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Full-Text Articles in Physical Sciences and Mathematics

On The Extended Hensel Construction And Its Application To The Computation Of Real Limit Points, Masoud Ataei Jaliseh Dec 2017

On The Extended Hensel Construction And Its Application To The Computation Of Real Limit Points, Masoud Ataei Jaliseh

Electronic Thesis and Dissertation Repository

The Extended Hensel Construction (EHC) is a procedure which, for an input bivariate polyno- mial with complex coefficients, can serve the same purpose as the Newton-Puiseux algorithm. We show that the EHC requires only linear algebra and univariate polynomial arithmetic. We deduce complexity estimates and report on a software implementation together with experimental results. This work is motivated and illustrated by two applications. The first one is the computation of real branches of space curves. The second one is the computation of limits of real multivariate rational function. For the latter, we present an algorithm for determining the existence of …


Mitigating Non-Linearity In Full Waveform Inversion Using Scaled-Sobolev Norms, Mohammad Akbar Hosain Zuberi Dec 2017

Feasible Computation In Symbolic And Numeric Integration, Robert H.C. Moir Dec 2017

Feasible Computation In Symbolic And Numeric Integration, Robert H.C. Moir

Electronic Thesis and Dissertation Repository

Two central concerns in scientific computing are the reliability and efficiency of algorithms. We introduce the term feasible computation to describe algorithms that are reliable and efficient given the contextual constraints imposed in practice. The main focus of this dissertation then, is to bring greater clarity to the forms of error introduced in computation and modeling, and in the limited context of symbolic and numeric integration, to contribute to integration algorithms that better account for error while providing results efficiently.

Chapter 2 considers the problem of spurious discontinuities in the symbolic integration problem, proposing a new method to restore continuity …


Adsorbed Gas Behaviour And Guest-Host Interactions In Ultramicroporous Metal-Organic Frameworks, Bligh Desveaux Dec 2017

Adsorbed Gas Behaviour And Guest-Host Interactions In Ultramicroporous Metal-Organic Frameworks, Bligh Desveaux

Electronic Thesis and Dissertation Repository

Metal-organic frameworks (MOFs) are a class of porous materials that have attracted much attention due to their large surface areas, high tunability and their high selectivity for gas adsorption applications. In this work, solid-state nuclear magnetic resonance (SSNMR) experiments and single crystal X-ray diffraction (SCXRD) experiments are used to investigate carbon dioxide adsorption within the ultramicroporous MOFs SIFSIX-3-Zn (Chapter 2) and ZnAtzOx. (Chapter 3). Analysis finds that the CO2 SIFSIX-3-Zn undergoes wobbling motions with a low temperature dependence, and in ZnAtzOx undergoes wobbling and hopping motions with a low temperature dependence. SCXRD is used to precisely determine the CO …


Rethinking Holocene Ecological Relationships Among Caribou, Muskoxen, And Human Hunters On Banks Island, Nwt, Canada: A Stable Isotope Approach, Jordon S. Munizzi Dec 2017

Rethinking Holocene Ecological Relationships Among Caribou, Muskoxen, And Human Hunters On Banks Island, Nwt, Canada: A Stable Isotope Approach, Jordon S. Munizzi

Electronic Thesis and Dissertation Repository

This dissertation explores the ecology of caribou (Rangifer tarandus spp.) and muskoxen (Ovibos moschatus), and its relevance to human hunters on Banks Island, NWT, Canada, over the last 4000 years, primarily through the isotopic analysis of modern and archaeological faunal remains.

First, we establish baseline carbon and nitrogen isotope relationships between modern vegetation and caribou and muskox bone collagen using Bayesian mixing models. The models indicate that dwarf shrub (Salix arctica) does not contribute significantly to bone collagen isotopic compositions in either species, while sedges and yellow lichen (Cetraria tilesii) do. These findings …


Fabrication And Modification Of Titania Nanotube Arrays For Harvesting Solar Energy And Drug Delivery Applications, Ahmed El Ruby Abdel Rahman Mohamed Dec 2017

Fabrication And Modification Of Titania Nanotube Arrays For Harvesting Solar Energy And Drug Delivery Applications, Ahmed El Ruby Abdel Rahman Mohamed

Electronic Thesis and Dissertation Repository

The fast diminishing of fossil fuels in the near future, as well as the global warming caused by increasing greenhouse gases have motivated the urgent quest to develop advanced materials as cost-effective photoanodes for solar light harvesting and many other photocatalytic applications. Recently, titania nanotube arrays (TNTAs) fabricated by anodization process has attracted great interest due to their excellent properties such as: high surface area, vertically oriented, highly organized, one-dimensional, nanotubular structure, photoactivity, chemical stability and biocompatibility. This unique combination of excellent properties makes TNTAs an excellent photoanode for solar light harvesting. However, the relatively wide band gap energy of …


Polarimetric Synthetic Aperture Radar (Sar) Application For Geological Mapping And Resource Exploration In The Canadian Arctic, Byung-Hun Choe Dec 2017

Polarimetric Synthetic Aperture Radar (Sar) Application For Geological Mapping And Resource Exploration In The Canadian Arctic, Byung-Hun Choe

Electronic Thesis and Dissertation Repository

The role of remote sensing in geological mapping has been rapidly growing by providing predictive maps in advance of field surveys. Remote predictive maps with broad spatial coverage have been produced for northern Canada and the Canadian Arctic which are typically very difficult to access. Multi and hyperspectral airborne and spaceborne sensors are widely used for geological mapping as spectral characteristics are able to constrain the minerals and rocks that are present in a target region. Rock surfaces in the Canadian Arctic are altered by extensive glacial activity and freeze-thaw weathering, and form different surface roughnesses depending on rock type. …


The Development Of Peptide Analogues As Potential Fluorescent And Pet Imaging Probes., Neha Sharma Dec 2017

The Development Of Peptide Analogues As Potential Fluorescent And Pet Imaging Probes., Neha Sharma

Electronic Thesis and Dissertation Repository

Molecular imaging is a non-invasive way to diagnose disease. Molecular imaging probes consist of a targeting entity that has a high affinity for a biological target and a signaling source for external detection. Multimodality imaging combines the advantages of different imaging modalities, at the same time eliminating their shortcomings, thereby providing more accurate results. This thesis focuses on the development of novel dual PET/fluorescence imaging agents based on peptides as targeting entities.

Porphyrins are suitable for multimodality imaging applications due to their innate characteristics such as an ability to fluoresce and to coordinate metals. A gallium-protoporphyrin IX(PPIX)-ghrelin based analogue was …


Three Experiments On Complex Fluids, Yang Liu Dec 2017

Three Experiments On Complex Fluids, Yang Liu

Electronic Thesis and Dissertation Repository

The behaviour of complex fluids is fundamentally interesting and important in many applications. This thesis reports on three experiments on the thermal and rheological behaviour of complex fluids. The first is a study of the rheological properties of and heat transport in a saline solution of hydroxyethyl cellulose. This material has been used as a tissue phantom in testing the behavior of medical devices in MRI scanners. We find it behaves as a typical entangled polymer, and flows in response to local heating, such as could occur due to eddy-current heating of metallic devices in an MR scanner. We use …


Ordovician Continental Paleogeography And Paleoenvironment For The Michigan Basin From Paleomagnetic Analysis, Michelle Macrae Dec 2017

Ordovician Continental Paleogeography And Paleoenvironment For The Michigan Basin From Paleomagnetic Analysis, Michelle Macrae

Electronic Thesis and Dissertation Repository

This study investigates the paleomagnetic record of Paleozoic rocks from two Michigan basin localities in southwestern Ontario to help close the 40 myr gap in Paleozoic paleomagnetic data. Paleomagnetic data from the Queenston (Upper Ordovician) formation consistently exhibits easily removed viscous remanence, an intermediate and a high temperature component consistent with the unblocking temperatures of magnetite and hematite respectively. Alternating-field and thermal demagnetization in 16–20 steps up to 670º C typically reveal a southeastern, shallow up direction removed from magnetite, and a southwestern, steep up direction removed from hematite. A Late Paleozoic overprint was preserved in the magnetite and a …


A Method For The Geometric Analysis Of Rugose Coral Growth Ridges As Paleoenvironmental Indicators In The Middle Devonian Hungry Hollow Member Of Widder Formation, Michigan Basin, Andrew Thomson Dec 2017

A Method For The Geometric Analysis Of Rugose Coral Growth Ridges As Paleoenvironmental Indicators In The Middle Devonian Hungry Hollow Member Of Widder Formation, Michigan Basin, Andrew Thomson

Electronic Thesis and Dissertation Repository

Skeletons of Devonian rugose corals feature submillimetre-scale growth ridges on their outer surface (epitheca) that record the successive positions of the coral polyp during longitudinal corallite growth. Specimens of rugose corals Eridophyllum and Cystiphylloides from the Hungry Hollow Member of the Middle Devonian Widder Formation were sectioned longitudinally and imaged by SEM, and image processing techniques were applied to extract a line representing the epithecal surface. Local extrema found through peak detection allowed growth ridges to be represented as simplified triangles, so that geometric measurements (area, length) could be related to coral growth and analyzed in reference to possible paleoenvironmental …


Studying Metal-Organic Frameworks Via Solid-State Nmr: Gas Dynamics, Structure Determination, And Phase Transition, Yue Zhang Dec 2017

Studying Metal-Organic Frameworks Via Solid-State Nmr: Gas Dynamics, Structure Determination, And Phase Transition, Yue Zhang

Electronic Thesis and Dissertation Repository

Metal-organic frameworks (MOFs) are a class of microporous materials constructed from virtually endless combinations of metal centres and organic linkers. MOFs have attracted intense research interest in recent decades, since MOFs have outstanding properties such as extremely high surface area, tuneable pore topology, good stability, and many others. MOFs are also promising candidates for gas storage. In this work, solid-state NMR (SSNMR) spectroscopy has been investigated to study MOFs and their guest molecules, since SSNMR can provide information on the short-range environment about target nuclei and can also reveal the dynamics of guest molecules.

An introduction to MOFs and SSNMR …


Stable Cu, Fe, And Ni Isotopic Systematics Of The Sudbury Offset Dikes And Associated Rocks, Peter Christoffersen Dec 2017

Stable Cu, Fe, And Ni Isotopic Systematics Of The Sudbury Offset Dikes And Associated Rocks, Peter Christoffersen

Electronic Thesis and Dissertation Repository

The stable isotope ratio compositions of Fe, Ni, and Cu (δ56Fe, δ60Ni, and δ65Cu) are reported for the first time in rocks from the Sudbury Igneous Complex (SIC). Massive sulfide ores, Quartz Diorite (QD), Inclusion bearing Quartz Diorite (IQD), and rocks from members of the Main Mass of the SIC were analyzed. The objective was to better understand the origin(s) and source(s) of the Offset Dikes and the associated sulfide mineralization. Based on stable isotope ratios and petrographic observations, two distinct types of sulfide mineralization hosted within the Offset Dikes are identified. Massive sulfide …


Rendering Real-Time Dashboards Using A Graphql-Based Ui Architecture, Naresh Eeda Dec 2017

Rendering Real-Time Dashboards Using A Graphql-Based Ui Architecture, Naresh Eeda

Electronic Thesis and Dissertation Repository

With the increase in the complexity of the systems being built and demand in the quality of service by the customers, developing and providing highly efficient real-time systems is one of the biggest challenges today for software enterprises. BluemixTM ─ IBM’s cloud offering implemented on Cloud Foundry, an open source “Platform as a Service” (PaaS), is an example of such a system. Currently, there are approx. 26 infrastructural services running in the background from where the data is fetched and is rendered on different dashboards of the system. However, the system suffers from performance issues.

This thesis explores the …


Investigating The Mechanism Of Deep-Focus Earthquakes Via In-Situ Acoustic Emission Experiments On Fe2sio4 At High Temperature And Pressure, Timothy Officer Dec 2017

Investigating The Mechanism Of Deep-Focus Earthquakes Via In-Situ Acoustic Emission Experiments On Fe2sio4 At High Temperature And Pressure, Timothy Officer

Electronic Thesis and Dissertation Repository

In subduction zones, earthquakes are thought to be associated with faulting that arises from phase transformations. In order to test the viability of this mechanism experimentally, it was necessary to make microseismic measurements while the mineral under investigation was subjected to the pressure and temperature (P,T) conditions corresponding to their environment at depth. A system has been developed capable of making in situ acoustic emission (AE) measurements on samples under P,T conditions representative of the upper mantle and transition zone. Experiments were performed in a 3000-ton multi-anvil press using an 18/11 octahedral cell with 6 piezoelectric transducers mounted on the …


Self-Assembly Of Tiles: Theoretical Models, The Power Of Signals, And Local Computing, Amirhossein Simjour Dec 2017

Self-Assembly Of Tiles: Theoretical Models, The Power Of Signals, And Local Computing, Amirhossein Simjour

Electronic Thesis and Dissertation Repository

DNA-based self-assembly is an autonomous process whereby a disordered system of DNA sequences forms an organized structure or pattern as a consequence of Watson-Crick complementarity of DNA sequences, without external direction.

Here, we propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language.

Moreover, we investigate the …


Time Series Analysis Of Surface Deformation Associated With Fluid Injection And Induced Seismicity In Timpson, Texas Using Dinsar Methods, Simon Thorpe Nov 2017

Time Series Analysis Of Surface Deformation Associated With Fluid Injection And Induced Seismicity In Timpson, Texas Using Dinsar Methods, Simon Thorpe

Electronic Thesis and Dissertation Repository

In recent years, a rise in unconventional oil and gas production in North America has been linked to an increase in seismicity rate in these regions (Ellsworth, 2013). As fluid is pumped into deep formations, the state of stress within the subsurface changes, potentially reactivating pre-existing faults and/or causing subsidence or uplift of the surface. Therefore, hydraulic fracturing and/or fluid disposal injection can significantly increase the seismic hazard to communities and structures surrounding the injection sites (Barnhart et al., 2014). On 17th May 2012 an Mw4.8 earthquake occurred near Timpson, TX and has been linked with wastewater injection operations in …


Geophysical Study Of Complex Meteorite Impact Structures, William Zylberman Nov 2017

Geophysical Study Of Complex Meteorite Impact Structures, William Zylberman

Electronic Thesis and Dissertation Repository

Hypervelocity impact craters are the most abundant morphologic features on rocky planetary bodies of the Solar System, except on Earth where they have mostly been erased by plate tectonics, erosion, or are buried under sediments. The internal structure of complex impact craters can only be studied on Earth by using ground-truth geophysical and geological studies. Such approaches - combined with modeling - can reveal how impact cratering, target geological composition, erosion and other post-impact processes can lead to the observed geophysical anomalies, which could also be detected by remote geophysical data on other planetary surfaces. In this work, a multidisciplinary …


Nbpmf: Novel Network-Based Inference Methods For Peptide Mass Fingerprinting, Zhewei Liang Nov 2017

Nbpmf: Novel Network-Based Inference Methods For Peptide Mass Fingerprinting, Zhewei Liang

Electronic Thesis and Dissertation Repository

Proteins are large, complex molecules that perform a vast array of functions in every living cell. A proteome is a set of proteins produced in an organism, and proteomics is the large-scale study of proteomes. Several high-throughput technologies have been developed in proteomics, where the most commonly applied are mass spectrometry (MS) based approaches. MS is an analytical technique for determining the composition of a sample. Recently it has become a primary tool for protein identification, quantification, and post translational modification (PTM) characterization in proteomics research. There are usually two different ways to identify proteins: top-down and bottom-up. Top-down approaches …


Physical Properties Of Faint Meteors Through High-Resolution Observations, Dilini Subasinghe Nov 2017

Physical Properties Of Faint Meteors Through High-Resolution Observations, Dilini Subasinghe

Electronic Thesis and Dissertation Repository

Small, faint meteors (with masses between 10-7 and 10-4 kg) were once part of an asteroid or comet, and collide with Earth's atmosphere daily. Studying meteors is an effective way to survey the physical properties of their parent bodies. Meteor light curves and orbital information is easily obtained from wide-field observations, from which meteoroid structure can be inferred through meteoroid ablation modelling. A high-resolution narrow-field camera can provide much more detail about the poorly understood ablation processes and physical properties of the meteoroid. The goal of this thesis is to better understand the physical properties of meteors using …


Identification Of Thresholds In Benthic Macroinvertebrate Communities Associated With Agricultural Land Cover, Jeremy Peter Grimstead Nov 2017

Identification Of Thresholds In Benthic Macroinvertebrate Communities Associated With Agricultural Land Cover, Jeremy Peter Grimstead

Electronic Thesis and Dissertation Repository

Agricultural land use affects benthic macroinvertebrate (BMI) community structure but riparian forest may mitigate its impact to within a specific threshold. BMI communities were sampled in small streams within the Grand River, Thames River, and Long Point watersheds in southwestern Ontario. The study assessed the location and amount of agricultural land use associated with variation in BMI assemblage structure. Three land use distribution scenarios were evaluated to isolate specific ranges of agricultural land use at either the riparian or catchment scale, with the adjoining scale covering as wide a gradient of agricultural land use as possible. We did identify thresholds …


Statistical Modelling, Optimal Strategies And Decisions In Two-Period Economies, Jiang Wu Nov 2017

Statistical Modelling, Optimal Strategies And Decisions In Two-Period Economies, Jiang Wu

Electronic Thesis and Dissertation Repository

Motivated by some real problems, our thesis puts forward two general two-period pricing models and explore optimal buying and selling strategies in two states of the two-period decision, when buyer/seller's decisions in the two periods are uncertain: commodity valuations may or may not be independent, may or may not follow the same distribution, be heavily or just lightly influenced by exogenous economic conditions, and so on. For both the example of buying laptops and the example of selling houses, the connections between each example and the two-envelope paradox encourage us to explore optimal strategies based on the works of McDonnell …


Coordination And Organometallic Chemistry Of Novel Gallium Complexes: Synthesis, Reactivity And Spectroscopy, Jeremy L. Bourque Nov 2017

Coordination And Organometallic Chemistry Of Novel Gallium Complexes: Synthesis, Reactivity And Spectroscopy, Jeremy L. Bourque

Electronic Thesis and Dissertation Repository

The work described in this thesis incorporates three main themes: the synthesis and reactivity of new coordination and organometallic gallium compounds, and the chemical state determination of molecular gallium complexes using XPS and XAS. The coordination chemistry of low valent gallium cations was explored using macrocyclic ethers as ligands. The experimental oxidation number, or chemical state, of newly synthesized low valent gallium cationic complexes was compared to known compounds to allow for the assessment of the electronic environment at gallium. The organometallic chemistry of gallium was examined using donor ligands to stabilize monomeric organogallium(III) compounds, demonstrating the ability to substitute …


Gamma-Radiation Induced Corrosion Of Alloy 800, Mojtaba Momeni Nov 2017

Gamma-Radiation Induced Corrosion Of Alloy 800, Mojtaba Momeni

Electronic Thesis and Dissertation Repository

This thesis presents a newly developed mechanism and predictive model for the corrosion of Alloy 800. The Fe-Cr-Ni Alloy (Incoloy 800) is mainly used for steam generator (SG) tubing in CANDU and PWR reactors and is a candidate material for the proposed Canadian Supercritical Water Reactor (SCWR) in which it will be exposed to extreme conditions of high radiation flux and large temperature gradients. The influence of gamma radiation and water chemistry conditions on the corrosion behaviour of Alloy 800 are studied in this work. Ionizing radiation creates reducing (•eaq, •H, •O2-) and oxidizing …


Geochemistry Of The Dome Mine Ankerite Veins: Insights Into The Multi-Stage Enrichment Of A World-Class Orogenic Gold Deposit, Jessica M. Stromberg Nov 2017

Geochemistry Of The Dome Mine Ankerite Veins: Insights Into The Multi-Stage Enrichment Of A World-Class Orogenic Gold Deposit, Jessica M. Stromberg

Electronic Thesis and Dissertation Repository

The Dome Mine in the world-class Timmins camp has produced over 16 Moz of gold during its 108 year production history. This gold endowment is the result of multistage enrichment of which the first stage is a set of ankerite veins that extend over 5,400 m in strike and 1,500 m vertically. A deposit wide geochemical study of the Dome ankerite veins was undertaken to characterize their genesis, geochemistry, and role in the deposit mineralization history. Samples and mapping from new and historic mine workings, bulk rock geochemistry, and stable isotope geochemistry were used to constrain the depositional context of …


Paleogeography Of Early Paleozoic Laurentia And Meguma, Avalonia Terranes Via Paleomagnetism And Faunal Review, Halima S. Warsame Nov 2017

Paleogeography Of Early Paleozoic Laurentia And Meguma, Avalonia Terranes Via Paleomagnetism And Faunal Review, Halima S. Warsame

Electronic Thesis and Dissertation Repository

Paleomagnetic assessment of 821 Cambrian to Silurian-aged rock specimens of igneous and sedimentary origin was used as a means to provide insight on the ancient geographies of the region in which these rocks are currently found. The Earth’s magnetic field direction can be recorded at the time of rock formation and/or at a later significant event by magnetic minerals, allowing these signatures to be used to track the past motions of the continents. Stepwise demagnetization of the Port au Port, St. George and Table Head Groups in western Newfoundland, and the Mavillette gabbro (426 +/- 2 Ma, U-Pb baddeleyite) of …


Data-Adaptive Kernel Support Vector Machine, Xin Liu Nov 2017

Data-Adaptive Kernel Support Vector Machine, Xin Liu

Electronic Thesis and Dissertation Repository

In this thesis, we propose the data-adaptive kernel Support Vector Machine (SVM), a new method with a data-driven scaling kernel function based on real data sets. This two-stage approach of kernel function scaling can enhance the accuracy of a support vector machine, especially when the data are imbalanced. Followed by the standard SVM procedure in the first stage, the proposed method locally adapts the kernel function to data locations based on the skewness of the class outcomes. In the second stage, the decision rule is constructed with the data-adaptive kernel function and is used as the classifier. This process enlarges …


Spatio-Temporal Variation Of Benthic Metabolism In A Large Regulated River, Craig Irwin Nov 2017

Spatio-Temporal Variation Of Benthic Metabolism In A Large Regulated River, Craig Irwin

Electronic Thesis and Dissertation Repository

Spatio-temporal patterns of benthic metabolism were measured to determine associations with substrate (cobble vs sand), channel location (main vs side channel), flow regulation (medium-head vs low-head) and temporal variability during the summer months. Benthic metabolism was estimated in two reaches of the Saint John River in New Brunswick, Canada using benthic chambers. General linear models indicated gross primary production (GPP) and community respiration (CR) was greater in cobble substrate in June, but only GPP was greater in July. CR differed between channel locations in July with greater rates in the side channel. Assessment of flow regulation showed greater GPP in …


Metallogenic Setting Of High-Grade Gold Mineralization In The Neoarchean Hearne Craton, Kivalliq Region, Whale Cove, Nunavut, Canada, Mo Asmail Oct 2017

Metallogenic Setting Of High-Grade Gold Mineralization In The Neoarchean Hearne Craton, Kivalliq Region, Whale Cove, Nunavut, Canada, Mo Asmail

Electronic Thesis and Dissertation Repository

The Pistol Bay Gold Project is located on the northwestern shores of Hudson Bay, in the Tavani Segment of the Neoarchean Kaminak Greenstone Belt in the Hearne Craton of the Western Churchill Province. This project covers several gold prospects whose genesis is hotly debated. The primary objectives of this research are to answer critical questions regarding the nature and timing of gold mineralization. The investigation includes: (1) establish the absolute age of the felsic and mafic intrusions and the relative timing of gold mineralization; (2) document the nature of primary and hydrothermal mineral assemblages related to gold mineralization; and (3) …


New Gps Time Series Analysis And A Simplified Model To Compute An Accurate Seasonal Amplitude Of Tropospheric Delay, Hadis Samadi Alinia Oct 2017

New Gps Time Series Analysis And A Simplified Model To Compute An Accurate Seasonal Amplitude Of Tropospheric Delay, Hadis Samadi Alinia

Electronic Thesis and Dissertation Repository

Horizontal and vertical deformation of the Earth’s crust is due to a variety of different geophysical processes that take place on various spatiotemporal scales. The quality of the observations from spaced-based geodesy instruments such as Global Positioning System (GPS) and differential interferometric synthetic aperture radar (DInSAR) data for monitoring these deformations are dependent on numerous error sources. Therefore, accurately identifying and eliminating the dominant sources of the error, such as troposphere error in GPS signals, is fundamental to obtain high quality, sub-centimeter accuracy levels in positioning results.

In this work, I present the results of double-differenced processing of five years …