐illumination changes in δ¹³C_res (30 min), which increased from 2.6‰ to 5‰ over the course of the day, were examined by positional ¹³C‐labelling to quantify changes in pyruvate dehydrogenase (PDH) and Krebs cycle (KC) activity. We investigated the origin of these dynamics with Rayleigh mass balance calculations based on theoretical assumptions on fractionation processes. Neither the estimated changes of PDH and KC, nor decarboxylation of a malate pool entirely explained the observed pattern in δ¹³C_res. However, a Rayleigh fractionation of ¹²C‐discriminating enzymes and/or a rapid decline in the decarboxylation rate of an enriched substrate pool may explain the post‐illumination peak in δ¹³C_res. These results are highly relevant since δ¹³C_res is used in large‐scale carbon cycle studies. Copyright © 2009 John Wiley & Sons, Ltd.     

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