## Open Topics

Prerequisites: basic knowledge of the Mathematica programming language and LaTeX, interest in writing/formating mathematical documents, working in a bigger team, and structured software development.

Working area: 50% mathematics, 50% informatics.

## Theses in Progress

### Radu’s Ramanujan-Kolberg Algorithm in Mathematica

Master Thesis

Advisor: Peter Paule

Investigator: Bernhard Kepplinger

### Implementation of symbolic geometric method for rational solutions of AODEs

Master Thesis

Advisor: Franz Winkler

Investigator: Fabrizio Zucca

### Formal Design Method For Reasoning about Algorithms and Representing Efficient Programs

PhD Thesis

Advisor: Tudor Jebelean

Investigator: Jakob Praher

### Difference Ring Algorithms for Nested Products

PhD Thesis

Advisor: Carsten Schneider

Investigator: Evans Doe Ocansey

### A Contribution to the Algebro-Geometric Approach for Finding Exact Solutions of ADEs

PhD Thesis

Advisor: Franz Winkler

Investigator: Sebastian Falkensteiner

### Unification and Anti-Unification Algorithms with Proximity Relations

PhD Thesis

Advisor: Teimuraz Kutsia

Investigator: Ioana-Cleopatra Pau

## Finished Theses

### 2019

### Some Problems in Analytic Number Theory

#### Ankush Goswami

University of Florida. PhD Thesis. 2019. First part of this thesis is to appear in Proceedings of Analytic and Combinatorial Number Theory: The Legacy of Ramanujan - A CONFERENCE IN HONOR OF BRUCE C. BERNDT'S 80TH BIRTHDAY.@

author = {Ankush Goswami},

title = {{Some Problems in Analytic Number Theory}},

language = {english},

year = {2019},

note = {First part of this thesis is to appear in Proceedings of Analytic and Combinatorial Number Theory: The Legacy of Ramanujan -- A CONFERENCE IN HONOR OF BRUCE C. BERNDT'S 80TH BIRTHDAY},

translation = {0},

school = {University of Florida},

length = {90}

}

**phdthesis**{RISC5961,author = {Ankush Goswami},

title = {{Some Problems in Analytic Number Theory}},

language = {english},

year = {2019},

note = {First part of this thesis is to appear in Proceedings of Analytic and Combinatorial Number Theory: The Legacy of Ramanujan -- A CONFERENCE IN HONOR OF BRUCE C. BERNDT'S 80TH BIRTHDAY},

translation = {0},

school = {University of Florida},

length = {90}

}

### Flexible and Rigid Labelings of Graphs

#### Jan Legerský

Research Institute for Symbolic Computation, Johannes Kepler University Linz. PhD Thesis. 2019. [url] [pdf]@

author = {Jan Legerský},

title = {{Flexible and Rigid Labelings of Graphs}},

language = {english},

year = {2019},

translation = {0},

school = {Research Institute for Symbolic Computation, Johannes Kepler University Linz},

length = {108},

url = {https://jan.legersky.cz/project/movablegraphs/}

}

**phdthesis**{RISC5941,author = {Jan Legerský},

title = {{Flexible and Rigid Labelings of Graphs}},

language = {english},

year = {2019},

translation = {0},

school = {Research Institute for Symbolic Computation, Johannes Kepler University Linz},

length = {108},

url = {https://jan.legersky.cz/project/movablegraphs/}

}

### A Parallel, In-Place, Rectangular Matrix Transpose Algorithm

#### Stefan Amberger

Research Institute for Symbolic Computatation (RISC), Johannes Kepler University, Linz, Austria. Master Thesis. March 2019. [pdf]@

author = {Stefan Amberger},

title = {{A Parallel, In-Place, Rectangular Matrix Transpose Algorithm}},

language = {english},

abstract = {This thesis presents a novel algorithm for Transposing Rectangular matrices In-place and in Parallel(TRIP) including a proof of correctness and an analysis of work, span and parallelism.After almost 60 years since its introduction, the problem of in-place rectangular matrix transpositionstill does not have a satisfying solution. Increased concurrency in today's computers, and the need for low overhead algorithms to solve memory-intense challenges are motivating the development of algorithmslike TRIP. The algorithm is based on recursive splitting of the matrix into sub-matrices, independent, paralleltransposition of these sub-matrices, and subsequent combining of the results by a parallel, perfect shuffle.We prove correctness of the algorithm for different matrix shapes (ratios of dimensions), and analyzework and span . Compared to out-of-place algorithms, TRIP, implemented in Cilk, trades work-efficiency for parallelism and for being in-place.},

year = {2019},

month = {March},

translation = {0},

institution = {Research Institute for Symbolic Computatation (RISC), Johannes Kepler University, Linz, Austria},

keywords = {linear algebra, parallel computation},

length = {67}

}

**misc**{RISC5916,author = {Stefan Amberger},

title = {{A Parallel, In-Place, Rectangular Matrix Transpose Algorithm}},

language = {english},

abstract = {This thesis presents a novel algorithm for Transposing Rectangular matrices In-place and in Parallel(TRIP) including a proof of correctness and an analysis of work, span and parallelism.After almost 60 years since its introduction, the problem of in-place rectangular matrix transpositionstill does not have a satisfying solution. Increased concurrency in today's computers, and the need for low overhead algorithms to solve memory-intense challenges are motivating the development of algorithmslike TRIP. The algorithm is based on recursive splitting of the matrix into sub-matrices, independent, paralleltransposition of these sub-matrices, and subsequent combining of the results by a parallel, perfect shuffle.We prove correctness of the algorithm for different matrix shapes (ratios of dimensions), and analyzework and span . Compared to out-of-place algorithms, TRIP, implemented in Cilk, trades work-efficiency for parallelism and for being in-place.},

year = {2019},

month = {March},

translation = {0},

institution = {Research Institute for Symbolic Computatation (RISC), Johannes Kepler University, Linz, Austria},

keywords = {linear algebra, parallel computation},

length = {67}

}

### Migrating Mathematical Programs to Web Interface Frameworks

#### Hsuan-Ming Chen

Research Institute for Symbolic Computatation (RISC), Johannes Kepler University, Linz, Austria. Master Thesis. April 2019. Internationaler Universitätslehrgang: Informatics: Engineering & Management. [pdf]@

author = {Hsuan-Ming Chen},

title = {{Migrating Mathematical Programs to Web Interface Frameworks}},

language = {english},

abstract = {A mathematical software system, the RISC Algorithm Language (RISCAL), has beenimplemented in Java; however, it can be only executed on the local machine of the user.The aim of this master thesis is to migrate RISCAL to the web, such that users can accessthe software via a conventional web browser without needing a local installation of thesoftware. In a preparatory phase, this thesis evaluates various web interface frameworksand how these can be executed on the web. Based in the result of this investigation whichcompares the advantages and disadvantages of the frameworks, one framework is selectedas the most promising candidate for future work. The core of the thesis is then themigration of RISCAL to the web on the basis of this framework and the subsequentevaluation of how the demands have been met and how well all of the RISCAL programsare working after the migration.},

year = {2019},

month = {April},

note = {Internationaler Universitätslehrgang: Informatics: Engineering & Management},

translation = {0},

institution = {Research Institute for Symbolic Computatation (RISC), Johannes Kepler University, Linz, Austria},

length = {85}

}

**misc**{RISC5917,author = {Hsuan-Ming Chen},

title = {{Migrating Mathematical Programs to Web Interface Frameworks}},

language = {english},

abstract = {A mathematical software system, the RISC Algorithm Language (RISCAL), has beenimplemented in Java; however, it can be only executed on the local machine of the user.The aim of this master thesis is to migrate RISCAL to the web, such that users can accessthe software via a conventional web browser without needing a local installation of thesoftware. In a preparatory phase, this thesis evaluates various web interface frameworksand how these can be executed on the web. Based in the result of this investigation whichcompares the advantages and disadvantages of the frameworks, one framework is selectedas the most promising candidate for future work. The core of the thesis is then themigration of RISCAL to the web on the basis of this framework and the subsequentevaluation of how the demands have been met and how well all of the RISCAL programsare working after the migration.},

year = {2019},

month = {April},

note = {Internationaler Universitätslehrgang: Informatics: Engineering & Management},

translation = {0},

institution = {Research Institute for Symbolic Computatation (RISC), Johannes Kepler University, Linz, Austria},

length = {85}

}

### 2018

### A Gateway for the Generic Conversion of Protocols for Smart Meters and IoT Applications

#### Ramez Elbaroudy

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Master Thesis. July 2018. [pdf]@

author = {Ramez Elbaroudy},

title = {{A Gateway for the Generic Conversion of Protocols for Smart Meters and IoT Applications}},

language = {english},

abstract = {In the recent years the number of Internet of things (IoT) devices have increased in a remarkable way.Due to this increase of devices many challenges have appeared. One of the most markable challenge isinteroperability challenge, where devices use different standards, protocols and conventions to exchangeinformation. This challenge has appeared because of the different devices’ specifications and the differentmanufacturers of the different types of IoT devices. The current thesis proposes a generic API that canbe used for communication with different IoT devices, which use different conventions and protocols;understanding the underlying conventions or protocols used. In this thesis, we used smart meters as theIoT devices for testing the generic API. The generic API is first described in an abstract way; then wedescribe the Java binding in order to use the API with the Java programming language. The implementedgeneric API enables developers to communicate with different IoT devices without the need of knowing thespecification of each protocol. The current thesis can be considered as an important point of extendingthe research field of interoperability of IoT devices. Furthermore, the generic API can be extended inorder to support other types of protocols and conventions.},

year = {2018},

month = {July},

translation = {0},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria},

length = {85}

}

**misc**{RISC5727,author = {Ramez Elbaroudy},

title = {{A Gateway for the Generic Conversion of Protocols for Smart Meters and IoT Applications}},

language = {english},

abstract = {In the recent years the number of Internet of things (IoT) devices have increased in a remarkable way.Due to this increase of devices many challenges have appeared. One of the most markable challenge isinteroperability challenge, where devices use different standards, protocols and conventions to exchangeinformation. This challenge has appeared because of the different devices’ specifications and the differentmanufacturers of the different types of IoT devices. The current thesis proposes a generic API that canbe used for communication with different IoT devices, which use different conventions and protocols;understanding the underlying conventions or protocols used. In this thesis, we used smart meters as theIoT devices for testing the generic API. The generic API is first described in an abstract way; then wedescribe the Java binding in order to use the API with the Java programming language. The implementedgeneric API enables developers to communicate with different IoT devices without the need of knowing thespecification of each protocol. The current thesis can be considered as an important point of extendingthe research field of interoperability of IoT devices. Furthermore, the generic API can be extended inorder to support other types of protocols and conventions.},

year = {2018},

month = {July},

translation = {0},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria},

length = {85}

}

### Das Shifting-Bottleneck Verfahren für das Job-Shop Scheduling-Problem

#### M. Schlenkrich

JKU Linz. Bachelor Thesis. September 2018. [pdf]@

author = {M. Schlenkrich},

title = {{Das Shifting-Bottleneck Verfahren für das Job-Shop Scheduling-Problem}},

language = {deutsch},

abstract = {Schedulingprobleme treten in unserer Welt in den verschiedensten Bereichen auf.Egal ob in Krankenhäusern bei der Zuteilung von Patienten zu Behandlungs-räumen, in Tischlereien und anderen Manufakturen bei der Abfolge von Ar-beitsschritten auf Maschinen oder der Nutzung von Schienentrassen im Bahn-verkehr. Das Lösen dieser Ablaufplanungsprobleme ist oftmals essentiell, umeinen reibungsfreien Arbeitsalltag garantieren zu können oder um Produktions-prozesse zu optimieren.Eine besonders häufig auftretende Variante dieser Schedulingprobleme istdas sogenannte Job-Shop Ablaufplanungsproblem, bei dem die Aufträge aufallen zur Verfügung stehenden Ressourcen in einer definierten Reihenfolge be-arbeitet werden müssen. Für große Problemdaten mit einer hohen Anzahl anAufträgen und Maschinen ist das Lösen dieser Probleme sehr aufwändig und immathematisch-wissenschaftlichen Bereich noch nicht zur Gänze erforscht.Eine Methode zur Lösung dieser Problemklasse ist die Shifting-BottleneckHeuristik. Wie der Name schon verrät, handelt es sich dabei nicht um ein exaktesVerfahren, sondern um eine Heuristik, die zwar eine zulässige Lösung liefert, diesjedoch nicht unbedingt das Optimum sein muss. In der Regel sind die Lösungendieses Verfahrens jedoch sehr gute Näherungen.Dieses Verfahren löst mehrere kleinere Hilfsprobleme und gelangt nach mIterationen zu einem Ergebnis, wobei m die Anzahl der Ressourcen bzw. Ma-schinen ist. Das Lösen dieser Hilfsprobleme geschieht zwar exakt, was Zeit undRechenaufwand kostet, diese sind jedoch um einiges einfacher zu lösen als dasGesamtproblem und somit bleibt der Aufwand in einem akzeptablen Rahmen.Die Basisversion der Shifting-Bottleneck Heuristik wurde im Rahmen dieserArbeit in Python implementiert und mit Benchmarkproblemdaten aus der Li-teratur getestet.},

year = {2018},

month = {September},

translation = {0},

institution = {JKU Linz},

length = {36}

}

**misc**{RISC5874,author = {M. Schlenkrich},

title = {{Das Shifting-Bottleneck Verfahren für das Job-Shop Scheduling-Problem}},

language = {deutsch},

abstract = {Schedulingprobleme treten in unserer Welt in den verschiedensten Bereichen auf.Egal ob in Krankenhäusern bei der Zuteilung von Patienten zu Behandlungs-räumen, in Tischlereien und anderen Manufakturen bei der Abfolge von Ar-beitsschritten auf Maschinen oder der Nutzung von Schienentrassen im Bahn-verkehr. Das Lösen dieser Ablaufplanungsprobleme ist oftmals essentiell, umeinen reibungsfreien Arbeitsalltag garantieren zu können oder um Produktions-prozesse zu optimieren.Eine besonders häufig auftretende Variante dieser Schedulingprobleme istdas sogenannte Job-Shop Ablaufplanungsproblem, bei dem die Aufträge aufallen zur Verfügung stehenden Ressourcen in einer definierten Reihenfolge be-arbeitet werden müssen. Für große Problemdaten mit einer hohen Anzahl anAufträgen und Maschinen ist das Lösen dieser Probleme sehr aufwändig und immathematisch-wissenschaftlichen Bereich noch nicht zur Gänze erforscht.Eine Methode zur Lösung dieser Problemklasse ist die Shifting-BottleneckHeuristik. Wie der Name schon verrät, handelt es sich dabei nicht um ein exaktesVerfahren, sondern um eine Heuristik, die zwar eine zulässige Lösung liefert, diesjedoch nicht unbedingt das Optimum sein muss. In der Regel sind die Lösungendieses Verfahrens jedoch sehr gute Näherungen.Dieses Verfahren löst mehrere kleinere Hilfsprobleme und gelangt nach mIterationen zu einem Ergebnis, wobei m die Anzahl der Ressourcen bzw. Ma-schinen ist. Das Lösen dieser Hilfsprobleme geschieht zwar exakt, was Zeit undRechenaufwand kostet, diese sind jedoch um einiges einfacher zu lösen als dasGesamtproblem und somit bleibt der Aufwand in einem akzeptablen Rahmen.Die Basisversion der Shifting-Bottleneck Heuristik wurde im Rahmen dieserArbeit in Python implementiert und mit Benchmarkproblemdaten aus der Li-teratur getestet.},

year = {2018},

month = {September},

translation = {0},

institution = {JKU Linz},

length = {36}

}

### 2017

### An Online Auction System for Selling Fiber Products

#### C. Ilonka

ISI Hagenberg, JKU Linz. Master Thesis. July 2017. [pdf]@

author = {C. Ilonka},

title = {{An Online Auction System for Selling Fiber Products}},

language = {english},

abstract = {The thesis presents the design and development of the Lenzing Global Auction Portalproject. The Lenzing Global Auction Portal is a software system for running multiplesimultaneous online auctions. The system implements the Dutch auction model, butprovides the means to integrate different auction models as well.The system is based on the Client/Server architecture model. The server-side follows themicroservice based architecture model combined with the multi-layer architecture model.The client-side consists of two mobile-first web applications following the single-pageapplication principle.},

year = {2017},

month = {July},

translation = {0},

institution = {ISI Hagenberg, JKU Linz},

length = {60}

}

**misc**{RISC5873,author = {C. Ilonka},

title = {{An Online Auction System for Selling Fiber Products}},

language = {english},

abstract = {The thesis presents the design and development of the Lenzing Global Auction Portalproject. The Lenzing Global Auction Portal is a software system for running multiplesimultaneous online auctions. The system implements the Dutch auction model, butprovides the means to integrate different auction models as well.The system is based on the Client/Server architecture model. The server-side follows themicroservice based architecture model combined with the multi-layer architecture model.The client-side consists of two mobile-first web applications following the single-pageapplication principle.},

year = {2017},

month = {July},

translation = {0},

institution = {ISI Hagenberg, JKU Linz},

length = {60}

}

### Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities

#### Liangjie Ye

RISC and the DK program Linz. PhD Thesis. 2017. Updated version in June 2017. [pdf]@

author = {Liangjie Ye},

title = {{Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities}},

language = {english},

year = {2017},

note = {Updated version in June 2017},

translation = {0},

school = {RISC and the DK program Linz},

length = {122}

}

**phdthesis**{RISC5463,author = {Liangjie Ye},

title = {{Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities}},

language = {english},

year = {2017},

note = {Updated version in June 2017},

translation = {0},

school = {RISC and the DK program Linz},

length = {122}

}

### 2016

### Axiomatic Description of Gröbner Reduction

#### Christoph Fuerst

RISC, JKU Linz. PhD Thesis. December 2016. [pdf]@

author = {Christoph Fuerst},

title = {{Axiomatic Description of Gröbner Reduction}},

language = {english},

year = {2016},

month = {December},

translation = {0},

school = {RISC, JKU Linz},

length = {154}

}

**phdthesis**{RISC5388,author = {Christoph Fuerst},

title = {{Axiomatic Description of Gröbner Reduction}},

language = {english},

year = {2016},

month = {December},

translation = {0},

school = {RISC, JKU Linz},

length = {154}

}

### Algebraic Geometry methods in Kinematics: Mobile Pods

#### Matteo Gallet

Johannes Kepler University. PhD Thesis. October 2016.@

author = {Matteo Gallet},

title = {{Algebraic Geometry methods in Kinematics: Mobile Pods}},

language = {English},

year = {2016},

month = {October},

translation = {0},

school = {Johannes Kepler University},

length = {82}

}

**phdthesis**{RISC5393,author = {Matteo Gallet},

title = {{Algebraic Geometry methods in Kinematics: Mobile Pods}},

language = {English},

year = {2016},

month = {October},

translation = {0},

school = {Johannes Kepler University},

length = {82}

}

### Computer-Assisted Exploration of Gröbner Bases Theory in Theorema

#### A. Maletzky

RISC, Johannes Kepler University Linz. PhD Thesis. May 2016.@

author = {A. Maletzky},

title = {{Computer-Assisted Exploration of Gröbner Bases Theory in Theorema}},

language = {english},

year = {2016},

month = {May},

translation = {0},

school = {RISC, Johannes Kepler University Linz},

length = {197}

}

**phdthesis**{RISC5361,author = {A. Maletzky},

title = {{Computer-Assisted Exploration of Gröbner Bases Theory in Theorema}},

language = {english},

year = {2016},

month = {May},

translation = {0},

school = {RISC, Johannes Kepler University Linz},

length = {197}

}

### Formally Modeling and Analyzing Mathematical Algorithms with Software Specification Languages & Tools

#### Daniela Ritirc

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Master Thesis. January 2016. [pdf]@

author = {Daniela Ritirc},

title = {{Formally Modeling and Analyzing Mathematical Algorithms with Software Specification Languages & Tools}},

language = {english},

abstract = {In this thesis the behaviour of software specification languages and tools on mathematicalalgorithms shall be investigated. The main goal is to investigate how tools which havebeen designed for modeling and analyzing software in other application contexts can beapplied to mathematical algorithms. For this purpose, two different mathematical algorithms,namely the DPLL method and Dijkstra’s Shortest Path Algorithm are selected.Furthermore five well-known software specification languages are selected: JML, Alloy,TLA/PlusCal, VDM and Event-B. It shall be examined how far the algorithms can bemodeled and how far model checking respectively verification succeeds. The goal of thethesis is not a proper verification/check of every model with every tool but a survey ofthe potential as well as the difficulties of the usage of software specification languagesfor the analysis of mathematical algorithms.As a starting point for each algorithm a formal specification is derived and the algorithmsare supplied in pseudo-code. A Java prototype is implemented for each algorithmwhich is then specified by JML annotations. Furthermore the algorithms are modelled inTLA/PlusCal, Alloy, VDM and Event-B and for each language the appropriate analysissupported by the tool is selected (visualizing, model checking, verification).The main result of the thesis is that each tool shows some success when it is usedfor specifying and analyzing mathematical algorithms, because modeling the algorithmssucceeded in every language. In TLA, VDM and Alloy it was possible to completelymodel check the specifications. Furthermore it was possible to visualize the algorithmsin Alloy. In JML and Event-B it was possible to verify major parts of the model;},

year = {2016},

month = {January},

translation = {0},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria},

keywords = {formal methods, model checking, program verification},

length = {167}

}

**misc**{RISC5224,author = {Daniela Ritirc},

title = {{Formally Modeling and Analyzing Mathematical Algorithms with Software Specification Languages & Tools}},

language = {english},

abstract = {In this thesis the behaviour of software specification languages and tools on mathematicalalgorithms shall be investigated. The main goal is to investigate how tools which havebeen designed for modeling and analyzing software in other application contexts can beapplied to mathematical algorithms. For this purpose, two different mathematical algorithms,namely the DPLL method and Dijkstra’s Shortest Path Algorithm are selected.Furthermore five well-known software specification languages are selected: JML, Alloy,TLA/PlusCal, VDM and Event-B. It shall be examined how far the algorithms can bemodeled and how far model checking respectively verification succeeds. The goal of thethesis is not a proper verification/check of every model with every tool but a survey ofthe potential as well as the difficulties of the usage of software specification languagesfor the analysis of mathematical algorithms.As a starting point for each algorithm a formal specification is derived and the algorithmsare supplied in pseudo-code. A Java prototype is implemented for each algorithmwhich is then specified by JML annotations. Furthermore the algorithms are modelled inTLA/PlusCal, Alloy, VDM and Event-B and for each language the appropriate analysissupported by the tool is selected (visualizing, model checking, verification).The main result of the thesis is that each tool shows some success when it is usedfor specifying and analyzing mathematical algorithms, because modeling the algorithmssucceeded in every language. In TLA, VDM and Alloy it was possible to completelymodel check the specifications. Furthermore it was possible to visualize the algorithmsin Alloy. In JML and Event-B it was possible to verify major parts of the model;},

year = {2016},

month = {January},

translation = {0},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria},

keywords = {formal methods, model checking, program verification},

length = {167}

}

### Rational and Algebraic Solutions of First-Order Algebraic ODEs

#### N. Thieu Vo

Research Institute for Symbolic Computation. PhD Thesis. 2016. [pdf]@

author = {N. Thieu Vo},

title = {{Rational and Algebraic Solutions of First-Order Algebraic ODEs}},

language = {english},

year = {2016},

translation = {0},

school = {Research Institute for Symbolic Computation},

length = {93}

}

**phdthesis**{RISC5399,author = {N. Thieu Vo},

title = {{Rational and Algebraic Solutions of First-Order Algebraic ODEs}},

language = {english},

year = {2016},

translation = {0},

school = {Research Institute for Symbolic Computation},

length = {93}

}

### 2015

### Anti-Unification Algorithms: Design, Analysis, and Implementation

#### Alexander Baumgartner

RISC, JKU Linz. PhD Thesis. September 2015. [pdf]@

author = {Alexander Baumgartner},

title = {{Anti-Unification Algorithms: Design, Analysis, and Implementation}},

language = {english},

year = {2015},

month = {September},

translation = {0},

school = {RISC, JKU Linz},

length = {169}

}

**phdthesis**{RISC5180,author = {Alexander Baumgartner},

title = {{Anti-Unification Algorithms: Design, Analysis, and Implementation}},

language = {english},

year = {2015},

month = {September},

translation = {0},

school = {RISC, JKU Linz},

length = {169}

}

### Symbolic solutions of first-order algebraic differential equations

#### Georg Grasegger

Johannes Kepler University Linz. PhD Thesis. 06 2015. [url]@

author = {Georg Grasegger},

title = {{Symbolic solutions of first-order algebraic differential equations}},

language = {english},

year = {2015},

month = {06},

translation = {0},

school = {Johannes Kepler University Linz},

length = {154},

url = {http://epub.jku.at/obvulihs/content/titleinfo/753082}

}

**phdthesis**{RISC5160,author = {Georg Grasegger},

title = {{Symbolic solutions of first-order algebraic differential equations}},

language = {english},

year = {2015},

month = {06},

translation = {0},

school = {Johannes Kepler University Linz},

length = {154},

url = {http://epub.jku.at/obvulihs/content/titleinfo/753082}

}

### Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points

#### H. Rahkooy

RISC, JKU Linz. PhD Thesis. July 2015.@

author = {H. Rahkooy},

title = {{Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points}},

language = {english},

year = {2015},

month = {July},

translation = {0},

school = {RISC, JKU Linz},

length = {69}

}

**phdthesis**{RISC5288,author = {H. Rahkooy},

title = {{Dual Space Algorithms for Computing Multiplicity Structure of Isolated Points}},

language = {english},

year = {2015},

month = {July},

translation = {0},

school = {RISC, JKU Linz},

length = {69}

}

### Gröbner Bases and Generalized Sylvester Matrices

#### Manuela Wiesinger-Widi

Johannes Kepler University Linz. PhD Thesis. 07 2015. [url]@

author = {Manuela Wiesinger-Widi},

title = {{Gröbner Bases and Generalized Sylvester Matrices}},

language = {english},

year = {2015},

month = {07},

translation = {0},

school = {Johannes Kepler University Linz},

length = {116},

url = {http://epub.jku.at/obvulihs/content/titleinfo/776913}

}

**phdthesis**{RISC5170,author = {Manuela Wiesinger-Widi},

title = {{Gröbner Bases and Generalized Sylvester Matrices}},

language = {english},

year = {2015},

month = {07},

translation = {0},

school = {Johannes Kepler University Linz},

length = {116},

url = {http://epub.jku.at/obvulihs/content/titleinfo/776913}

}

### 2014

### Fast and rigorous computation of special functions to high precision

#### F. Johansson

RISC. PhD Thesis. 2014. [pdf]@

author = {F. Johansson},

title = {{Fast and rigorous computation of special functions to high precision}},

language = {english},

year = {2014},

translation = {0},

school = {RISC},

length = {0}

}

**phdthesis**{RISC4972,author = {F. Johansson},

title = {{Fast and rigorous computation of special functions to high precision}},

language = {english},

year = {2014},

translation = {0},

school = {RISC},

length = {0}

}

### Computer Algebra and Analysis: Complex Variables Visualized

#### Thomas Ponweiser

RISC Institute, JKU Linz, Austria. Diploma Thesis. 2014. [pdf]@

author = {Thomas Ponweiser},

title = {{Computer Algebra and Analysis: Complex Variables Visualized}},

language = {english},

year = {2014},

translation = {0},

school = {RISC Institute, JKU Linz, Austria},

length = {102}

}

**mastersthesis**{RISC5011,author = {Thomas Ponweiser},

title = {{Computer Algebra and Analysis: Complex Variables Visualized}},

language = {english},

year = {2014},

translation = {0},

school = {RISC Institute, JKU Linz, Austria},

length = {102}

}

### 2013

### 3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS

#### Alexander Hasselhuhn

TU Dortmund University. PhD Thesis. 2013. [url]@

author = {Alexander Hasselhuhn},

title = {{3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS}},

language = {english},

abstract = {The present thesis presents the calculation of higher order corrections to the structure functions of deep-inelastic scattering. In particular heavy quark effects in QCD corrections are determined on the 3-loop level. In the asymptotic region Q^2 >> m^2, the heavy flavor Wilson coefficients can be represented in terms of the light flavor Wilson coefficients and the massive operator matrix elements (OMEs). New contributions to the OMEs A_{gq,Q} and A_{gg,Q} are obtained. Furthermore, methods for the computer algebraic computation of ladder diagrams are given, making use of different representations of generalized hypergeometric functions and Appell functions. Here symbolic summation techniques are applied. For the calculation of graphs with two disjoint massive cycles, these methods are altered including Mellin-Barnes integrals and properties of iterated integrals. Finally, for the process of charged current deep-inelastic scattering, the complete 2-loop corrections to the heavy flavor Wilson coefficients are constructed and given in x-space and Mellin-space. The results of the thesis are necessary for the precise determination of the parton densities (PDFs) and the strong coupling constant at 3-loop precision.},

year = {2013},

translation = {0},

school = {TU Dortmund University},

length = {179},

url = {http://www.ub.tu-dortmund.de/katalog/titel/1435872}

}

**phdthesis**{RISC4942,author = {Alexander Hasselhuhn},

title = {{3-loop contributions to heavy flavor Wilson coefficients of neutral and charged current DIS}},

language = {english},

abstract = {The present thesis presents the calculation of higher order corrections to the structure functions of deep-inelastic scattering. In particular heavy quark effects in QCD corrections are determined on the 3-loop level. In the asymptotic region Q^2 >> m^2, the heavy flavor Wilson coefficients can be represented in terms of the light flavor Wilson coefficients and the massive operator matrix elements (OMEs). New contributions to the OMEs A_{gq,Q} and A_{gg,Q} are obtained. Furthermore, methods for the computer algebraic computation of ladder diagrams are given, making use of different representations of generalized hypergeometric functions and Appell functions. Here symbolic summation techniques are applied. For the calculation of graphs with two disjoint massive cycles, these methods are altered including Mellin-Barnes integrals and properties of iterated integrals. Finally, for the process of charged current deep-inelastic scattering, the complete 2-loop corrections to the heavy flavor Wilson coefficients are constructed and given in x-space and Mellin-space. The results of the thesis are necessary for the precise determination of the parton densities (PDFs) and the strong coupling constant at 3-loop precision.},

year = {2013},

translation = {0},

school = {TU Dortmund University},

length = {179},

url = {http://www.ub.tu-dortmund.de/katalog/titel/1435872}

}