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2018

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Articles 541 - 570 of 11790

Full-Text Articles in Physical Sciences and Mathematics

Measurement Errors In R, Iñaki Ucar, Edzer Pebesma, Arturo Azcorra Dec 2018

Measurement Errors In R, Iñaki Ucar, Edzer Pebesma, Arturo Azcorra

The R Journal

This paper presents an R package to handle and represent measurements with errors in a very simple way. We briefly introduce the main concepts of metrology and propagation of uncertainty, and discuss related R packages. Building upon this, we introduce the errors package, which provides a class for associating uncertainty metadata, automated propagation and reporting. Working with errors enables transparent, lightweight, less error-prone handling and convenient representation of measurements with errors. Finally, we discuss the advantages, limitations and future work of computing with errors.


Spatial Uncertainty Propagation Analysis With The Spup R Package, Kasia Sawicka, Gerard B.M. Heuvelink, Dennis J.J. Walvoort Dec 2018

Spatial Uncertainty Propagation Analysis With The Spup R Package, Kasia Sawicka, Gerard B.M. Heuvelink, Dennis J.J. Walvoort

The R Journal

Many environmental and geographical models, such as those used in land degradation, agroecological and climate studies, make use of spatially distributed inputs that are known imperfectly. The R package spup provides functions for examining the uncertainty propagation from input data and model parameters onto model outputs via the environmental model. The functions include uncertainty model specification, stochastic simulation and propagation of uncertainty using Monte Carlo (MC) techniques. Uncertain variables are described by probability distributions. Both numerical and categorical data types are handled. The package also accommodates spatial auto-correlation within a variable and cross-correlation between variables. The MC realizations may be …


The Utiml Package: Multi-Label Classification In R, Adriano Rivolli, Andre C.P.L.F. De Carvalho Dec 2018

The Utiml Package: Multi-Label Classification In R, Adriano Rivolli, Andre C.P.L.F. De Carvalho

The R Journal

Learning classification tasks in which each instance is associated with one or more labels are known as multi-label learning. The implementation of multi-label algorithms, performed by different researchers, have several specificities, like input/output format, different internal functions, distinct programming language, to mention just some of them. As a result, current machine learning tools include only a small subset of multi-label decomposition strategies. The utiml package is a framework for the application of classification algorithms to multi-label data. Like the well known MULAN used with Weka, it provides a set of multi-label procedures such as sampling methods, transformation strategies, threshold functions, …


Nsroc: An R Package For Non-Standard Roc Curve Analysis, Sonia Pérez-Fernández, Pablo Martínez-Camblor, Peter Filzmoser, Norberto Corral Dec 2018

Nsroc: An R Package For Non-Standard Roc Curve Analysis, Sonia Pérez-Fernández, Pablo Martínez-Camblor, Peter Filzmoser, Norberto Corral

The R Journal

The receiver operating characteristic (ROC) curve is a graphical method which has become standard in the analysis of diagnostic markers, that is, in the study of the classification ability of a numerical variable. Most of the commercial statistical software provide routines for the standard ROC curve analysis. Of course, there are also many R packages dealing with the ROC estimation as well as other related problems. In this work we introduce the nsROC package which incorporates some new ROC curve procedures. Particularly: ROC curve comparison based on general distances among functions for both paired and unpaired designs; efficient confidence bands …


Stilt: Easy Emulation Of Time Series Ar(1) Computer Model Output In Multidimensional Parameter Space, Roman Olson, Kelsey L. Ruckert, Won Chang, Klaus Keller, Murali Haran, Soon-Il An Dec 2018

Stilt: Easy Emulation Of Time Series Ar(1) Computer Model Output In Multidimensional Parameter Space, Roman Olson, Kelsey L. Ruckert, Won Chang, Klaus Keller, Murali Haran, Soon-Il An

The R Journal

Statistically approximating or “emulating” time series model output in parameter space is a common problem in climate science and other fields. There are many packages for spatio-temporal modeling. However, they often lack focus on time series, and exhibit statistical complexity. Here, we present the R package stilt designed for simplified AR(1) time series Gaussian process emulation, and provide examples relevant to climate modelling. Notably absent is Markov chain Monte Carlo estimation – a challenging concept to many scientists. We keep the number of user choices to a minimum. Hence, the package can be useful pedagogically, while still applicable to real …


Sarima Analysis And Automated Model Reports With Bets, An R Package, Talitha F. Speranza, Pedro C. Ferreira, Jonatha A. Da Costa Dec 2018

Sarima Analysis And Automated Model Reports With Bets, An R Package, Talitha F. Speranza, Pedro C. Ferreira, Jonatha A. Da Costa

The R Journal

This article aims to demonstrate how the powerful features of the R package BETS can be applied to SARIMA time series analysis. BETS provides not only thousands of Brazilian economic time series from different institutions, but also a range of analytical tools, and educational resources. In particular, BETS is capable of generating automated model reports for any given time series. These reports rely on a single function call and are able to build three types of models (SARIMA being one of them). The functions need few inputs and output rich content. The output varies according to the inputs and usually …


Editorial, John Verzani Dec 2018

Editorial, John Verzani

The R Journal

On behalf of the editorial board, I am pleased to present Volume 10, Issue 2 of the R Journal.

This issue covers a wide range of topics through its 37 articles. As is typical, many of these are related to packages that provide tools for new statistical modeling in R. Examples in this issue include "clustMixType: User-Friendly Clustering of Mixed-Type Data in R" by Szepannek and "BNSP: an R Package for Fitting Bayesian Semiparametric Regression Models and Variable Selection" by Papageorgiou.


Geospatial Point Density, Paul F. Evangelista, David Beskow Dec 2018

Geospatial Point Density, Paul F. Evangelista, David Beskow

The R Journal

This paper introduces a spatial point density algorithm designed to be explainable, meaning ful, and efficient. Originally designed for military applications, this technique applies to any spatial point process where there is a desire to clearly understand the measurement of density and maintain fidelity of the point locations. Typical spatial density plotting algorithms, such as kernel density estimation, implement some type of smoothing function that often results in a density value that is difficult to interpret. The purpose of the visualization method in this paper is to understand spatial point activity density with precision and meaning. The temporal tendency of …


Discovery Of Paleotsunami Deposits Along Eastern Sunda Arc: Potential For Megathrust Earthquakes In Bali, Hanif Ibadurrahman Sulaeman Dec 2018

Discovery Of Paleotsunami Deposits Along Eastern Sunda Arc: Potential For Megathrust Earthquakes In Bali, Hanif Ibadurrahman Sulaeman

Theses and Dissertations

Several laterally extensive candidate tsunami deposits are preserved along coastlines facing the eastern Java Trench, indicating it has experienced mega-thrust earthquakes in the past. We investigated 37 coastal sites in Bali, Lombok, Sumba and Timor islands, many of which preserve course sand and pebble layers that overlie sharp basal contacts with scour marks into the mud, fine upward in grain size, and have bimodal grain size distributions. Other unique features are the common occurrence of marine fossils and concentrations of heavy minerals. The occurrence of these high-energy deposits interlayered with clay-rich units indicates the coarse clastics are anomalous because they …


Security Analysis And Recommendations For Coniks As A Pki Solution For Mobile Apps, George Bradley Spendlove Dec 2018

Security Analysis And Recommendations For Coniks As A Pki Solution For Mobile Apps, George Bradley Spendlove

Theses and Dissertations

Secure mobile apps, including end-to-end encrypted messaging apps such as Whats-App and Signal, are increasingly popular today. These apps require trust in a centralized key directory to automatically exchange the public keys used to secure user communication. This trust may be abused by malicious, subpoenaed, or compromised directories. A public key infrastructure (PKI) solution that requires less trust would increase the security of these commonly used apps.CONIKS is a recent PKI proposal that features transparent key directories which publish auditable digests of the public keys they present to queriers. By monitoring its key every time a new digest is published, …


Impact Of Bubble Baths On Stainless Steel Sphere Water Entry, Wesley Robinson Dec 2018

Impact Of Bubble Baths On Stainless Steel Sphere Water Entry, Wesley Robinson

Physics Capstone Projects

Soap Bubbles on the water surface would seem to be an intuitive means for splash suppression, but their presence appears to be a double edged sword. We present on the water entry of hydrophilic spheres where the liquid surface is augmented by the presence of a bubble layer, similar to a bubble bath. While the presence of a bubble layer can diminish splashing upon impact at low Weber numbers, it also induces cavity formation at speeds below the critical velocity. The formation of a cavity generally results in larger Worthington jets and thus, larger amounts of ejected liquid. Bubble layers …


An Early Late Cretaceous Nodosaur From The Marine Eagle Ford Group Of North Central Texas, A Test Of The Endothermy In The Mosasaurs From The Late Cretaceous Of Angola, And The Ontogeny Of A New Pipid Frog From The Miocene Of Ethiopia, Matt Clemens Dec 2018

An Early Late Cretaceous Nodosaur From The Marine Eagle Ford Group Of North Central Texas, A Test Of The Endothermy In The Mosasaurs From The Late Cretaceous Of Angola, And The Ontogeny Of A New Pipid Frog From The Miocene Of Ethiopia, Matt Clemens

Earth Sciences Theses and Dissertations

The first two chapters of this dissertation detail the study of the newly recovered Holland Farm nodosaur (SMU 77100) from the Eagle Ford Group (95.29 ± 0.04 MA) of Mansfield in north central Texas. The objectives of this research are (1) to describe the anatomy of the Holland Farm nodosaur, (2) to determine its phylogenetic position within Ankylosauria, (3) to elaborate the substantial differences in body size and osteoderm morphology in armored dinosaurs occurring in north central Texas during the short duration of the Late Albian and Early Cenomanian, and (4) to provide a radiometric date for the lowermost member …


Optimal Control Methods For Chagas Disease, Francis Mastrome Dec 2018

Optimal Control Methods For Chagas Disease, Francis Mastrome

Mathematics Theses - Archive

Chagas disease is the world's most neglected tropical disease. Having a lack of cure makes the primary focus on the disease preventing it and controlling it. This study takes into account three different control measures: bed nets, low-volume insecticide spraying, and improving housing conditions, analyzes their cost effectiveness compared to each other, and determines which combination of the three control measures prevents the most T. cruzi infections in a rural Latin American village over a decade. It was shown that there is a a hierarchical importance in the control measures when preventing the spread of Chagas disease. In order of …


Fusulinid And Conodont Biostratigraphy Of The Upper Pennsylvanian–Cisuralian Riepe Spring Limestone, Spruce Mountain Ridge, Elko County, Nevada, U.S.A., Michael Taylor Read Dec 2018

Fusulinid And Conodont Biostratigraphy Of The Upper Pennsylvanian–Cisuralian Riepe Spring Limestone, Spruce Mountain Ridge, Elko County, Nevada, U.S.A., Michael Taylor Read

Earth & Environmental Sciences Dissertations - Archive

The Upper Pennsylvanian-Cisuralian (lower Permian) mixed carbonate-siliciclastic strata exposed at Spruce Mountain Ridge, Elko County, Nevada, record the shallow-marine microfauna and oscillating depositional history of the Ferguson Trough during the final glacial interval of the late Paleozoic ice age. The 420 m thick North Spruce Mountain Ridge (NSMR) section includes the uppermost part of the Ely Limestone, the Riepe Spring Limestone, and the base of the Rib Hill Formation. A discontinuous Pennsylvanian-Permian transition is preserved within the approximately 390 m thick Riepe Spring Limestone along the west side of Spruce Mountain Ridge, where an erosional disconformity separates upper Gzhelian (Upper …


Geochemical Evolution Of The Iron Ore Group -- A Mid-Archean Greenstone Belt Of The Eastern Indian Craton, Jordan Kent Wright Dec 2018

Geochemical Evolution Of The Iron Ore Group -- A Mid-Archean Greenstone Belt Of The Eastern Indian Craton, Jordan Kent Wright

Earth & Environmental Sciences Theses - Archive

The Iron Ore Group (IOG) greenstone belt is located along the Eastern Indian Shield. It preserves a mid-Archean segment of Earth’s history, which consists of conformable sequences of lower basaltic-andesitic lava at the base (~2 km), followed successively upwards by lower-shales (2.3 km) gradating into a tuffacious horizon (30 m at the top), an extensive Algoma-type banded-iron formation (0.7 km), upper basaltic-andesitic lava and upper-shales (~3 km). This succession provides ideal investigative conditions considering each stratigraphic unit as only been lightly-metamorphosed to the low greenschist facies, lacks penetrative deformation, preserves pristine depositional characteristics and great antiquity (~3.4 Ga). The concentrations …


Zgjerueshmëria E Infrastrukturës Përmes Metodave Të Virtualizimit Të Aplikacioneve Në Nivel Të Sistemit Operativ, Altin Ukshini Dec 2018

Zgjerueshmëria E Infrastrukturës Përmes Metodave Të Virtualizimit Të Aplikacioneve Në Nivel Të Sistemit Operativ, Altin Ukshini

Theses and Dissertations

Zhvillimi dhe menaxhimi i aplikacioneve fleksibile dhe të zgjerueshme lehtë është një sfidë operacionale dhe e dizajnimit të infrastrukturës kur kemi të bëjmë me aplikacione dhe platforma të mëdha. Virtualizimi i aplikacioneve në nivel të Sistemit Operativ (konteinerizimi) ka bërë bujë në përdorim tek infrastrukturat dhe serverët në cloud, si dhe në mënyrën se si sot zhvillohen softuerët që të jenë të zgjerueshëm në aspekt të infrastrukturës dhe fleksibilitetit të zhvillimit. Në këtë punim shtjellohet veçmas për teknologjitë e ndryshme të konteinerizimit të aplikacioneve dhe për rëndësinë që ka sot kjo teknologji në zhvillimin e softuerit dhe dizajnimin e arkitekturave …


Krahasimi Në Mes Spring Boot Framework Dhe Jee Framework, Astrit Berisha Dec 2018

Krahasimi Në Mes Spring Boot Framework Dhe Jee Framework, Astrit Berisha

Theses and Dissertations

Në këtë punim ne do të bëjmë dallimin dhe ngjajshmerin në mes dy framework se cila prej këtyre dy framework mundëson zhvillimin e shpejtë të aplikacioneve, zvogëlon nevojën për programim si dhe sa janë të sigurta. Meqë përdorimi i këtyre dy framework është për zhvillimin e aplikacioneve, atëherë edhe përdorimi i tyre është po aq i rëndësishëm, të cilat na tregojn se çfarë lloj programesh mund ose duhet të ndërtohet dhe si do të ndërlidhen. Gjetjet janë të bazuara në një rishikim të historisë së të dy framework, dhe veçanërisht në atë se si kane ardhur deri te zhvillimi për …


Aplikimi I Internet Of Things Në Smart City, Genita Tahiri Dec 2018

Aplikimi I Internet Of Things Në Smart City, Genita Tahiri

Theses and Dissertations

Që kur u prezantua koncepti i një Smart City, Internet of Things është konsideruar infrastruktura kryesore në një smart city. Studimi aktual përshkruan rëndësinë e teknologjive IoT në teknologji udhërrëfyesi (TRM) të një smart city. Për më tepër, rreth 200 ekspertë hulumtojnë rëndësinë dhe thelbin e komponentëve të detajuar të teknologjive IoT për një smart city. Aplikacionet e reja të IoT janë duke bërë të mundur iniciativat e Smart City në të gjithë botën. Ai siguron aftësinë për të monitoruar, menaxhuar dhe kontrolluar pajisjet në distancë, dhe për të krijuar njohuri të reja dhe informacion të zbatueshëm nga rrjedhat masive …


Analizimi Dhe Implementimi I Kornizave Të Testimit Të Automatizuar Selenium Dhe Sahi, Kaltrina Baftiu Dec 2018

Analizimi Dhe Implementimi I Kornizave Të Testimit Të Automatizuar Selenium Dhe Sahi, Kaltrina Baftiu

Theses and Dissertations

Testimi është bërë pjesë integrale e ciklit të zhvillimit të softuerit (SDLC). Përmes mjeteve të automatizuara të testimit me burim të hapur, kostoja e tërë procesit të testimit, si dhe koha që duhet për të kryer procesin e testimit, është zvogëluar ndjeshëm. Qëllimi kryesor i këtij materiali hulumtues është të analizojë mjetet e testimit të internetit Selenium dhe Sahi për të krahasuar karakteristikat e tyre dhe performancën në mënyrë që një përdorues i veçantë të mund të zgjedhë një mjet që është i përshtatshëm në aspektin e përdorshmërisë dhe karakteristikat e kërkuara për një detyrë specifike. Zgjedhja e një kornize …


Siguria E Të Dhënave Në Implementimet E Iot Në Sistemet Ehealth, Iliriana Shala Dec 2018

Siguria E Të Dhënave Në Implementimet E Iot Në Sistemet Ehealth, Iliriana Shala

Theses and Dissertations

Në jetën tonë të sotme ne gjithmonë duhet të merremi me informacionin që luan një rol të rëndësishem në jetën tonë.Njëra nga burimet kryesore të informacionit është padyshim interneti.Gjërat që na rrethojnë po veprojnë me zgjuarsi dhe po e bëjnë jetën tonë njerëzore më të mençur.Këto gjëra veprojnë me zgjuarsi pasi janë të lidhura me internetin dhe kështu quhen “Internet of Things (IoT)”.Pajisjet e IoT mbledhin dhe i shpërndajnë informatat direkt me njëra tjetrën në cloud platforma, duke e bërë të mundur grumbullimin, ruajtjen dhe analizimin e të dhënave më shpejtë dhe më saktë.IoT ofron një premtim të madh në …


Umphlett Qci Dec 2018, Natalie A. Umphlett Dec 2018

Umphlett Qci Dec 2018, Natalie A. Umphlett

High Plains Regional Climate Center: Staff Publications

Highlights for the Basin

Temperature and Precipitation Anomalies

Mountain Snowpack

Water Resources and Drought

Agriculture

Temperature

Precipitation


Eye Pressure Monitior, Andrea Nella Levy Dec 2018

Eye Pressure Monitior, Andrea Nella Levy

Computer Engineering

The document describes a mobile application that takes information from an attached device which tests eye pressure. The device consists of an IOIO board connected to a custom device that measures the frequency of a given waveform. The device was designed by another student for their senior project, which I am taking over. This device is connected to an IOIO board which is a board designed by a Google employee which works with an android phone in order to create applications that work with embedded systems. The board comes with an API and connects to the phone via a micro-USB. …


Diamond Intracrystalline Stable Isotope Chemical Image Analysis By Time-Of-Flight Secondary Ionization Mass Spectrometery, Tyler J. Sundell Dec 2018

Diamond Intracrystalline Stable Isotope Chemical Image Analysis By Time-Of-Flight Secondary Ionization Mass Spectrometery, Tyler J. Sundell

Graduate Theses/Dissertations

The chemical resistance of diamond allows in-situ study of the diamond source regions. For a majority of gem quality diamonds, this source region is the sublithospheric mantle keel of a cratonic nuclei. Through analysis of stable isotopes, radiogenic isotopes and trace elements, diamond geochemical analyses can define chemical fluxes in the mantle keel. However, such studies require multiple methodologies for each chemical suite, high spatial resolution and analytical precision. Here, I evaluate Time-of-Flight Secondary Ionization Mass Spectrometer (ToF-SIMS) as an alternative method for diamond geochemical analyses. ToF-SIMS analysis can perform in cation and anion mode to measure the entire periodic …


Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert Dec 2018

Euclidian Geometry: Proposed Lesson Plans To Teach Throughout A One Semester Course, Joseph Willert

Mathematics Undergraduate Theses

Overview We provide several engaging lesson plans that would aid in the teaching of geometry, specifically targeting Euclidian Geometry, towards students of high school age. The audience of this piece would be high school or college students who have not yet had an introduction to geometry, but have completed the standard mathematical courses leading up to this point (i.e. algebra, elementary math, etc.). This being the case the lessons and concepts realized in Chapter 1 target a basic understanding of what Euclidian Geometry is and the subsequent chapters aim specifically at underlying properties of a geometry. The main source of …


Coupling Light Into Siliconwaveguide Using Surface Plasmon Polaritons, Jeong Rok Kim Dec 2018

Coupling Light Into Siliconwaveguide Using Surface Plasmon Polaritons, Jeong Rok Kim

Graduate Theses - Physics and Optical Engineering

No abstract provided.


Simulation Of Climate Across The Permian-Triassic Boundary With A Focus On Phytogeographical Data Analysis, Mitali Dinesh Gautam Dec 2018

Simulation Of Climate Across The Permian-Triassic Boundary With A Focus On Phytogeographical Data Analysis, Mitali Dinesh Gautam

Earth & Environmental Sciences Theses - Archive

The present study aims at reconstructing the paleoclimate across the Permian-Triassic Boundary (PTB, 251.9 ± 0.024 Ma) which encompasses one of the major mass extinction events of the Earth’s history. Results are analyzed from sensitivity experiments that have been previously been carried out with a community climate system model (CCSM3) for 4x CO2 higher than the pre-industrial levels of 280 ppmv, 12.7x CO2 and 12.7x CO2 with a lower cloud cover . This study attempts to reconstruct the climate using the floristic patterns derived from plant-fossil data. Finally, simulated biomes are compared with data-derived biomes, in order to validate the …


Influence Of High Aspect Ratio Nanoparticle Filler Addition On Piezoelectric Nanocomposites, Jeremy A. Armas Dec 2018

Influence Of High Aspect Ratio Nanoparticle Filler Addition On Piezoelectric Nanocomposites, Jeremy A. Armas

Master's Theses

Piezoelectric nanogenerators (PNGs) are a new class of energy harvesting materials that show potential as a direct energy source for low powered electronics. Recently, piezoelectric polymers have been utilized for PNG technology due to low toxicity, high flexibility, and facile solution processing which provide manufacturing opportunities such as screen printing. Throughout the last decade, countless projects have focused on how to enhance the energy harvesting capabilities of these PNGs through the incorporation of nanoparticle fillers, which have been reported to enhance the piezoelectric properties of the film either directly through their intrinsic piezoelectric properties or through acting as surfaces for …


Adaptive Parallelism For Coupled, Multithreaded Message-Passing Programs, Samuel K. Gutiérrez Dec 2018

Adaptive Parallelism For Coupled, Multithreaded Message-Passing Programs, Samuel K. Gutiérrez

Computer Science ETDs

Hybrid parallel programming models that combine message passing (MP) and shared- memory multithreading (MT) are becoming more popular, especially with applications requiring higher degrees of parallelism and scalability. Consequently, coupled parallel programs, those built via the integration of independently developed and optimized software libraries linked into a single application, increasingly comprise message-passing libraries with differing preferred degrees of threading, resulting in thread-level heterogeneity. Retroactively matching threading levels between independently developed and maintained libraries is difficult, and the challenge is exacerbated because contemporary middleware services provide only static scheduling policies over entire program executions, necessitating suboptimal, over-subscribed or under-subscribed, configurations. In …


High-Performance Self-Powered Uv Detector Based On Sno2-Tio2 Nanomace Arrays, Duo Chen, Lin Wei, Lingpan Meng, Yanxue Chen, Yufeng Tian, Shishen Yan, Liangmo Mei, Jun Jiao Dec 2018

High-Performance Self-Powered Uv Detector Based On Sno2-Tio2 Nanomace Arrays, Duo Chen, Lin Wei, Lingpan Meng, Yanxue Chen, Yufeng Tian, Shishen Yan, Liangmo Mei, Jun Jiao

Physics Faculty Publications and Presentations

Photoelectrochemical cell-typed self-powered UV detectors have attracted intensive research interest due to their low cost, simple fabrication process, and fast response. In this paper, SnO2-TiO2 nanomace arrays composed of SnO2 nanotube trunk and TiO2 nanobranches were prepared using soft chemical methods, and an environment-friendly self-powered UV photodetector using this nanostructure as the photoanode was assembled. Due to the synergistic effect of greatly accelerated electron-hole separation, enhanced surface area, and reduced charge recombination provided by SnO2-TiO2 nanomace array, the nanostructured detector displays an excellent performance over that based on bare SnO2 arrays. The impact of the growing time of TiO2 branches …


Numerical Study Of Singular And Delta Shock Solutions Using A Large Time Step Method, Ilija Jegdic Dec 2018

Numerical Study Of Singular And Delta Shock Solutions Using A Large Time Step Method, Ilija Jegdic

Applications and Applied Mathematics: An International Journal (AAM)

We illustrate recently proposed large time step method for hyperbolic conservation laws. In the scalar case, it was proved earlier that if the approximate solutions converge boundedly, then they converge to the entropy solution. The main goal of this paper is to consider the large time step method for several systems of hyperbolic conservation laws. We compute approximate solutions to Riemann problems for three genuinely nonlinear one-dimensional systems (the Keyfitz-Kranzer system, the isentropic generalized Chaplygin gas dynamics equations, and the isentropic gas dynamics equations for polytropic gases with vanishing pressure). Besides approximating solutions that contain shocks and rarefaction waves, the …