Universal convexity and range problems of shifted hypergeometric functions

In the present paper, we study the shifted hypergeometric function f(z)=z\Gauss(a,b;c;z) for real parameters with $0<a\le b\le c$ and its variant g(z)=z\Gauss(a,b;c;z^2). Our first purpose is to solve the range problems for $f$ and $g$ posed by Ponnusamy and Vuorinen in their 2001 paper. Ruscheweyh, Salinas and Sugawa developed in their 2009 paper the theory of universal prestarlike functions on the slit domain \C\setminus[1,+\infty) and showed universal starlikeness of $f$ under some assumptions on the parameters. However, there has been no systematic study of universal convexity of the shifted hypergeometric functions except for the case $b=1.$ Our second purpose is to show universal convexity of $f$ under certain conditions on the parameters.Comment: 15 page

Focusing particles by induced charge electrokinetic flow in a microchannel

This is the peer reviewed version of the following article: Song, Y., Wang, C., Li, M., Pan, X. and Li, D. (2016), Focusing particles by induced charge electrokinetic flow in a microchannel. ELECTROPHORESIS, 37: 666–675. doi:10.1002/elps.201500361, which has been published in final form at http://dx.doi.org/10.1002/elps.201500361. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A novel method of sheathless particle focusing by induced charge electrokinetic flow in a microchannel is presented in this paper. By placing a pair of metal plates on the opposite walls of the channel and applying an electrical field, particle focusing is achieved due to the two pairs of vortex that constrain the flow of the particle solution. As an example, the trajectories of particles under different electrical fields with only one metal plate on one side channel wall were numerically simulated and experimentally validated. Other flow focusing effects, such as the focused width ratio (focused width/channel width) and length ratio (focused length/half-length of metal plate) of the sample solution, were also numerically studied. The results show that the particle firstly passes through the gaps between the upstream vortices and the channel walls. Afterwards, the particle is focused to pass through the gap between the two downstream vortices that determine the focused particle position. Numerical simulations show that the focused particle stream becomes thin with the increases in the applied electrical field and the length of the metal plates. As regards to the focused length ratio of the focused stream, however, it slightly increases with the increase in the applied electrical field and almost keeps constant with the increase in the length of the metal plate. The size of the focused sample solution, therefore, can be easily adjusted by controlling the applied electrical field and the sizes of the metal plates

Liquid Mixing Based on Electrokinetic Vortices Generated in a T-Type Microchannel

This article proposes a micromixer based on the vortices generated in a T-type microchannel with nonuniform but same polarity zeta potentials under a direct current (DC) electric field. The downstream section (modified section) of the outlet channel was designed with a smaller zeta potential than others (unmodified section). When a DC electric field is applied in the microchannel, the electrokinetic vortices will form under certain conditions and hence mix the solution. The numerical results show that the mixing performance is better when the channel width and the zeta potential ratio of the modified section to the unmodified section are smaller. Besides, the electrokinetic vortices formed in the microchannel are stronger under a larger length ratio of the modified section to the unmodified section of the outlet channel, and correspondingly, the mixing performance is better. The micromixer presented in the paper is quite simple in structure and has good potential applications in microfluidic devices

Improving Ambiguity Resolution for Medium Baselines Using Combined GPS and BDS Dual/Triple-Frequency Observations

The regional constellation of the BeiDou navigation satellite system (BDS) has been providing continuous positioning, navigation and timing services since 27 December 2012, covering China and the surrounding area. Real-time kinematic (RTK) positioning with combined BDS and GPS observations is feasible. Besides, all satellites of BDS can transmit triple-frequency signals. Using the advantages of multi-pseudorange and carrier observations from multi-systems and multi-frequencies is expected to be of much benefit for ambiguity resolution (AR). We propose an integrated AR strategy for medium baselines by using the combined GPS and BDS dual/triple-frequency observations. In the method, firstly the extra-wide-lane (EWL) ambiguities of triple-frequency system, i.e., BDS, are determined first. Then the dual-frequency WL ambiguities of BDS and GPS were resolved with the geometry-based model by using the BDS ambiguity-fixed EWL observations. After that, basic (i.e., L1/L2 or B1/B2) ambiguities of BDS and GPS are estimated together with the so-called ionosphere-constrained model, where the ambiguity-fixed WL observations are added to enhance the model strength. During both of the WL and basic AR, a partial ambiguity fixing (PAF) strategy is adopted to weaken the negative influence of new-rising or low-elevation satellites. Experiments were conducted and presented, in which the GPS/BDS dual/triple-frequency data were collected in Nanjing and Zhengzhou of China, with the baseline distance varying from about 28.6 to 51.9 km. The results indicate that, compared to the single triple-frequency BDS system, the combined system can significantly enhance the AR model strength, and thus improve AR performance for medium baselines with a 75.7% reduction of initialization time on average. Besides, more accurate and stable positioning results can also be derived by using the combined GPS/BDS system

Combined GPS and BDS for single-frequency continuous RTK positioning through real-time estimation of differential inter-system biases

Double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can be fixed to integers if the associated differential inter-system biases (DISBs) are well known. In this case, only one common pivot satellite is sufficient for inter-system ambiguity resolution. This will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning especially when only a few satellites are observed. However, for GPS and current operational BDS-2, there are no overlapping frequencies. Due to the influence of different frequencies, the inter-system DD ambiguities still cannot be fixed to integers even if the DISBs are precisely known. In this contribution, we present an inter-system differencing model for combined GPS and BDS single-frequency RTK positioning through real-time estimation of DISBs. The stability of GPS L1 and BDS B1 DISBs is analyzed with different receiver types. Along with parameterization and using the short-term stability of DISBs, the DD ambiguities between GPS and BDS pivot satellites and the between-receiver single-difference ambiguity of the GPS pivot satellite can be estimable jointly with the differential phase DISB term from epoch to epoch. Then the inter-system differencing model can benefit from the near time-constant DISB parameters and thus has better multi-epoch positioning performance than the classical intra-system differencing model. The combined GPS and BDS single-frequency RTK positioning performance is evaluated with various simulated satellite visibilities. It will be shown that compared with the classical intra-system differencing model, the proposed model can effectively improve the positioning accuracy and reliability, especially for severely obstructed situations with only a few satellites observed

Single-epoch Positioning Method in Network RTK with BDS Triple-frequency Widelane Combinations

Using the advantage that triple-frequency extra-widelane or widelane ambiguities have much longer wavelength and thus are easy to be fixed, a new network RTK (real-time kinematic) single-epoch positioning method based on BDS widelane combinations is proposed. The data processing center uses reference stations to calculate and broadcast the real-time virtual observations including double difference (DD) tropospheric and ionospheric delay correction. Then using single-satellite-pair and single-epoch mode, two extra-widelane or widelane ambiguities are resolved reliably by carrier-pseudo combination and TCAR (three-carrier ambiguity resolution) method at the rover station. Finally, the ambiguity-fixed widelane observations with the minimum observation noise and the broadcast atmospheric correction are used together to calculate the real-time kinematic positioning results. Experimental results show that the correct rates of single-epoch widelane ambiguity resolution at rover stations are larger than 99.9%. The statistical positioning error in plane is 3-4 cm, and the error in up direction is about 5 cm

Support Vector Machine for Regional Ionospheric Delay Modeling

The distribution of total electron content (TEC) in the ionosphere is irregular and complex, and it is hard to model accurately. The polynomial (POLY) model is used extensively for regional ionosphere modeling in two-dimensional space. However, in the active period of the ionosphere, the POLY model is difficult to reflect the distribution and variation of TEC. Aiming at the limitation of the regional POLY model, this paper proposes a new ionosphere modeling method with combining the support vector machine (SVM) regression model and the POLY model. Firstly, the POLY model is established using observations of regional continuously operating reference stations (CORS). Then the SVM regression model is trained to compensate the model error of POLY, and the TEC SVM-P model is obtained by the combination of the POLY and the SVM. The fitting accuracies of the models are verified with the root mean square errors (RMSEs) and static single-frequency precise point positioning (PPP) experiments. The results show that the RMSE of the SVM-P is 0.980 TECU (TEC unit), which produces an improvement of 17.3% compared with the POLY model (1.185 TECU). Using SVM-P models, the positioning accuracies of single-frequency PPP are improved over 40% compared with those using POLY models. The SVM-P is also compared with the back-propagation neural network combined with POLY (BPNN-P), and its performance is also better than BPNN-P (1.070 TECU)

Quantifying the growth of continental crust through crustal thickness and zircon Hf-O isotopic signatures: A case study from the southern Central Asian Orogenic Belt

Accretionary orogens function as major sites for the generation of continental crust, but the growth model of continental crust remains poorly constrained. The Central Asian Orogenic Belt, as one of the most important Phanerozoic accretionary orogens on Earth, has been the focus of debates regarding the proportion of juvenile crust present. Using published geochemical and zircon Hf-O isotopic data sets for three belts in the Eastern Tianshan terrane of the southern Central Asian Orogenic Belt, we first explore the variations in crustal thickness and isotopic composition in response to tectono-magmatic activity over time. Steady progression to radiogenic zircon Hf isotopic signatures associated with syn-collisional crustal thickening indicates enhanced input of mantle-derived material, which greatly contributes to the growth of the continental crust. Using the surface areas and relative increases in crustal thickness as the proxies for magma volumes, in conjunction with the calculated mantle fraction of the mixing flux, we then are able to determine that a volume of ~14–22% of juvenile crust formed in the southern Central Asian Orogenic Belt during the Phanerozoic. This study highlights the validity of using crustal thickness and zircon isotopic signatures of magmatic rocks to quantify the volume of juvenile crust in complex accretionary orogens. With reference to the crustal growth pattern in other accretionary orogens and the Nd-Hf isotopic record at the global scale, our work reconciles the rapid crustal growth in the accretionary orogens with its episodic generation pattern in the formation of global continental crust.12 month embargo; published: 23 December 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning

An inter-system differencing model between two Global Navigation Satellite Systems (GNSS) enables only one reference satellite for all observations. If the associated differential inter-system biases (DISBs) are priori known, double-differenced (DD) ambiguities between overlapping frequencies from different GNSS constellations can also be fixed to integers. This can provide more redundancies for the observation model, and thus will be beneficial to ambiguity resolution (AR) and real-time kinematic (RTK) positioning. However, for Global Positioning System (GPS) and the regional BeiDou Navigation Satellite System (BDS-2), there are no overlapping frequencies. Tight combination of GPS and BDS needs to process not only the DISBs but also the single-difference ambiguity of the reference satellite, which is caused by the influence of different frequencies. In this paper, we propose a tightly combined dual-frequency GPS and BDS RTK positioning model for medium baselines with real-time estimation of DISBs. The stability of the pseudorange and phase DISBs is analyzed firstly using several baselines with the same or different receiver types. The dual-frequency ionosphere-free model with parameterization of GPS-BDS DISBs is proposed, where the single-difference ambiguity is estimated jointly with the phase DISB parameter from epoch to epoch. The performance of combined GPS and BDS RTK positioning for medium baselines is evaluated with simulated obstructed environments. Experimental results show that with the inter-system differencing model, the accuracy and reliability of RTK positioning can be effectively improved, especially for the obstructed environments with a small number of satellites available