Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

Design and Test of a 0.5 THz Dipole Antenna With Integrated Schottky Diode Detector on a High Dielectric Constant Ceramic Electromagnetic Bandgap Substrate

This paper presents the first analysis of the input impedance and radiation properties of a dipole antenna, placed on top of Fan 's three-dimensional electromagnetic bandgap (EBG) structure, (Applied Physics Letters, 1994) constructed using a high dielectric constant ceramic. The best position of the dipole on the EBG surface is determined following impedance and radiation pattern analyses. Based on this optimum configuration an integrated Schottky heterodyne detector was designed, manufactured and tested from 0.48 to 0.52 THz. The main antenna features were not degraded by the high dielectric constant substrate due to the use of the EBG approach. Measured radiation patterns are in good agreement with the predicted ones.

The Deep Blue Color of HD 189733b: Albedo Measurements with Hubble Space Telescope/Space Telescope Imaging Spectrograph at Visible Wavelengths

We present a secondary eclipse observation for the hot Jupiter HD 189733b across the wavelength range 290-570 nm made using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope. We measure geometric albedos of Ag = 0.40 ± 0.12 across 290-450 nm and Ag < 0.12 across 450-570 nm at 1σ confidence. The albedo decrease toward longer wavelengths is also apparent when using six wavelength bins over the same wavelength range. This can be interpreted as evidence for optically thick reflective clouds on the dayside hemisphere with sodium absorption suppressing the scattered light signal beyond ~450 nm. Our best-fit albedo values imply that HD 189733b would appear a deep blue color at visible wavelengths.

Antinociceptive effects of three escalating dexmedetomidine and lignocaine constant rate infusions in conscious horses.

Dexmedetomidine and lignocaine IV are used clinically to provide analgesia in horses. The aims of this study were to investigate the antinociceptive effects, plasma concentrations and sedative effects of 2, 4 and 6 µg/kg/h dexmedetomidine IV, with a bolus of 0.96 µg/kg preceding each continuous rate infusion (CRI), and 20, 40 and 60 µg/kg/min lignocaine IV, with a bolus of 550 µg/kg preceding each CRI, in 10 Swiss Warmblood horses. Electrically elicited nociceptive withdrawal reflexes were evaluated by deltoid muscle electromyography. Nociceptive threshold and tolerance were determined by electromyography and behaviour following single and repeated stimulation. Plasma concentrations of drugs were determined by liquid chromatography and mass spectrometry. Sedation was scored on a visual analogue scale. Dexmedetomidine increased nociceptive threshold to single and repeated stimulation for all CRIs, except at 2 µg/kg/h, where no increase in single stimulation nociceptive threshold was observed. Dexmedetomidine increased nociceptive tolerance to single and repeated stimulation at all CRIs. There was large individual variability in dexmedetomidine plasma concentrations and levels of sedation; the median plasma concentration providing antinociceptive effects to all recorded parameters was 0.15 ng/mL, with a range from <0.02 ng/mL (below the lower limit of quantification) to 0.25 ng/mL. Lignocaine increased nociceptive threshold and tolerance to single and repeated stimulation at CRIs of 40 and 60 µg/kg/min, corresponding to plasma lignocaine concentrations >600 ng/mL. Only nociceptive tolerance to repeated stimulation increased at 20 µg/kg/min lignocaine. Lignocaine at 40 µg/kg/min and dexmedetomidine at 4 µg/kg/h were the lowest CRIs resulting in consistent antinociception. Lignocaine did not induce significant sedation.

The pharmacokinetics of dexmedetomidine administered as a constant rate infusion in horses.

Dexmedetomidine, the most selective α2 -adrenoceptor agonist in clinical use, is increasingly being used in both conscious and anaesthetized horses; however, the pharmacokinetics and sedative effects of this drug administered alone as an infusion are not previously described in horses. Seven horses received an infusion of 8 μg dexmedetomidine/kg/h for 150 min, venous blood samples were collected, and dexmedetomidine concentrations were assayed using liquid chromatography-mass spectrometry (LC/MS) and analyzed using noncompartmental pharmacokinetic analysis. Sedation was scored as the distance from the lower lip of the horse to the ground measured in centimetre. The harmonic mean (SD) plasma elimination half-life (Lambda z half-life) for dexmedetomidine was 20.9 (5.1) min, clearance (Cl) was 0.3 (0.20) L/min/kg, and volume of distribution at steady-state (Vdss ) was 13.7 (7.9) L/kg. There was a considerable individual variation in the concentration of dexmedetomidine vs. time profile. The level of sedation covaried with the plasma concentration of dexmedetomidine. This implies that for clinical use of dexmedetomidine constant rate infusion in conscious horses, infusion rates can be easily adjusted to effect, and this is preferable to an infusion at a predetermined value.

Accurate rotational constant and bond lengths of hexafluorobenzene by femtosecond rotational Raman coherence spectroscopy and ab initio calculations

The gas-phase rotational motion of hexafluorobenzene has been measured in real time using femtosecond (fs) time-resolved rotational Raman coherence spectroscopy (RR-RCS) at T = 100 and 295 K. This four-wave mixing method allows to probe the rotation of non-polar gas-phase molecules with fs time resolution over times up to ∼5 ns. The ground state rotational constant of hexafluorobenzene is determined as B 0 = 1029.740(28) MHz (2σ uncertainty) from RR-RCS transients measured in a pulsed seeded supersonic jet, where essentially only the v = 0 state is populated. Using this B 0 value, RR-RCS measurements in a room temperature gas cell give the rotational constants B v of the five lowest-lying thermally populated vibrationally excited states ν7/8, ν9, ν11/12, ν13, and ν14/15. Their B v constants differ from B 0 by between −1.02 MHz and +2.23 MHz. Combining the B 0 with the results of all-electron coupled-cluster CCSD(T) calculations of Demaison et al. [Mol. Phys.111, 1539 (2013)] and of our own allow to determine the C-C and C-F semi-experimental equilibrium bond lengths r e(C-C) = 1.3866(3) Å and r e(C-F) = 1.3244(4) Å. These agree with the CCSD(T)/wCVQZ r e bond lengths calculated by Demaison et al. within ±0.0005 Å. We also calculate the semi-experimental thermally averaged bond lengths r g(C-C)=1.3907(3) Å and r g(C-F)=1.3250(4) Å. These are at least ten times more accurate than two sets of experimental gas-phase electron diffraction r g bond lengths measured in the 1960s.

Feasible Dose Reduction in Routine Chest Computed Tomography Maintaining Constant Image Quality Using the Last Three Scanner Generations: From Filtered Back Projection to Sinogram-affirmed Iterative Reconstruction and Impact of the Novel Fully Integrated Detector Design Minimizing Electronic Noise

OBJECTIVE The aim of the present study was to evaluate a dose reduction in contrast-enhanced chest computed tomography (CT) by comparing the three latest generations of Siemens CT scanners used in clinical practice. We analyzed the amount of radiation used with filtered back projection (FBP) and an iterative reconstruction (IR) algorithm to yield the same image quality. Furthermore, the influence on the radiation dose of the most recent integrated circuit detector (ICD; Stellar detector, Siemens Healthcare, Erlangen, Germany) was investigated. MATERIALS AND METHODS 136 Patients were included. Scan parameters were set to a thorax routine: SOMATOM Sensation 64 (FBP), SOMATOM Definition Flash (IR), and SOMATOM Definition Edge (ICD and IR). Tube current was set constantly to the reference level of 100 mA automated tube current modulation using reference milliamperes. Care kV was used on the Flash and Edge scanner, while tube potential was individually selected between 100 and 140 kVp by the medical technologists at the SOMATOM Sensation. Quality assessment was performed on soft-tissue kernel reconstruction. Dose was represented by the dose length product. RESULTS Dose-length product (DLP) with FBP for the average chest CT was 308 mGy*cm ± 99.6. In contrast, the DLP for the chest CT with IR algorithm was 196.8 mGy*cm ± 68.8 (P = 0.0001). Further decline in dose can be noted with IR and the ICD: DLP: 166.4 mGy*cm ± 54.5 (P = 0.033). The dose reduction compared to FBP was 36.1% with IR and 45.6% with IR/ICD. Signal-to-noise ratio (SNR) was favorable in the aorta, bone, and soft tissue for IR/ICD in combination compared to FBP (the P values ranged from 0.003 to 0.048). Overall contrast-to-noise ratio (CNR) improved with declining DLP. CONCLUSION The most recent technical developments, namely IR in combination with integrated circuit detectors, can significantly lower radiation dose in chest CT examinations.

Organisation of the equine immunoglobulin constant heavy chain genes. II. Equine cgamma genes.

The number of immunoglobulin G constant heavy chain genes (cgamma genes) varies broadly among mammalian species, reflecting structural and functional differences between expressed immunoglobulin G (IgG) isotypes and allotypes. Up to now equine IgG isotypes have been defined only at the biochemical and serological level. It is still not clear how many IgG isotypes exist in horses and whether there are any allotypes. Here, we describe the isolation and characterisation of equine cgamma genes. An equine genomic lambda phage library was screened with a human cgamma4 probe. Cross-hybridising equine cgamma sequences were cloned twice and characterised by restriction mapping with the human cgamma4 and a murine sgamma1 probe. Genomic equine DNA probes for both, cgamma genes and corresponding switch regions (sgamma), were isolated and used for a more detailed BamHI restriction analysis, comparing genomic DNA of various horses. This analysis reveals the existence of at least five, or probably six cgamma genes in the equine haploid genome. Beside the porcine system, this is the highest number of cgamma genes described for any mammalian species. Moreover, for two of these cgamma genes, BamHI restriction fragment length polymorphism became evident.

Organization of the equine immunoglobulin heavy chain constant region genes; III. Alignment of c mu, c gamma, c epsilon and c alpha genes.

Previous restriction analysis of cloned equine DNA and genomic DNA of equine peripheral blood mononuclear cells had indicated the existence of one c epsilon, one c alpha and up to six c gamma genes in the haploid equine genome. The c epsilon and c alpha genes have been aligned on a 30 kb DNA fragment in the order 5' c epsilon-c alpha 3'. Here we describe the alignment of the equine c mu and c gamma genes by deletion analysis of one IgM, four IgG and two equine light chain expressing heterohybridomas. This analysis establishes the existence of six c gamma genes per haploid genome. The genomic alignment of the cH-genes is 5' c mu/(/) c gamma 1/(/) c gamma 2/(/) c gamma 3/(/) c gamma 4/(/) c gamma 5/(/) c gamma 6/(/) c epsilon-c alpha 3', naming the c gamma genes according to their position relative to c mu. For three of the c gamma genes the corresponding IgG isotypes could be identified as IgGa for c gamma 1, IgG(T) for c gamma 3 and IgGb for c gamma 4.

Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.