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The establishment of pulsar space–time reference frame is of great significance for X‐ray pulsar deep space navigation. To demonstrate that the pulsar parameters are accurate enough to be used as a spatial reference, the transformation parameters, that is, α, β, and γ, of different reference frames determined based on pulsar timing are shown and compared with that of the heliocentric coordinates of Earth‐Moon barycenter. The JPL ephemerides such as DE421, DE200 and INPOP series, are mainly selected for conversion parameter calculation. For the best‐determined parameter γ, the discrepancy between the two different data is 0.38 mas/1.33σ. The timing positions of pulsars clearly show the frame‐tie of different ephemerides, indicating that MSPs have the potential to be a candidate for constructing time–space standard. It is also found that the rotation angles change linearly with time, and PSR J0437 − 4715 plays a critical role in the fitting of α. By employing a few high‐quality MSPs, the transformation precision of the right ascension is evaluated to be on the order of sub‐milliarcsecond, which is an order of magnitude higher than that of the declination. [ABSTRACT FROM AUTHOR]

The independent latitude stations (INDLS) catalog of proper motion in declination μδ for 682 bright Hipparcos (HIP) stars is presented. It is obtained in the Hipparcos reference frame, and only the Hipparcos mean position at epoch 1991.25 is used for INDLS data to calculate independent μδ (the HIP μδ values are not included in the INDLS data). Catalog comparisons were made in pairs for the four catalogs (HIP, new Hipparcos—NHIP, Gaia DR2, INDLS) to look for possible systematic differences as a function of brightness, color, and position coordinates (α, δ). All catalogs were found to be in agreement, except 0.21 mas year−1 for differences in INDLS–DR2 in line with the brightness; −0.13 and 0.24 mas year−1 for differences in HIP–DR2 in line with the free term and brightness, respectively; and −0.16, 0.23, and 0.13 mas year−1 for differences NHIP–DR2 in line with the free term, brightness, and color, respectively. A slightly better consistency is observed in the cases of INDLS–NHIP and INDLS–DR2 than HIP–DR2 and NHIP–DR2. The systematic error is in line with brightness on the level 0.1 mas year−1 in DR2 and, near 0.1 mas year−1, in line with color. An indication that the bright reference frame of DR2 rotates by about 0.1 mas year−1 relative to the faint quasar frame is in line with a presented sinusoidal curve of differences μδ as a function of α. Its amplitude is A = 0.53 ± 0.11 mas year−1 for INDLS–DR2 (0.26 ± 0.07 for INDLS–NHIP); about 0.2 belongs to DR2. The level of formal errors is near 1.9 mas year−1 for the case INDLS–DR2 and near 1.5 for: INDLS–NHIP, HIP–DR2, and NHIP–DR2. The values μδ of bright DR2 stars could be underestimated; the astrometry is unreliable for G ≤ 6 mag due to detector saturation. [ABSTRACT FROM AUTHOR]

This study is concerned with the finite‐time observer (FTO) design for a class of singular systems subject to unknown inputs in both the state and the output equations. First, in order to overcome the restriction of the classical FTO method, two different non‐singular auxiliary dynamic systems, which are simultaneously equivalent to the original singular system, are constructed to act as the new reference systems for the sub‐observers' design. Second, based on the observer matching condition and strong observability condition, it is proven that an FTO can be designed where the observer parameters are given by an algebraic method. Also, in order to present a systematical method to compute the observer parameters, an alternative linear matrix inequality method is proposed. The advantages of the FTO over the conventional asymptotic convergence observer are discussed and numerical examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Quantifying soil organic carbon (SOC) changes is a fundamental issue in ecology and sustainable agriculture. However, the algorithm‐derived biases in comparing SOC status have not been fully addressed. Although the methods based on equivalent soil mass (ESM) and mineral‐matter mass (EMMM) reduced biases of the conventional methods based on equivalent soil volume (ESV), they face challenges in ensuring both data comparability and accuracy of SOC estimation due to unequal basis for comparison and using unconserved reference systems. We introduce the basal mineral‐matter reference systems (soils at time zero with natural porosity but no organic matter) and develop an approach based on equivalent mineral‐matter volume (EMMV). To show the temporal bias, SOC change rates were recalculated with the ESV method and modified methods that referenced to soils at time t1 (ESM, EMMM, and EMMV‐t1) or referenced to soils at time zero (EMMV‐t0) using two datasets with contrasting SOC status. To show the spatial bias, the ESV‐ and EMMV‐t0‐derived SOC stocks were compared using datasets from six sites across biomes. We found that, in the relatively C‐rich forests, SOC accumulation rates derived from the modified methods that referenced to t1 soils and from the EMMV‐t0 method were 5.7%–13.6% and 20.6% higher than that calculated by the ESV method, respectively. Nevertheless, in the C‐poor lands, no significant algorithmic biases of SOC estimation were observed. Finally, both the SOC stock discrepancies (ESV vs. EMMV‐t0) and the proportions of this unaccounted SOC were large and site‐dependent. These results suggest that although the modified methods that referenced to t1 soils could reduce the biases derived from soil volume changes, they may not properly quantify SOC changes due to using unconserved reference systems. The EMMV‐t0 method provides an approach to address the two problems and is potentially useful since it enables SOC comparability and integrating SOC datasets. [ABSTRACT FROM AUTHOR]

This paper presents the results of the comparison of the galactic reference frames realized by the catalogues XPM and UCAC4. Based on about 40 million stars common to both catalogues, the systematic differences of the galactic coordinates and proper motions have been derived for 12 magnitudes in 0.5 m width bins with the mean J-values from 10 m.25 to 15 m.75. The systematic differences were represented by vector spherical harmonics, with the magnitude equation taken into consideration. The mutual orientation of the frames was found to be at the level of 10 mas. It is concluded that these differences are negligible in comparison with the accuracy of the implementation of the standard galactic coordinate system MAS 1958. We investigated two features of the XPM catalogue. First, unlike the HCRF and UCAC4 catalogues, whose proper motions are tied to the quasars and galaxies, the XPM catalogue implements a reference system based only on galaxies. Second, the XPM catalogue has two systems of proper motions-XPM x and XPM p, referred to the two galaxy sub-catalogues of the project 2MASS-PSC and XSC. The study of the differences XPM x−XPM p showed that they are free of the magnitude equation. The speed of relative rotation of XPM x over XPM p was found to be ω=0.453±0.003 mas/year, which exceeds the residual rotation of the HCRF (0.25 mas/year). Analysis of systematic differences XPM x−UCAC4 and XPM p−UCAC4 showed that both frames XPM x and XPM p have an appreciable rotation speed relative to the UCAC4 (hence the ICRF), especially large (up to 2 mas/year) for the brightest stars in our range. This shows that a relatively high speed of rotation of the two frames XPM x and XPM p with respect to the UCAC4 is a consequence of the transition from a combined 'quasar-galaxy' to a purely 'galactic' reference system. It is shown that the systematic difference between the proper motions of stars can be interpreted within the Ogorodnikov-Milne kinematic model of the velocity field. [ABSTRACT FROM AUTHOR]

Ecological restoration is set to play a key role in mitigating biodiversity loss. While many restorationists worry about what to do about and what to call rapidly changing ecosystems (no-analog, novel, or other terms), ecologists and managers in some parts of the world have avoided these controversies and proceeded with developing and implementing innovative restoration projects. We discuss examples from South Korea, including the Cheonggyecheon river project in Seoul and the new National Institute of Ecology, which combines scientific research, planted reference systems for future restoration, and an Ecorium for outreach and education. South Korea faces a range of restoration challenges, including managing even-aged planted forests, major land use changes (especially urbanization) affecting valuable tidal flats, and fragmented landscapes caused by intensive land use and the fenced Demilitarized Zone ( DMZ). The examples from South Korea provide insights that might guide future actions more broadly. These include flexible targets for restoration not based on historical precedents, considering ecosystem functions and functional trait diversity as well as species composition, creating model restoration projects, and managing adaptively. [ABSTRACT FROM AUTHOR]

We present comparison results of our Independent Latitude (IL) catalogue of μδ determinations for 1120 bright stars with the Hipparcos, new Hipparcos and Earth Orientation Catalogue (EOC-2) values. Also, we took into consideration the EOC3 and EOC4 (recent versions of EOC catalogues). Our μδ values are based on zenith telescope observations from seven Independent Latitude (IL) observatories. The IL measures are spanning a time baseline of up to 90 years which is the key advantage to the accurate determination of μδ. The short interval of the Hipparcos satellite observations is a disadvantage for a good accuracy of stellar proper motion, especially in the case of double and multiple stars. For this reason many astrometric catalogues have appeared after the publication of the Hipparcos including our IL catalogue. These catalogues are an appropriate combination of the Hipparcos satellite and ground-based data which yields more accurate stellar coordinates and/or their proper motions. Among various types of ground-based observations the latitude and universal time variations obtained from several million observations of stars reduced to the Hipparcos reference system were used for this purpose. These observations were obtained during almost the entire last century and were originally used to determine the Earth Orientation Parameters. It is also possible to use these data in the inverse task of checking the accuracy of stellar coordinates and/or their proper motions listed in the Hipparcos Catalogue. Such latitude and universal time variations data are the basis of the EOC and IL catalogues. In this paper, we computed the differences in μδ values between pairs of catalogues and analyzed the results to characterize the μδ errors for the four catalogues with a special focus on our IL catalogue. The standard errors of μδ for IL stars observed over more than 20 years are mostly smaller than or equal to the Hipparcos errors, and close to the accuracy level of the EOC-2 (EOC-3, EOC-4) and the new Hipparcos. The resulting investigations of errors of differences of μδ, show that all four catalogues have relatively small random and systematic errors which are close to each other meaning that the corresponding μδ values have a high accuracy. Our sample also contains detected double and multiple stars for which the effects of the orbital and proper motions are difficult to separate. The differences of μδ values for these stars generally exceed those obtained for single stars. Also, these discrepancies could be attributed to effect of possible, still unrecognized, astrometric binaries. These investigations about the proper motions and double stars are in line with the activity of the IAU Working Group on Astrometry by Small Ground-Based Telescopes. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Known and unknown properties of Hansen Ideal coordinates are summarized. It is shown that the ideal space frame is a general and necessary component of basic celestial mechanics and astrodynamics, as well as of any theory of motion. A typical consequence is the intimate correlation of the Hansen frame with the Lagrange constraint within the method of the variation of the parameters. The use of observations in the ideal frame may allow conclusions on the intergalactic fundamental coordinate system (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Purpose: Several authors studied the problem of geometrical matching of fields produced by medical linear accelerators. However, a general solution has yet to be published. Currently available solutions are based on parallelism arguments. This study provides a general solution, considering not only parallelism but also field sizes. Methods: A fixed field with arbitrary field size, gantry, collimator, and couch angle is considered, and another field with a fixed gantry angle is matched to it. A single reference system attached to the treatment couch is used, and two approaches are followed. In the first approach, fixed field sizes are assumed and parallelism of the adjacent field-side planes is imposed. In the second approach, fixed isocenter positions are considered and both parallelism and coincidence between field-side planes are required. Results: When fixed field sizes are assumed, rotation angles are obtained; however, the isocenters may need to be shifted to make side planes coincident and therefore achieve a proper match. When fixed isocenter positions are considered, solutions for all parameters, including the field size, are obtained and an exact geometrical match is achieved. Conclusions: General expressions to the field-matching problem are found for the two approaches followed, fixed field sizes, and fixed isocenter positions. These results can be applied to any treatment technique and can easily be implemented in modern treatment planning systems. [ABSTRACT FROM AUTHOR]