Unambiguous Solution Research Articles

A comparative study on the reliability of open cluster parameters

Open clusters are known as excellent tracers of the structure and chemical evolution of the Galactic disk, however, the accuracy and reliability of open cluster parameters is poorly known. In recent years, several studies aimed to present homogeneous open cluster parameter compilations, which are based on some different approaches and photometric data. These catalogues are excellent sources to facilitate testing of the actual accuracy of open cluster parameters. We compare seven cluster parameter compilations statistically and with an external sample, which comprises the mean results of individual studies. Furthermore, we selected the objects IC 4651, NGC 2158, NGC 2383, NGC 2489, NGC 2627, NGC 6603, and Trumpler 14, with the main aim to highlight differences in the fitting solutions. We derived correction terms for each cluster parameter, using the external calibration sample. Most results by the compilations are reasonable scaled, but there are trends or constant offsets of different degree. We also identified one data set, which appears too erroneous to allow adjustments. After the correction, the mean intrinsic errors amount to about 0.2 dex for the age, 0.08 mag for the reddening, and 0.35 mag for the distance modulus. However, there is no study that characterises the cluster morphologies of all test cases in a correct and consistent manner. Furthermore, we found that the largest compilations probably include at least 20 percent of problematic objects, for which the parameters differ significantly. These could be among others doubtful or unlikely open clusters that do not facilitate an unambiguous fitting solution.

Phase methods for measuring the spatial orientation of objects using satellite navigation equipment

This paper discusses phase methods for measuring the spatial orientation of objects using satellite navigation equipment. An analysis of methods for resolving phase ambiguity is presented in the paper. The effectiveness and applicability of the single-step methods are discussed in detail. The authors have shown that applying the exhaustive method requires a constellation of 5 - 6 visible satellites. The measurement of signals, having a base length of 1 m transmitted from 8 satellites, demonstrates that an unambiguous solution is achieved practically in all cases.

Unambiguous analytical inversion of multiple thickness ellipsometric data for an embedded nonabsorbing uniform layer

We give an unambiguous analytical solution of the inverse problem of multiple ellipsometric data, taken at different (arbitrary and preliminary unknown) thicknesses of an embedded nonabsorbing uniform layer. The solution uses all available data in the least square sense for the determination of the layer refractive index and then the corresponding thickness for each measured point is determined. Its usage is illustrated with treating experimental ellipsometric data for two systems. The error propagation analysis of the above solution shows its very high robustness to uncertainties in the input data.

Exploration of describing the vector-parametric bi-spline, defined by the cubic spline with control points incident with surface of appropriate smoothness

The article proposes description technique for spline vector & parametrical surfaces of the fourth degree with control points incidental to the surface and gives testing examples of application of this technique. Main purpose of researches is to develop an algorithm for solving some application problems which often impose specific demands to tools available with developers’ or designers’ workplace. For instance, it sometime becomes troublesome to produce smooth configuration, since the obtained curve does not belong to pre-set dotted carcass. The technique of producing a vector & parametrical bispline with control points incidental (belonging) to relevant surface is proposed to overcome such inconvenience. Hence, a polynomial function of the fourth degree determined with five points x 0, y 0, x 1, y 1, x 2, y 2, x 3, y 3, x 4, y 4 may be represented, as below: with function α i (u) being the Lagrange polynomial coefficients. Polynomial equation in matrix format may be expressed, as follows: With provided derivatives equity up to the third degree (inclusive) the equity of compound derivatives along the gluing line criterion is also met (i. e. continuity of the second quadric form is achieved throughout the entire surface). Equity of the compound derivatives should be achieved to obtain fine smoothness of the third degree surface, i. e.: Calculation formulae for spline with third degree of smoothness should be applied to achieve this effect. Thus linear equations system with quadrodiagonal leading matrix may be obtained by means of preset three boundary conditions (thus increasing the flexibility of the method) providing a stable and unambiguous solution. Algorithm for development of the fourth degree bispline with control points belonging to relevant surface is developed. Results of the research may be helpful for developers, designers, APS users providing them with additional opportunities in developing smooth curved contours for elements and parts of machinery operating in mobile environments. Test examples are provided for the fourth degree bisplines with third degree smoothness with control points incidental to the surface. The proposed algorithm is suggested for implementation to improve efficient work of constructors, designers, developers.

The use of different methods of augmentation horizontally and vertically on the atrophy of the alveolar bone of the upper and alveolar part of the mandible

Introduction. The main problem, which is increasingly faced professionals in planning restoration of the integrity of the dentition with the help of dental implants is not enough bone in the area of the supposed implantation. Given the availability of a variety of techniques osteoplasty alveolar defects and a variety of osteoplastic materials, unambiguous solution to the problem does not exist. Planning method and the osteoplasty graft depends on the exact determination of the degree of bone atrophy, nature and extent of the defect. This article on clinical examples demonstrates methods of volume restoration bones of the upper and lower jaws using grafts of different origin. Materials and Methods. In our study we use bone block, taken from the chin of the mandible and the greater wing of the ilium. Also we use bone substitutes, the membranes, the clips (the cortical screw), powder Bio Oss®. For the isolation of the area augmentation applies collagen membrane Bio Gide® (Geistlich Pharma AG, Wolhusen, Switzerland). All surgeries were performed a standard set of surgical instruments and apparatus piezo surgery. Findings and discussion. Through the use of block the autogenous graft and auxiliary materials was successful augmentation of the alveolar bone of the upper and lower jaws with a strong vertical and horizontal atrophy. It was possible to achieve the goals set in the planning phase of treatment. The increase in the cost of therapy is justified for preserving intact adjacent teeth, optimal recovery of the dentition and high functionality and aesthetics prosthetic. It is achieved one of the main goals of dental rehabilitation - improving the quality of life of patients

An algorithm for 3D-object reconstruction from video using stereo correspondences

An algorithm for automatic reconstruction of three-dimensional scenes from a video recording is discussed. The algorithm is based on finding point correspondences between frames. A priori information about objects that are being reconstructed is used to increase the accuracy of reconstruction. Optimization is performed in the course of reconstruction to find an unambiguous solution. The results of the work of the algorithm are presented.

Expression, purification and crystallization of MnSOD from Arabidopsis thaliana.

Manganese superoxide dismutase (MnSOD) is an essential primary antioxidant enzyme. MnSOD plays an important role in plant tolerance to abiotic stress and is a target candidate for increasing stress tolerance in crop plants. Although the structure and kinetic parameters of MnSODs from several organisms have been determined, this information is still lacking for plant MnSODs. Here, recombinant MnSOD from Arabidopsis thaliana (AtMnSOD) was expressed, purified and crystallized. A nearly complete data set could only be obtained when a total rotation range of 180° was imposed during data collection, despite the seemingly tetragonal metric of the AtMnSOD crystal diffraction. The data set extended to 1.95 Å resolution and the crystal belonged to space group P1. Molecular-replacement calculations using an ensemble of homologous SOD structures as a search model gave a unique and unambiguous solution corresponding to eight molecules in the asymmetric unit. Structural and kinetic analysis of AtMnSOD is currently being undertaken.

Forward and inverse problems of optical engineering when a two-dimensional illuminance distribution is being formed

Based on the fundamental law of geometrical optics and the concept of the eikonal, a definition is given of the forward and inverse problems of calculating the light field when a two-dimensional illuminance distribution is being formed. It is shown that, when there is an unambiguous solution of the forward problem, any solution of the inverse problem is a particular solution that can be reached by consistently selecting the required shape of the wave front. Progress in the selection is easily checked at all of its stages by solving the forward problem.

Overview of baryon resonances

The quest to understand the physics of any system cannot be said to be complete as long as one cannot predict and fully understand its resonance spectrum. Despite this, due to the experimental challenge of the required double polarization measurements and the difficulty in achieving unambiguous, model-independent extraction and interpretation of the nucleon resonance spectrum of many broad and overlapping resonances, understanding of the structure and dynamics of the nucleon has suffered. The recent improvement in statistical quality and kinematic range of the data made available by such full-solid-angle systems as the CB and TAPS constellation at MAMI, coupled with the high flux polarized photon beam provided by the Glasgow Photon Tagger, and the excellent properties of the Mainz Frozen Spin Target, when paired with new developments in Partial Wave Analysis (PWA) methodology make this a very exciting and fruitful time in nucleon resonance studies. Here the recent influx of data and PWA developments are summarized, and the requirements for a complete, unambiguous PWA solution over the first and second resonance region are briefly reviewed.

The double polarization program of CBELSA/TAPS

The excitation spectrum of the proton consists of resonances with substancial width which are often strongly overlapping and are therefore difficult to disentangle. To determine the exact contributions and identify these resonances, a partial wave analysis solution has to be found. For a complete experiment, which leads to an unambiguous solution, several single and double polarization observables are needed. With the Crystal Barrel/TAPS experiment at ELSA, the measurement of double polarization observables in different reactions is possible by using a circularly or linearly polarized photon beam on a transversely or longitudinally polarized butanol target.

Application of Hamilton's and Divisor Methods to Degressively Proportional Allocation Functions

The most recognizable historically approved methods of proportional division of mandates in collegiate bodies refer to an ideal assumption where each vote is associated with identical number of representatives. Proportional methods of distribution such as Hamilton's and divisor methods of Jefferson, Adams or Webster cannot be directly applied to the allocation of seats between the Member States in the European Parliament because of the wide variation in their population. A desire to ensure appropriate representation have triggered legal acceptance of degressive proportionality rule contained in the Lisbon Treaty. The new principle, however, does not allow determining an unambiguous solution. The article presents the allocations which can be obtained reaching the classical methods of proportional division, taking into account degressively proportional allocation functions.

Influence of Boundary Conditions of Digressively Proportional Division on the Potential Application of Proportional Rules

The most commonly used principle of division of assets and debts is the principle of proportionality, which derived from Aristotle. The main area of application of that rule is the electoral law. An example of another solution can be found in the Lisbon Treaty, which sets out the rule of digressively proportional representation of EU Member States in the European Parliament. The problem is that there are many acceptable solutions. In this paper an attempt is made to determine the boundary conditions in such a way that the rules used for the proportional divisions would also lead to an unambiguous solution in the case of digressively proportional division.

Cloning, overexpression, purification and preliminary X-ray analysis of a feast/famine regulatory protein (Rv2779c) fromMycobacterium tuberculosisH37Rv

Rv2779c from Mycobacterium tuberculosis is a feast/famine regulatory protein. This class of proteins are also known as the leucine-responsive regulatory protein/asparagine synthase C family (Lrp/AsnC) of transcriptional regulators and are known to be involved in various metabolic processes in bacteria and fungi. They contain a RAM (regulator of amino-acid metabolism) domain that is rarely found in humans and acts as the oligomerization domain. Since the oligomeric status is often linked to the particular functional role in these proteins, binding of ligands to the domain can elicit specific functional responses. Full-length Rv2779c corresponding to a molecular mass of 19.8 kDa and 179 residues was cloned and purified to homogeneity following transformation into Escherichia coli C41 (DE3) cells. Crystals were grown by vapour diffusion using the hanging-drop method. Diffraction data extending to 2.8 Å resolution were collected from a single crystal that belonged to space group P2(1)2(1)2, with unit-cell parameters a = 99.6, b = 146.0, c = 49.9 Å. Matthews coefficient (VM) calculations suggest that four molecules are present in the asymmetric unit, corresponding to a solvent content of ∼46%. Molecular-replacement calculations using the crystal structure of a homologue, Rv3291c, as the search model gave an unambiguous solution corresponding to four subunits in the asymmetric unit.

Multiwavelength modelling the SED of supersoft X-ray sources I. The method and examples

Radiation of supersoft X-ray sources (SSS) dominates both the supersof X-ray and the far-UV domain. A fraction of their radiation can be reprocessed into the thermal nebular emission, seen in the spectrum from the near-UV to longer wavelengths. In the case of symbiotic X-ray binaries (SyXBs) a strong contribution from their cool giants is indicated in the optical/near-IR. In this paper I introduce a method of multiwavelength modelling the spectral energy distribution (SED) of SSSs from the supersoft X-rays to the near-IR with the aim to determine the physical parameters of their composite spectra. The method is demonstrated on two extragalactic SSSs, the SyXB RXJ0059.1-7505 (LIN 358) in the Small Magellanic Cloud (SMC), RXJ0439.8-6809 in the Large Magellanic Cloud (LMC) and two Galactic SSSs, the classical nova RXJ2030.5+5237 (V1974 Cyg) during its supersoft phase and the classical symbiotic star RXJ1601.6+6648 (AG Dra) during its quiescent phase. The multiwavelength approach overcomes the problem of the mutual dependence between the temperature, luminosity and amount of absorption, which appears when only the X-ray data are fitted. Thus, the method provides an unambiguous solution. It was found that selection of the model (a blackbody or an atmospheric model) is not of crucial importance in fitting the global X-ray/IR SED. The multiwavelength modelling of the SED of SSSs is essential in determining their physical parameters.

RADIUS CONSTRAINTS AND MINIMAL EQUIPARTITION ENERGY OF RELATIVISTICALLY MOVING SYNCHROTRON SOURCES

A measurement of the synchrotron self-absorption flux and frequency provides tight constraints on the physical size of the source and a robust lower limit on its energy. This lower limit is also a good estimate of the magnetic field and electrons' energy, if the two components are at equipartition. This well-known method was used for decades to study numerous astrophysical sources moving at non-relativistic (Newtonian) speeds. Here we generalize the Newtonian equipartition theory to sources moving at relativistic speeds including the effect of deviation from spherical symmetry expected in such sources. Like in the Newtonian case, minimization of the energy provides an excellent estimate of the emission radius and yields a useful lower limit on the energy. We find that the application of the Newtonian formalism to a relativistic source would yield a smaller emission radius, and would generally yield a larger lower limit on the energy (within the observed region). For sources where the Synchrotron-self-Compton component can be identified, the minimization of the total energy is not necessary and we present an unambiguous solution for the parameters of the system.

Archaeological and archaeomagnetic dating at a site from the ager Tarraconensis (Tarragona, Spain): El Vila-sec Roman pottery

A very accurate archaeological dating of a Roman site in NE Spain (El Vila-sec) was made based on the typology of pottery artifacts. Three different phases were identified with activity ranging from the mid-1st century BC to the early-3rd century AD. Analyses of bricks from kilns at El Vila-sec produced data on their stored archaeomagnetic vector. These data were compared with the secular variation curve for the Iberian Peninsula and the SCHA.DIF.3K regional archaeomagnetic model. Both, the reference curve and the model, produced probability distributions for the final period of use for two kilns from the second archaeological phase that were not used during the third phase. At a 95% confidence level, both time distributions cover a wide chronological range including the presumed archaeological age. Both the Iberian secular variation curve and the SCHA.DIF.3K regional model proved to be suitable models for dating the site, although on their own they do not produce a single unambiguous solution. This archaeomagnetic approach could also be applied to neighbouring archaeological sites that have an imprecise archaeological age.

Development and Evaluation of an Automated Path Planning Aid

M ODERN air transportation has an excellent flight safety record. When failures do occur in flight, owing to the training and experience of the pilots almost always results in a safe landing. This is evidenced by a rate of only 1.35 accidents per one million hours flown in 2007 by U.S. air carriers [1]. Despite this excellent record, the pilots’ responsibility to land safely in case of an emergency can be very demanding. When an emergency situation occurs during a flight, the pilots’ workload is very high and a number of tasks demand the pilots’ attention. One of the important tasks is the planning and execution of a trajectory resulting in a safe landing. However, this task is complicated by multiple, often conflicting goals, including reducing time to land, staying within the flight envelope limits of the airplane, weather issues, aswell asmeeting any relevant regulatory requirements. Moreover, all of these tasks must be accomplished in a stressful environment, often under severe time pressure [2]. Although fault-tolerant adaptive automation is currently being developed, for the foreseeable future of civil transport aviation, pilots will be the ultimate decision makers, especially in cases of emergencies involving any type of aircraft performance degradation or flight envelope reduction. As a result, current research is being directed at pilot aids that aim at enhancing the pilot’s situation awareness (SA), as well as at supporting the pilot’s decision-making process through the provision of relevant situation-related information. The purpose of this paper is to report on a human factors study related to efforts to develop an automated planning aid (APA) (in terms of both an acceptable interface and control algorithms) that could assist pilots in generating a plan to safely land at alternative landing sites. To do so, the pilots must first determine the “best” landing site and then formulate an expedient and safe trajectory to the ground. This paper presents the results of an evaluation of an APA interface prototype by means of a human-in-the-loop test with commercial airline pilots, focusing on the selection of alternate landing sites during an emergency. Although the implemented APA in the simulator was also able to compute emergency paths to those sites, a detailed description and discussion of this part of the process is omitted in this paper because it had no immediate effect on theAPA interface evaluation. The results of the study are evaluated in comparison to the opinion and judgment of a single subject matter expert. This expert had more than 20,000 h of flight experience in over 20 years of service as a commercial pilot. The authors do acknowledge that this comparison might be improved by incorporating more experts, more test cases, and a larger sample.However, given the fact that these scenarioswere designed in cooperation with that expert to have an unambiguous best solution, it is likely that, given enough time to review each scenario, the vast majority of trained pilots would come to the same conclusion as to which landing site was the best alternative. As such, the authors do believe that the metrics used, and the comparison with the experts ranking of the landing sites, is valid for the evaluation of the APA for selecting an alternate landing site under tight time constraints.

Overexpression, purification, crystallization and preliminary X-ray analysis of putative molybdenum cofactor biosynthesis protein C (MoaC2) from Mycobacterium tuberculosis H37Rv.

Rv0864 (MoaC2) from Mycobacterium tuberculosis is one of the enzymes in the molybdenum cofactor (Moco) biosynthesis pathway. Together with MoaA, MoaC is involved in the conversion of guanosine triphosphate (GTP) to precursor Z, the first step in Moco synthesis. Full-length MoaC2 (17.5 kDa, 167 residues) was cloned in Escherichia coli and purified to homogeneity. Crystals of recombinant M. tuberculosis MoaC2 were grown by vapour diffusion using a hanging-drop setup. Diffracting crystals grew in a condition in which 3 µl protein solution at 10.5 mg ml(-1) was mixed with 1.5 µl reservoir solution (0.025 M potassium sodium tartrate tetrahydrate pH 8.0) and equilibrated against 1000 µl reservoir solution. Diffraction data extending to 2.5 Å resolution were collected at 100 K. The crystal belonged to the cubic space group P2(1)3, with unit-cell parameter 94.5 Å. Matthews coefficient (V(M)) calculations suggested the presence of two molecules in the asymmetric unit, corresponding to a solvent content of about 39%. Molecular-replacement calculations using the E. coli homologue as the search model gave an unambiguous solution.

Measurement of the double polarization observable E in the reactionγp→pη′

The main goal of the CBELSA/TAPS experiment is the investigation of the nucleon excitation spectrum, which consists of many overlapping resonances. In order to disentangle the different resonance contributions, a partial wave analysis is necessary. In the field of photoproduction of single pseudoscalar mesons, the measurement of a well chosen set of at least eight single and double polarization observables allows for the determination of an unambiguous solution. Of particular interest is the η ′ meson since it couples only to resonances with isospin , thus reducing the number of overlapping resonances. Additionally, its comparatively high mass gives access to the poorly understood regime of high-lying resonances.With the CBELSA/TAPS experiment at the electron stretcher accelerator ELSA, double polarization observables such as E can be obtained by studying photoproduction reactions using a circularly polarized photon beam in combination with a longitudinally polarized butanol target. The decay mode η′ → γγ was analyzed for a beam photon energy range of 1447-2350 MeV. The preliminary results for the double polarization observable E are shown.

Using sparse photometric data sets for asteroid lightcurve studies

With the advent of wide-field imagers, it has become possible to conduct a photometric lightcurve survey of many asteroids simultaneously, either for that single purpose (e.g., Dermawan, B., Nakamura, T., Yoshida, F. [2011]. Publ. Astron. Soc. Japan 63, S555–S576; Masiero, J., Jedicke, R., Ďurech, J., Gwyn, S., Denneau, L., Larsen, J. [2009]. Icarus 204, 145–171), or as a part of a multipurpose survey (e.g., Pan-STARRS, LSST). Such surveys promise to yield photometric data for many thousands of asteroids, but these data sets will be “sparse” compared to most of those taken in a “targeted” mode directed to one asteroid at a time.We consider the potential limitations of sparse data sets using different sampling rates with respect to specific research questions that might be addressed with lightcurve data. For our study we created synthetic sparse data sets similar to those from wide-field surveys by generating more than 380,000 individual lightcurves that were combined into more than 47,000 composite lightcurves. The variables in generating the data included the number of observations per night, number of nights, noise, and the intervals between observations and nights, in addition to periods ranging from 0.1 to 400h and amplitudes ranging from 0.1 to 2.0mag.A Fourier analysis pipeline was used to find the period for each composite lightcurve and then review the derived period and period spectrum to gauge how well an automated analysis of sparse data sets would perform in finding the true period. For this part of the analysis, a normally distributed noise level of 0.03mag was added to the data, regardless of amplitude, thus simulating a relatively high SNR for the observations. For the second part of the analysis, a smaller set of composite curves was generated with fixed core parameters of eight observations per night, 8 nights within a 14-day span, periods ranging from 2 to 6h, and an amplitude of either 0.3mag or 0.4mag. Individual data sets using these fixed parameters added normally-distributed noise of 0.05, 0.1, or 0.2mag. The analysis examined the success rates for finding the true period as the noise increased towards levels simulating data for objects close to sky background levels.After applying a filter to remove highly-ambiguous solution sets, the best chance for success was found to be when the true period was in the range of P≈2–5h and amplitudes were A⩾0.5mag. The solution sets for lightcurves with low amplitude, long periods, and/or those that were sampled too sparsely in comparison to the period were often too ambiguous to be considered reliable for statistical rotation studies. Analysis of slow rotators (P>24h) found that somewhat reasonable solutions of P<6h could be found for about 15–20% of those objects, even at higher amplitudes, indicating that the Fourier analysis had locked onto the noise in the data.Efforts to produce an automated pipeline to help determine an unambiguous (or nearly so) solution based on the period spectrum from the Fourier analysis were made. These proved unsuccessful because of the number of parameters that must be considered and the difficulties in assigning an objective weight to each one in finding a final result. Despite this initial failure, further attempts will be made to quantify the U rating system.Comparison of the synthetic data analysis results to those from two actual surveys shows a reasonable agreement between the two. A review of the pros and cons of sparse versus dense data sets shows that each has a significant role in future studies and that it will be critical to establish open lines of communications and data exchange between the deep wide-field sparse data surveys and dense data programs.