Total differential scattering cross section of {Ar^+}-Ar at 15 to 400 keV

We report on the measurement of the total differential scattering cross section of {Ar^+}-Ar at laboratory energies between 15 and 400 keV. Using an ab initio relativistic molecular program which calculates the interatomic potential energy curve with high accuracy, we are able to reproduce the detailed structure found in the experiment.

An introduction to ordinary differential equations by computer algebra-systems

We report on an elementary course in ordinary differential equations (odes) for students in engineering sciences. The course is also intended to become a self-study package for odes and is is based on several interactive computer lessons using REDUCE and MATHEMATICA . The aim of the course is not to do Computer Algebra (CA) by example or to use it for doing classroom examples. The aim ist to teach and to learn mathematics by using CA-systems.

A High Order Finite Volume Scheme for the 2D Shallow Water Equations Including Topography

Inhalt dieser Arbeit ist ein Verfahren zur numerischen Lösung der zweidimensionalen Flachwassergleichung, welche das Fließverhalten von Gewässern, deren Oberflächenausdehnung wesentlich größer als deren Tiefe ist, modelliert. Diese Gleichung beschreibt die gravitationsbedingte zeitliche Änderung eines gegebenen Anfangszustandes bei Gewässern mit freier Oberfläche. Diese Klasse beinhaltet Probleme wie das Verhalten von Wellen an flachen Stränden oder die Bewegung einer Flutwelle in einem Fluss. Diese Beispiele zeigen deutlich die Notwendigkeit, den Einfluss von Topographie sowie die Behandlung von Nass/Trockenübergängen im Verfahren zu berücksichtigen. In der vorliegenden Dissertation wird ein, in Gebieten mit hinreichender Wasserhöhe, hochgenaues Finite-Volumen-Verfahren zur numerischen Bestimmung des zeitlichen Verlaufs der Lösung der zweidimensionalen Flachwassergleichung aus gegebenen Anfangs- und Randbedingungen auf einem unstrukturierten Gitter vorgestellt, welches in der Lage ist, den Einfluss topographischer Quellterme auf die Strömung zu berücksichtigen, sowie in sogenannten \glqq lake at rest\grqq-stationären Zuständen diesen Einfluss mit den numerischen Flüssen exakt auszubalancieren. Basis des Verfahrens ist ein Finite-Volumen-Ansatz erster Ordnung, welcher durch eine WENO Rekonstruktion unter Verwendung der Methode der kleinsten Quadrate und eine sogenannte Space Time Expansion erweitert wird mit dem Ziel, ein Verfahren beliebig hoher Ordnung zu erhalten. Die im Verfahren auftretenden Riemannprobleme werden mit dem Riemannlöser von Chinnayya, LeRoux und Seguin von 1999 gelöst, welcher die Einflüsse der Topographie auf den Strömungsverlauf mit berücksichtigt. Es wird in der Arbeit bewiesen, dass die Koeffizienten der durch das WENO-Verfahren berechneten Rekonstruktionspolynome die räumlichen Ableitungen der zu rekonstruierenden Funktion mit einem zur Verfahrensordnung passenden Genauigkeitsgrad approximieren. Ebenso wird bewiesen, dass die Koeffizienten des aus der Space Time Expansion resultierenden Polynoms die räumlichen und zeitlichen Ableitungen der Lösung des Anfangswertproblems approximieren. Darüber hinaus wird die wohlbalanciertheit des Verfahrens für beliebig hohe numerische Ordnung bewiesen. Für die Behandlung von Nass/Trockenübergangen wird eine Methode zur Ordnungsreduktion abhängig von Wasserhöhe und Zellgröße vorgeschlagen. Dies ist notwendig, um in der Rechnung negative Werte für die Wasserhöhe, welche als Folge von Oszillationen des Raum-Zeit-Polynoms auftreten können, zu vermeiden. Numerische Ergebnisse die die theoretische Verfahrensordnung bestätigen werden ebenso präsentiert wie Beispiele, welche die hervorragenden Eigenschaften des Gesamtverfahrens in der Berechnung herausfordernder Probleme demonstrieren.

Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Comparison of different methods in estimating potential evapotranspiration at Muda Irrigation Scheme of Malaysia

Evapotranspiration (ET) is a complex process in the hydrological cycle that influences the quantity of runoff and thus the irrigation water requirements. Numerous methods have been developed to estimate potential evapotranspiration (PET). Unfortunately, most of the reliable PET methods are parameter rich models and therefore, not feasible for application in data scarce regions. On the other hand, accuracy and reliability of simple PET models vary widely according to regional climate conditions. The objective of the present study was to evaluate the performance of three temperature-based and three radiation-based simple ET methods in estimating historical ET and projecting future ET at Muda Irrigation Scheme at Kedah, Malaysia. The performance was measured by comparing those methods with the parameter intensive Penman-Monteith Method. It was found that radiation based methods gave better performance compared to temperature-based methods in estimation of ET in the study area. Future ET simulated from projected climate data obtained through statistical downscaling technique also showed that radiation-based methods can project closer ET values to that projected by Penman-Monteith Method. It is expected that the study will guide in selecting suitable methods for estimating and projecting ET in accordance to availability of meteorological data.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

A storage scheme for an automated archive

Presentation given at the Al-Azhar Engineering First Conference, AEC’89, Dec. 9-12 1989, Cairo, Egypt. The paper presented at AEC'89 suggests an infinite storage scheme divided into one volume which is online and an arbitrary number of off-line volumes arranged into a linear chain which hold records which haven't been accessed recently. The online volume holds the records in sorted order (e.g. as a B-tree) and contains shortest prefixes of keys of records already pushed offline. As new records enter, older ones are retired to the first volume which is going offline next. Statistical arguments are given for the rate at which an off-line volume needs to be fetched to reload a record which had been retired before. The rate depends on the distribution of access probabilities as a function of time. Applications are medical records, production records or other data which need to be kept for a long time for legal reasons.

Identifikation spezieller Funktionen, die durch Rodriguesformeln gegeben sind

Es ist allgemein bekannt, dass sich zwei gegebene Systeme spezieller Funktionen durch Angabe einer Rekursionsgleichung und entsprechend vieler Anfangswerte identifizieren lassen, denn computeralgebraisch betrachtet hat man damit eine Normalform vorliegen. Daher hat sich die interessante Forschungsfrage ergeben, Funktionensysteme zu identifizieren, die über ihre Rodriguesformel gegeben sind. Zieht man den in den 1990er Jahren gefundenen Zeilberger-Algorithmus für holonome Funktionenfamilien hinzu, kann die Rodriguesformel algorithmisch in eine Rekursionsgleichung überführt werden. Falls die Funktionenfamilie überdies hypergeometrisch ist, sogar laufzeiteffizient. Um den Zeilberger-Algorithmus überhaupt anwenden zu können, muss es gelingen, die Rodriguesformel in eine Summe umzuwandeln. Die vorliegende Arbeit beschreibt die Umwandlung einer Rodriguesformel in die genannte Normalform für den kontinuierlichen, den diskreten sowie den q-diskreten Fall vollständig. Das in Almkvist und Zeilberger (1990) angegebene Vorgehen im kontinuierlichen Fall, wo die in der Rodriguesformel auftauchende n-te Ableitung über die Cauchysche Integralformel in ein komplexes Integral überführt wird, zeigt sich im diskreten Fall nun dergestalt, dass die n-te Potenz des Vorwärtsdifferenzenoperators in eine Summenschreibweise überführt wird. Die Rekursionsgleichung aus dieser Summe zu generieren, ist dann mit dem diskreten Zeilberger-Algorithmus einfach. Im q-Fall wird dargestellt, wie Rekursionsgleichungen aus vier verschiedenen q-Rodriguesformeln gewonnen werden können, wobei zunächst die n-te Potenz der jeweiligen q-Operatoren in eine Summe überführt wird. Drei der vier Summenformeln waren bislang unbekannt. Sie wurden experimentell gefunden und per vollständiger Induktion bewiesen. Der q-Zeilberger-Algorithmus erzeugt anschließend aus diesen Summen die gewünschte Rekursionsgleichung. In der Praxis ist es sinnvoll, den schnellen Zeilberger-Algorithmus anzuwenden, der Rekursionsgleichungen für bestimmte Summen über hypergeometrische Terme ausgibt. Auf dieser Fassung des Algorithmus basierend wurden die Überlegungen in Maple realisiert. Es ist daher sinnvoll, dass alle hier aufgeführten Prozeduren, die aus kontinuierlichen, diskreten sowie q-diskreten Rodriguesformeln jeweils Rekursionsgleichungen erzeugen, an den hypergeometrischen Funktionenfamilien der klassischen orthogonalen Polynome, der klassischen diskreten orthogonalen Polynome und an der q-Hahn-Klasse des Askey-Wilson-Schemas vollständig getestet werden. Die Testergebnisse liegen tabellarisch vor. Ein bedeutendes Forschungsergebnis ist, dass mit der im q-Fall implementierten Prozedur zur Erzeugung einer Rekursionsgleichung aus der Rodriguesformel bewiesen werden konnte, dass die im Standardwerk von Koekoek/Lesky/Swarttouw(2010) angegebene Rodriguesformel der Stieltjes-Wigert-Polynome nicht korrekt ist. Die richtige Rodriguesformel wurde experimentell gefunden und mit den bereitgestellten Methoden bewiesen. Hervorzuheben bleibt, dass an Stelle von Rekursionsgleichungen analog Differential- bzw. Differenzengleichungen für die Identifikation erzeugt wurden. Wie gesagt gehört zu einer Normalform für eine holonome Funktionenfamilie die Angabe der Anfangswerte. Für den kontinuierlichen Fall wurden umfangreiche, in dieser Gestalt in der Literatur noch nie aufgeführte Anfangswertberechnungen vorgenommen. Im diskreten Fall musste für die Anfangswertberechnung zur Differenzengleichung der Petkovsek-van-Hoeij-Algorithmus hinzugezogen werden, um die hypergeometrischen Lösungen der resultierenden Rekursionsgleichungen zu bestimmen. Die Arbeit stellt zu Beginn den schnellen Zeilberger-Algorithmus in seiner kontinuierlichen, diskreten und q-diskreten Variante vor, der das Fundament für die weiteren Betrachtungen bildet. Dabei wird gebührend auf die Unterschiede zwischen q-Zeilberger-Algorithmus und diskretem Zeilberger-Algorithmus eingegangen. Bei der praktischen Umsetzung wird Bezug auf die in Maple umgesetzten Zeilberger-Implementationen aus Koepf(1998/2014) genommen. Die meisten der umgesetzten Prozeduren werden im Text dokumentiert. Somit wird ein vollständiges Paket an Algorithmen bereitgestellt, mit denen beispielsweise Formelsammlungen für hypergeometrische Funktionenfamilien überprüft werden können, deren Rodriguesformeln bekannt sind. Gleichzeitig kann in Zukunft für noch nicht erforschte hypergeometrische Funktionenklassen die beschreibende Rekursionsgleichung erzeugt werden, wenn die Rodriguesformel bekannt ist.

Performance Evaluation of the Scheme 86 and HP Precision Architecture

The Scheme86 and the HP Precision Architectures represent different trends in computer processor design. The former uses wide micro-instructions, parallel hardware, and a low latency memory interface. The latter encourages pipelined implementation and visible interlocks. To compare the merits of these approaches, algorithms frequently encountered in numerical and symbolic computation were hand-coded for each architecture. Timings were done in simulators and the results were evaluated to determine the speed of each design. Based on these measurements, conclusions were drawn as to which aspects of each architecture are suitable for a high- performance computer.

Dissociated Dipoles: Image representation via non-local comparisons

A fundamental question in visual neuroscience is how to represent image structure. The most common representational schemes rely on differential operators that compare adjacent image regions. While well-suited to encoding local relationships, such operators have significant drawbacks. Specifically, each filter's span is confounded with the size of its sub-fields, making it difficult to compare small regions across large distances. We find that such long-distance comparisons are more tolerant to common image transformations than purely local ones, suggesting they may provide a useful vocabulary for image encoding. . We introduce the "Dissociated Dipole," or "Sticks" operator, for encoding non-local image relationships. This operator de-couples filter span from sub-field size, enabling parametric movement between edge and region-based representation modes. We report on the perceptual plausibility of the operator, and the computational advantages of non-local encoding. Our results suggest that non-local encoding may be an effective scheme for representing image structure.

A DHT-Based Grid Resource Indexing and Discovery Scheme

This paper presents a DHT-based grid resource indexing and discovery (DGRID) approach. With DGRID, resource-information data is stored on its own administrative domain and each domain, represented by an index server, is virtualized to several nodes (virtual servers) subjected to the number of resource types it has. Then, all nodes are arranged as a structured overlay network or distributed hash table (DHT). Comparing to existing grid resource indexing and discovery schemes, the benefits of DGRID include improving the security of domains, increasing the availability of data, and eliminating stale data.

A Conservative Front Tracking Algorithm

The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.

Differential effects of insulin signaling on individual carbon fluxes for fatty acid synthesis in brown adipocytes

Considering the major role of insulin signaling on fatty acid synthesis via stimulation of lipogenic enzymes, differential effects of insulin signaling on individual carbon fluxes for fatty acid synthesis have been investigated by comparing the individual lipogenic fluxes in WT and IRS-1 knockout (IRS-1 KO) brown adipocytes. Results from experiments on WT and IRS-1 KO cells incubated with [5-¹³C] glutamine were consistent with the existence of reductive carboxylation pathway. Analysis of isotopomer distribution of nine metabolites related to the lipogenic routes from glucose and glutamine in IRS-1 KO cells using [U-¹³C] glutamine as compared to that in WT cells indicated that flux through reductive carboxylation pathway was diminished while flux through conventional TCA cycle was stimulated due to absence of insulin signaling in IRS-1 KO cells. This observation was confirmed by quantitative estimation of individual lipogenic fluxes in IRS-1 KO cells and their comparison with fluxes in WT cells. Thus, these results suggest that glutamine’s substantial contribution to fatty acid synthesis can be directly manipulated by controlling the flux through reductive carboxylation of alpha-ketoglutarate to citrate using hormone (insulin).

SCAPA (Spacially Addressable Protein Array) – a Novel Protein Array for the Differential Profiling of Ligand-receptor Induced Signalling

While protein microarray technology has been successful in demonstrating its usefulness for large scale high-throughput proteome profiling, performance of antibody/antigen microarrays has been only moderately productive. Immobilization of either the capture antibodies or the protein samples on solid supports has severe drawbacks. Denaturation of the immobilized proteins as well as inconsistent orientation of antibodies/ligands on the arrays can lead to erroneous results. This has prompted a number of studies to address these challenges by immobilizing proteins on biocompatible surfaces, which has met with limited success. Our strategy relates to a multiplexed, sensitive and high-throughput method for the screening quantification of intracellular signalling proteins from a complex mixture of proteins. Each signalling protein to be monitored has its capture moiety linked to a specific oligo ‘tag’. The array involves the oligonucleotide hybridization-directed localization and identification of different signalling proteins simultaneously, in a rapid and easy manner. Antibodies have been used as the capture moieties for specific identification of each signaling protein. The method involves covalently partnering each antibody/protein molecule with a unique DNA or DNA derivatives oligonucleotide tag that directs the antibody to a unique site on the microarray due to specific hybridization with a complementary tag-probe on the array. Particular surface modifications and optimal conditions allowed high signal to noise ratio which is essential to the success of this approach.

Differential epipolar constraint in mobile robot egomotion estimation

The estimation of camera egomotion is a well established problem in computer vision. Many approaches have been proposed based on both the discrete and the differential epipolar constraint. The discrete case is mainly used in self-calibrated stereoscopic systems, whereas the differential case deals with a unique moving camera. The article surveys several methods for mobile robot egomotion estimation covering more than 0.5 million samples using synthetic data. Results from real data are also given