Numerical Simulation of the Cavitation in the Hydrodynamic Lubrication of Journal Bearings: a Parallel Algorithm

In this paper we present an algorithm for the numerical simulation of the cavitation in the hydrodynamic lubrication of journal bearings. Despite the fact that this physical process is usually modelled as a free boundary problem, we adopted the equivalent variational inequality formulation. We propose a two-level iterative algorithm, where the outer iteration is associated to the penalty method, used to transform the variational inequality into a variational equation, and the inner iteration is associated to the conjugate gradient method, used to solve the linear system generated by applying the finite element method to the variational equation. This inner part was implemented using the element by element strategy, which is easily parallelized. We analyse the behavior of two physical parameters and discuss some numerical results. Also, we analyse some results related to the performance of a parallel implementation of the algorithm.

Manipulation of adenovirus early region 1 rescue plasmids by homologous recombination in Saccharomyces cerevisiae

The manipulation of large (>10 kb) plasmid systems amplifies problems common to traditional cloning strategies. Unique or rare restriction enzyme recognition sequences are uncommon and very rarely located in opportunistic locations. Making site-specific deletions and insertions in larger plasmids consequently leads to multiple step cloning strategies that are often limited by time-consuming, low efficiency linker insertions or blunt-end cloning strategies. Manipulation ofthe adenovirus genome and the genomes ofother viruses as bacterial plasmids are systems that typify such situations. Recombinational cloning techniques based on homologous recombination in Saccharomyces cerevisiae that circumvent many ofthese common problems have been developed. However, these techniques are rarely realistic options for such large plasmid systems due to the above mentioned difficulties associated with the addition ofrequired yeast DNA replication, partitioning and selectable marker sequences. To determine ifrecombinational cloning techniques could be modified to simplify the manipulation of such a large plasmid system, a recombinational cloning system for the creation of human adenovirus EI-deletion rescue plasmids was developed. Here we report for the first time that the 1,456 bp TRP1/ARS fragment ofYRp7 is alone sufficient to foster successful recombinational cloning without additional partitioning sequences, using only slight modifications of existing protocols. In addition, we describe conditions for efficient recombinational cloning involving simultaneous deletion of large segments ofDNA (>4.2 kb) and insertion of donor fragment DNA using only a single non-unique restriction site. The discovery that recombinational cloning can foster large deletions has been used to develop a novel recombiliational cloillng technique, selectable inarker 'kilockouf" recombinational cloning, that uses deletion of a yeast selectable marker coupled with simultaneous negative and positive selection to reduce background transformants to undetectable levels. The modification of existing protocols as described in this report facilitates the use of recombinational cloning strategies that are otherwise difficult or impractical for use with large plasmid systems. Improvement of general recombinational cloning strategies and strategies specific to the manipulation ofthe adenovirus genome are considered in light of data presented herein.

Exploring Healthcare Experiences of Transgender Individuals

The purpose of this study was to explore how transgender individuals were supported to navigate the healthcare system to achieve positive healthcare experiences. A single case study was conducted in Southern Ontario, which included ten individual interviews. Data was analyzed through thematic analysis, allowing for seven themes to emerge within macro (large-scale system), meso (local/interpersonal), and micro (individual/internal) levels of healthcare system support. Themes that emerged within the levels of system support included: 1) existing deficits with hope for change; 2) significant external supports; 3) importance of informal networking; 4) support from local area family physicians and walk-in clinics; 5) navigating the healthcare system alone; 6) personality traits for successful healthcare experiences; and 7) the development of strategies to achieve positive healthcare experiences. This study outlined factors that contributed to positive healthcare experiences for transgender individuals, showing that meso and micro level support are compensating for large-scale healthcare system deficits.

Écologie et implications trophiques de la cyanobactérie Lyngbya wollei dans le fleuve Saint-Laurent

Les proliférations nuisibles de la cyanobactérie filamenteuse benthique Lyngbya wollei qui forme des tapis déposés sur les sédiments ont augmenté en fréquence au cours des 30 dernières années dans les rivières, lacs et sources de l'Amérique du Nord. Lyngbya wollei produit des neurotoxines et des composés organiques volatils (géosmin, 2-méthylisobornéol) qui ont des répercussions sur la santé publique de même que des impacts d'ordre socioéconomiques. Cette cyanobactérie est considérée comme un habitat et une source de nourriture de piètre qualité pour les invertébrés en raison de sa gaine robuste et de sa production de toxines. Les proliférations de L. wollei ont été observées pour la première fois en 2005 dans le fleuve Saint-Laurent (SLR; Québec, Canada). Nous avons jugé important de déterminer sa distribution sur un tronçon de 250 km afin d'élaborer des modèles prédictifs de sa présence et biomasse en se basant sur les caractéristiques chimiques et physiques de l'eau. Lyngbya wollei était généralement observé en aval de la confluence de petits tributaires qui irriguent des terres agricoles. L’écoulement d’eaux enrichies à travers la végétation submergée se traduisait par une diminution de la concentration d’azote inorganique dissous (DIN), alors que les concentrations de carbone organique dissous (DOC) et de phosphore total dissous (TDP) demeuraient élevées, produisant un faible rapport DIN :TDP. Selon nos modèles, DOC (effet positif), TP (effet négatif) et DIN :TDP (effet négatif) sont les variables les plus importantes pour expliquer la répartition de cette cyanobactérie. La probabilité que L. wollei soit présent dans le SLR a été prédite avec exactitude dans 72 % à 92 % des cas pour un ensemble de données indépendantes. Nous avons ensuite examiné si les conditions hydrodynamiques, c'est-à-dire le courant généré par les vagues et l'écoulement du fleuve, contrôlent les variations spatiales et temporelles de biomasse de L. wollei dans un grand système fluvial. Nous avons mesuré la biomasse de L. wollei ainsi que les variables chimiques, physiques et météorologiques durant trois ans à 10 sites le long d'un gradient d'exposition au courant et au vent dans un grand (148 km2) lac fluvial du SLR. L'exposition aux vagues et la vitesse du courant contrôlaient les variations de biomasses spatiales et temporelles. La biomasse augmentait de mai à novembre et persistait durant l'hiver. Les variations interannuelles étaient contrôlées par l'écoulement de la rivière (niveau d'eau) avec la crue printanière qui délogeait les tapis de l'année précédente. Les baisses du niveau d'eau et l'augmentation de l'intensité des tempêtes anticipées par les scénarios de changements climatiques pourraient accroître la superficie colonisée par L. wollei de même que son accumulation sur les berges. Par la suite, nous avons évalué l'importance relative de L. wollei par rapport aux macrophytes et aux épiphytes. Nous avons examiné l'influence structurante de l'échelle spatiale sur les variables environnementales et la biomasse de ces producteurs primaires (PP) benthiques. Nous avons testé si leur biomasse reflétait la nature des agrégats d'habitat basées sur l'écogéomorphologie ou plutôt le continuum fluvial. Pour répondre à ces deux questions, nous avons utilisé un design à 3 échelles spatiales dans le SLR: 1) le long d'un tronçon de 250 km, 2) entre les lacs fluviaux localisés dans ce tronçon, 3) à l'intérieur de chaque lac fluvial. Les facteurs environnementaux (conductivité et TP) et la structure spatiale expliquent 59% de la variation de biomasse des trois PP benthiques. Spécifiquement, les variations de biomasses étaient le mieux expliquées par la conductivité (+) pour les macrophytes, par le ratio DIN:TDP (+) et le coefficient d'extinction lumineuse (+) pour les épiphytes et par le DOC (+) et le NH4+ (-) pour L. wollei. La structure spatiale à l'intérieur des lacs fluviaux était la plus importante composante spatiale pour tous les PP benthiques, suggérant que les effets locaux tels que l'enrichissement par les tributaire plutôt que les gradients amont-aval déterminent la biomasse de PP benthiques. Donc, la dynamique des agrégats d'habitat représente un cadre général adéquat pour expliquer les variations spatiales et la grande variété de conditions environnementales supportant des organismes aquatiques dans les grands fleuves. Enfin, nous avons étudié le rôle écologique des tapis de L. wollei dans les écosystèmes aquatiques, en particulier comme source de nourriture et refuge pour l'amphipode Gammarus fasciatus. Nous avons offert aux amphipodes un choix entre des tapis de L. wollei et soit des chlorophytes filamenteuses ou un tapis artificiel de laine acrylique lors d'expériences en laboratoire. Nous avons aussi reconstitué la diète in situ des amphipodes à l'aide du mixing model (d13C et δ15N). Gammarus fasciatus choisissait le substrat offrant le meilleur refuge face à la lumière (Acrylique>Lyngbya=Rhizoclonium>Spirogyra). La présence de saxitoxines, la composition élémentaire des tissus et l'abondance des épiphytes n'ont eu aucun effet sur le choix de substrat. Lyngbya wollei et ses épiphytes constituaient 36 et 24 % de l'alimentation in situ de G. fasciatus alors que les chlorophytes, les macrophytes et les épiphytes associées représentaient une fraction moins importante de son alimentation. Les tapis de cyanobactéries benthiques devraient être considérés comme un bon refuge et une source de nourriture pour les petits invertébrés omnivores tels que les amphipodes.

Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

Development of Macrocyclics based Electrochemical Sensors

Electroanalytical techniques represent a class of powerful and versatile analytical method which is based on the electrical properties of a solution of the analyte when it is made part of an electrochemical cell. They offer high sensitivity, accuracy, precision and a large linear dynamic range. The cost of instrumentation is relatively low compared to other instrumental methods of analysis. Many solid state electrochemical sensors have been commercialised nowadays. Potentiometry is a very simple electroanalytical technique with extraordinary analytical capabilities. Since valinomycin was introduced as an ionophore for K+, Ion Selective Electrodes have become one of the best studied and understood analytical devices. It can be used for the determination of substances ranging from simple inorganic ions to complex organic molecules. It is a very attractive option owing to the wide range of applications and ease of the use of the instruments employed. They also possess the advantages of short response time, high selectivity and very low detection limits. Moreover, analysis by these electrodes is non-destructive and adaptable to small sample volumes. It has become a standard technique for medical researchers, biologists, geologists and environmental specialists. This thesis presents the synthesis and characterisation of five ionophores. Based on these ionophores, nine potentiometric sensors are fabricated for the determination of ions such as Pb2+, Mn2+, Ni2+, Cu2+ and Sal- ion (Salicylate ion). The electrochemical characterisation and analytical application studies of the developed sensors are also described. The thesis is divided into eight chapters

Spatio-Temporal Changes in the Wetland Ecosystem of Cochin City using Remote Sensing and GIS

Urban developments have exerted immense pressure on wetlands. Urban areas are normally centers of commercial activity and continue to attract migrants in large numbers in search of employment from different areas. As a result, habitations keep coming up in the natural areas / flood plains. This is happening in various Indian cities and towns and large habitations are coming up in low-lying areas, often encroaching even over drainage channels. In some cases, houses are constructed even on top of nallahs and drains. In the case of Kochi the situation is even worse as the base of the urban development itself stands on a completely reclaimed island. Also the topography and geology demanded more reclamation of land when the city developed as an agglomerative cluster. Cochin is a coastal settlement interspersed with a large backwater system and fringed on the eastern side by laterite-capped low hills from which a number of streams drain into the backwater system. The ridge line of the eastern low hills provides a welldefined watershed delimiting Cochin basin which help to confine the environmental parameters within a physical limit. This leads to an obvious conclusion that if physiography alone is considered, the western flatland is ideal for urban development. However it will result in serious environmental deterioration, as it comprises mainly of wetland and for availability of land there has to be large scale filling up of these wetlands which includes shallow mangrove-fringed water sheets, paddy fields, Pokkali fields, estuary etc.Chapter 1 School 4 of Environmental Studies The urban boundaries of Cochin are expanding fast with a consequent over-stretching of the existing fabric of basic amenities and services. Urbanisation leads to the transformation of agricultural land into built-up areas with the concomitant problems regarding water supply, drainage, garbage and sewage disposal etc. Many of the environmental problems of Cochin are hydrologic in origin; like water-logging / floods, sedimentation and pollution in the water bodies as well as shoreline erosion

Quadratic Predictor based Differential Encoding and Decoding of Speech Signals

Modeling nonlinear systems using Volterra series is a century old method but practical realizations were hampered by inadequate hardware to handle the increased computational complexity stemming from its use. But interest is renewed recently, in designing and implementing filters which can model much of the polynomial nonlinearities inherent in practical systems. The key advantage in resorting to Volterra power series for this purpose is that nonlinear filters so designed can be made to work in parallel with the existing LTI systems, yielding improved performance. This paper describes the inclusion of a quadratic predictor (with nonlinearity order 2) with a linear predictor in an analog source coding system. Analog coding schemes generally ignore the source generation mechanisms but focuses on high fidelity reconstruction at the receiver. The widely used method of differential pnlse code modulation (DPCM) for speech transmission uses a linear predictor to estimate the next possible value of the input speech signal. But this linear system do not account for the inherent nonlinearities in speech signals arising out of multiple reflections in the vocal tract. So a quadratic predictor is designed and implemented in parallel with the linear predictor to yield improved mean square error performance. The augmented speech coder is tested on speech signals transmitted over an additive white gaussian noise (AWGN) channel.

Diazafluoren-9-yliden als Bindungsmotiv für Metallfragmente in kreuzkonjugierten π-Systemen

In der vorliegenden Dissertation wurden kreuzkonjugierte organische Verbindungen basierend auf Diazafluorenmethyliden- sowie Dipyridylmethyliden-Bausteinen synthetisiert, die zum einen photoredoxaktive Metallfragmente komplexieren können und zum anderen erweiterte π-konjugierte Pfade auf der Grundlage von Alkineinheiten ermöglichen. Das kreuzkonjugierte Motiv wurde über die Kupplung von Alkineinheiten an halogenierte Methyliden-Einheiten, den so genannten Dibromolefinen, zugänglich gemacht. Zur Synthese von Dibromolefinen wurden verschiedene Methoden untersucht. Literaturbekannte Methoden wie die Wittig-Reaktion und ihre Modifikationen sowie die Corey-Fuchs-Reaktion konnten für die Diazafluoreneinheit nicht erfolgreich angewendet werden. Bei einer mikrowellenunterstützten Reaktion konnte sowohl ausgehend von Diazafluoren-9-on als auch von Di-2-pyridylketon eine Dibromolefinierung (55 % und 65 %) erreicht werden. Die Eignung der Mikrowellenstrahlung für Dibromolefinierungsreaktionen nach Corey und Fuchs wurde weiterhin an verschiedenen Aldehyden und Ketonen untersucht. In den meisten Fällen konnten gute bis sehr gute Ergebnisse erzielt werden. Durch die erfolgreiche Synthese von Dibromolefinen über Mikrowellensynthese wurde die Realisierung von diversen π-konjugierten Systemen möglich. Dies erfolgte exemplarisch durch die Kupplung der Alkine 5-Ethinyl-2,2’-bipyridin, 1-(Ferrocenylethinyl)-4-(ethinyl)benzol, Tri(tolyl)propin sowie der TIPS- und TMS-Acetylene. Neben der Vielfalt an Möglichkeiten zur Funktionalisierung von Dipyridyl- und Diazafluorenbausteinen zeigte sich zudem, dass sogar räumlich anspruchsvolle Verbindungen wie die geminale angeordneten voluminösen Tri(tolyl)propinyl-Substituenten an der Doppelbindung erfolgreich synthetisiert werden können. Die Koordinationseigenschaften der neu synthetisierten Verbindungen konnten durch Umsetzungen der Diazafluoren- und Dipyridylverbindungen mit PdCl2 und [RuCl2(bpy)2] erfolgreich gezeigt werden. Im Hinblick auf die Herstellung von Funktionsmaterialien eignen sich die Endiin-Strukturmotive aufgrund von diversen Variationsmöglichkeiten wie Koordination von Übergangsmetallen sowie Funktionalisierung der Peripherie gut. Dadurch können die elektronischen Eigenschaften wie die Absorption oder elektrochemische Potentiale der Verbindungen modifiziert werden. Die UV/Vis-Spektren der neu synthetisierten Verbindungen zeigen, dass Absorptionen in längerwelligen Bereichen durch Verlängerung des Konjugationspfades gesteuert werden können. Zudem lassen sich weitere photophysikalische Eigenschaften wie MC-, LC-, LMCT- oder MLCT-Übergänge durch Koordination von Metallen generieren. Die elektrochemischen Potentiale der Dipyridyl- und Diazafluorenbausteine konnten durch Anbindung von verschiedenen Substituenten beeinflusst werden. Es zeigte sich, dass sich die Reduktionswellen im Vergleich zu denen der Ketone zu niedrigeren Potentialen verschieben, wenn Alkine an die Dipyridylmethyliden- und Diazafluorenmethyliden-Bausteine geknüpft wurden. Zudem konnte beobachtet werden, dass die Signale nicht immer reversibel sind. Insbesondere die Dipyridylverbindungen zeichneten sich durch irreversible Reduktionswellen aus. Die Realisierung von π-konjugierten Systemen gelang auch mit cyclischen kohlenstoffbasierten Verbindungen. Über das separat synthetisierte 2,2’-Diethinyltolan konnte eine cyclische Verbindung, ein dehydroannulen-radialenisches System, erfolgreich hergestellt werden. Die Koordination von redoxaktiven Metallzentren wie [Ru(bpy)2] konnte für diese Verbindung ebenfalls erfolgreich gezeigt werden. Die elektronische Wechselwirkung zwischen dem Metallzentrum und dem dehydroannulenischen System könnte sowohl über theoretische Methoden (zeitabhängige Dichtefunktionaltheorie) als auch experimentell wie z. B. über transiente Absorptionsspektroskopie untersucht werden. Diese zukünftig durchzuführenden Untersuchungen können Aufschluss über die Ladungstransferraten und -dauer geben. Im Hinblick auf die Realisierung von Modellverbindungen für molekulare Drähte wurden lineare Systeme basierend auf der Diazafluoreneinheit synthetisiert. Zur Synthese von derartigen Systemen war es zunächst notwendig, die Dibromolefine unsymmetrisch zu alkinylieren. Die unsymmetrische Substitution gestaltete sich als Herausforderung, da eine Einfachkupplung mit einem Acetylen nicht möglich war. In den meisten Fällen wurden zweifach substituierte Spezies mit den identischen Alkinen erhalten. Die besten Ausbeuten konnten durch die konsekutive Zugabe von TIPS-Acetylen und darauffolgend TMS-Acetylen in die Reaktionsmischung erhalten werden. Offenbar spielt der räumliche Anspruch des Erstsubstituenten in diesem Zusammenhang eine Rolle. Die selektive Entschützung der unterschiedlich silylierten Verbindungen erfolgte mit K2CO3 in MeOH/THF (1:1). Die oxidative Homokupplungsreaktion erfolgte ohne Isolierung der entschützten Spezies, da diese instabil ist und zur Polymerisation neigt. Aufgrund der Instabilität der entschützten Spezies sowie möglichen Nebenreaktionen waren die Ausbeuten sowohl bei der TIPS-geschützten Verbindung als auch bei der TTP-geschützten Verbindung gering. Versuche, lineare Systeme von dipyridylbasierten Verbindungen zu erhalten, schlugen fehl. Die π-konjugierten Systeme lassen aufgrund der effektiven Überlappung der beteiligten π-Orbitale hohe Ladungsträgermobilitäten vermuten. Die im Rahmen dieser Arbeit synthetisierten Verbindungen könnten mit Schwefelverbindungen die Anbindung an Elektroden zulassen, worüber die Leitfähigkeiten der Verbindungen gemessen werden könnten.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Predictive control using feedback linearization based on dynamic neural models

This paper presents a hybrid control strategy integrating dynamic neural networks and feedback linearization into a predictive control scheme. Feedback linearization is an important nonlinear control technique which transforms a nonlinear system into a linear system using nonlinear transformations and a model of the plant. In this work, empirical models based on dynamic neural networks have been employed. Dynamic neural networks are mathematical structures described by differential equations, which can be trained to approximate general nonlinear systems. A case study based on a mixing process is presented.

Adaptive modelling with tunable RBF network using multi-innovation RLS algorithm assisted by swarm intelligence

In this paper, we propose a new on-line learning algorithm for the non-linear system identification: the swarm intelligence aided multi-innovation recursive least squares (SI-MRLS) algorithm. The SI-MRLS algorithm applies the particle swarm optimization (PSO) to construct a flexible radial basis function (RBF) model so that both the model structure and output weights can be adapted. By replacing an insignificant RBF node with a new one based on the increment of error variance criterion at every iteration, the model remains at a limited size. The multi-innovation RLS algorithm is used to update the RBF output weights which are known to have better accuracy than the classic RLS. The proposed method can produces a parsimonious model with good performance. Simulation result are also shown to verify the SI-MRLS algorithm.

State estimation using model order reduction for unstable systems

The problem of state estimation occurs in many applications of fluid flow. For example, to produce a reliable weather forecast it is essential to find the best possible estimate of the true state of the atmosphere. To find this best estimate a nonlinear least squares problem has to be solved subject to dynamical system constraints. Usually this is solved iteratively by an approximate Gauss–Newton method where the underlying discrete linear system is in general unstable. In this paper we propose a new method for deriving low order approximations to the problem based on a recently developed model reduction method for unstable systems. To illustrate the theoretical results, numerical experiments are performed using a two-dimensional Eady model – a simple model of baroclinic instability, which is the dominant mechanism for the growth of storms at mid-latitudes. It is a suitable test model to show the benefit that may be obtained by using model reduction techniques to approximate unstable systems within the state estimation problem.

Testing the expectations theory of the term structure in threshold models

We test the expectations theory of the term structure of U.S. interest rates in nonlinear systems. These models allow the response of the change in short rates to past values of the spread to depend upon the level of the spread. The nonlinear system is tested against a linear system, and the results of testing the expectations theory in both models are contrasted. We find that the results of tests of the implications of the expectations theory depend on the size and sign of the spread. The long maturity spread predicts future changes of the short rate only when it is high.

Strong surjectivity of maps from 2-complexes into the 2-sphere

Given a model 2-complex K(P) of a group presentation P, we associate to it an integer matrix Delta(P) and we prove that a cellular map f : K(P) -> S(2) is root free (is not strongly surjective) if and only if the diophantine linear system Delta(P) Y = (deg) over right arrow (f) has an integer solution, here (deg) over right arrow (f) is the so-called vector-degree of f