The aim of this work is to make some investigations concerning duality for multiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, under some appropriate assumptions, the existence of strong duality. Closely related to the strong duality we derive the optimality conditions for each of these three duals. By means of these considerations, we study the duality for two vector optimization problems, namely, a convex multiobjective problem with cone inequality constraints and a special fractional programming problem with linear inequality constraints. To each of these vector problems we associate a scalar primal and study the duality for it. The structure of both scalar duals give us an idea about how to construct a multiobjective dual. The existence of weak and strong duality is also shown. We conclude our investigations by making an analysis over different duality concepts in multiobjective optimization. To a general multiobjective problem with cone inequality constraints we introduce other six different duals for which we prove weak as well as strong duality assertions. Afterwards, we derive some inclusion results for the image sets and, respectively, for the maximal elements sets of the image sets of these problems. Moreover, we show under which conditions they become identical. A general scheme containing the relations between the six multiobjective duals and some other duals mentioned in the literature is derived. / Das Ziel dieser Arbeit ist die Durchführung einiger Untersuchungen bezüglich der Dualität für Mehrzieloptimierungsaufgaben. Zu diesem Zweck wird als erstes mit Hilfe des so genannten konjugierten Verfahrens die Dualität für skalare Optimierungsaufgaben untersucht. Das erlaubt uns zu einer primalen Aufgabe drei unterschiedliche duale Aufgaben zuzuordnen. Wir betrachten die Beziehungen zwischen den optimalen Zielfunktionswerten der drei Dualaufgaben und untersuchen die Existenz der starken Dualität unter naheliegenden Annahmen. Im Zusammenhang mit der starken Dualität leiten wir für jede dieser Dualaufgaben die Optimalitätsbedingungen her. Die obengenannten Ergebnisse werden beim Studium der Dualität für zwei Vektoroptimierungsaufgaben angewandt, und zwar für die konvexe Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen und für eine spezielle Quotientenoptimierungsaufgabe mit linearen Ungleichungen als Nebenbedingungen. Wir assoziieren zu jeder dieser vektoriellen Aufgaben eine skalare Aufgabe für welche die Dualität betrachtet wird. Die Formulierung der beiden skalaren Dualaufgaben führt uns zu der Konstruktion der Mehrzieloptimierungsaufgabe. Die Existenz von schwacher und starker Dualität wird bewiesen. Wir schliessen unsere Untersuchungen ab, indem wir eine Analyse von verschiedenen Dualitätskonzepten in der Mehrzieloptimierung durchführen. Zu einer allgemeinen Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen werden sechs verschiedene Dualaufgaben eingeführt, für die sowohl schwache als auch starke Dualitätsaussagen gezeigt werden. Danach leiten wir verschiedene Beziehungen zwischen den Bildmengen, bzw., zwischen den Mengen der maximalen Elemente dieser Bildmengen der sechs Dualaufgaben her. Dazu zeigen wir unter welchen Bedingungen werden diese Mengen identisch. Ein allgemeines Schema das die Beziehungen zwischen den sechs dualen Mehrzieloptimierungsaufgaben und andere Dualaufgaben aus der Literatur enthält, wird dargestellt.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

No description available.

The proton is a bound state of quarks which are held together by the strong force, mediated by gluons. The understanding of the proton structure is presently one of the central issues in hadron physics. The present work reports on phenomenological and experimental studies related to the possibilities offered by the future antiproton beam at the FAIR facility at Darmstadt, in the momentum range between 1.5 and 15 GeV/c. After a classification of the reaction channels which are accessible in antiproton-proton annihilation, the main features of the PANDA detector are described. A chapter of this thesis is dedicated to the study of the optical coupling between crystals and photodiodes in the electromagnetic calorimeter, which will be operated at low temperature (-25° C). Mechanical, thermal, optical properties and radiation hardness of two commercial glues are quantified.Feasibility studies of the reaction barp → e+e− for the Time-Like proton form factor measurements at PANDA are presented. The electromagnetic structure of the proton is parametrized in terms of electric GE and magnetic GM form factors. The electromagnetic interaction is well described by the theory of quantum electrodynamics. The traditional tool to determine proton electromagnetic form factors is polarized and unpolarized electron-proton elastic scattering, assuming that the interaction occurs through the exchange of one virtual photon. The crossed symmetry channels pbarp ↔ e+e− allowto access the Time-Like region. The background reactions are also studied, in particular the pbarp → π+π− channel. The results obtained from a realistic Monte Carlo simulation using PANDARoot show that the proton form factor ratio can be measured at PANDA with unprecedented accuracy. The effects of radiative corrections due to real and virtual photon emission are considered.Based on a model independent formalism, the calculation of the experimental observables for the pbarp → e+e− reaction is extended to the annihilation into a heavy lepton pair which carries the same physical information on the proton structure as the electrons. In this case, the lepton mass can not be neglected. The same formalism is also applied in Space-Like region to the elastic scattering of protons from electrons at rest (pe-inverse kinematics). We suggest that the elastic pe scattering can be used to polarize and/or to measure the polarization of high energy proton (antiproton) beams, and allows a precise measurement of the proton charge radius.

This thesis addresses two fundamental topics in Engineering Seismology; the application of Probabilistic Seismic Hazard Analysis (PSHA) methodology, and the estimation of measures of Strong Ground Motion. These two topics, while being related, are presented as separate sections. In the first section, state-of-the-art PSHA methodologies are applied to various sites in the Buller Region, South Island, New Zealand. These sites are deemed critical to the maintenance of economic stability in the region. A fault-source based seismicity model is developed for the region that is consistent with the governing tectonic loading, and seismic moment release of the region. In attempting to ensure this consistency the apparent anomaly between the rates of activity dictated by deformation throughout the Quaternary, and rates of activity dictated by observed seismicity is addressed. Individual fault source activity is determined following the application of a Bayesian Inference procedure in which observed earthquake events are attributed to causative faults in the study region. The activity of fault sources, in general, is assumed to be governed by bounded power law behaviour. An exception is made for the Alpine Fault which is modelled as a purely characteristic source. The calculation of rates of exceedance of various ground motion indices is made using a combination of Poissonian and time-dependent earthquake occurrence models. The various ground motion indices for which rates of exceedance are determined include peak ground acceleration, ordinates of 5% damped Spectral Acceleration, and Arias Intensity. The total hazard determined for each of these ground motion measures is decomposed using a four dimensional disaggregation procedure. From this disaggregation procedure, design earthquake scenarios are specified for the sites that are considered. The second part of the thesis is concerned with the estimation of ground motion measures that are more informative than the existing scalar measures that are available for use in New Zealand. Models are developed for the prediction of Fourier Amplitude Spectra (FAS) as well as Arias Intensity for use in the New Zealand environment. The FAS model can be used to generate ground motion time histories for use in structural and geotechnical analyses. Arias Intensity has been shown to be an important strong motion measure due to its positive correlation with damage in short period structures as well as its utility in predicting the onset of liquefaction and landslides. The models are based upon the analysis of a dataset of New Zealand Strong Motion records as well as supplementary near field records from major overseas events. While the two measures of ground motion intensity are strongly related, different methods have been adopted in order to develop the models. As part of the methodology used for the FAS model, Monte Carlo simulation coupled with a simple ray tracing procedure is employed to estimate source spectra from various New Zealand earthquakes and, consequently, a magnitude - corner-frequency relationship is obtained. In general, the parameters of the predictive equations are determined using the most state-of-the-art mixed effects regression procedures.

This work deals with spatially-evolving supersonic turbulent boundary layers over adiabatic and cold walls at M∞ = 2 and up to Re0 ≈ 2600 using 3 different SGS models. The numerical methodology is based on high-order split-centered scheme to discretize the convective fluxes of the Navier-Stokes equations . For the adiabatic case, it is demonstrated that all SGS models require a comparable minimum grid-refinement in order to capture accurately the near-wall-turbulence. Overall, the models exhibit correct behavior when predictiong the dynamic properties, but show different performances for the temperature distribution in the near-wall region. For the isothermal case, it is found that the compressibility effects are not enhanced due to the wall cooling. As expected, the total temperature fluctuations are not negligible in the near-wall region. The study shows that the anti-correlation linking both velocity and temperature fields, derived from the Morkovin's hypothesis, is not satisfied.

This dissertation studies two different aspects of two-player interaction in the model of quantum communication and quantum computation.First, we study two cryptographic primitives, that are used as basic blocks to construct sophisticated cryptographic protocols between two players, e.g. identification protocols. The first primitive is ''quantum bit commitment''. This primitive cannot be done in an unconditionally secure way. However, security can be obtained by restraining the power of the two players. We study this primitive when the two players can only create quantum Gaussian states and perform Gaussian operations. These operations are a subset of what is allowed by quantum physics, and plays a central role in quantum optics. Hence, it is an accurate model of communication through optical fibers. We show that unfortunately this restriction does not allow secure bit commitment. The proof of this result is based on the notion of ''intrinsic purification'' that we introduce to circumvent the use of Uhlman's theorem when the quantum states are Gaussian. We then examine a weaker primitive, ''quantum weak coin flipping'', in the standard model of quantum computation. Mochon has showed that there exists such a protocol with arbitrarily small bias. We give a clear and meaningful interpretation of his proof. That allows us to present a drastically shorter and simplified proof.The second part of the dissertation deals with different methods of proving lower bounds on the quantum query complexity. This is a very important model in quantum complexity in which numerous results have been proved. In this model, an algorithm has restricted access to the input: it can only query individual bits. We consider a generalization of the standard model, where an algorithm does not compute a classical function, but generates a quantum state. This generalization allows us to compare the strength of the different methods used to prove lower bounds in this model. We first prove that the ''multiplicative adversary method'' is stronger than the ''additive adversary method''. We then show a reduction from the ''polynomial method'' to the multiplicative adversary method. Hence, we prove that the multiplicative adversary method is the strongest one. Adversary methods are usually difficult to use since they involve the computation of norms of matrices with very large size. We show how studying the symmetries of a problem can largely simplify these computations. Last, using these principles we prove the tight lower bound of the INDEX-ERASURE problem. This a quantum state generation problem that has links with the famous GRAPH-ISOMORPHISM problem.

Den internasjonale Safe-Community (SC) bevegelsen vokser stadig. Denne studien setter søkelyset på de såkalte Affiliate Safe Community Support Centres (ASC) og deres rolle i bevegelsen. SC-begrepet blir behandlet både som en innovasjon og som en organisasjons- modell som utbres etter Rogers og Røviks teorier. ASCene ses på som ”forandrings-agenturer” i følge disse teoriene. Studien er en case-study i følge Yin, og dekker 9 av ialt 15 ASCer. Tre av dem har mistet sin status som ASC, seks av dem har sin status i behold. De følgende fem påstander blir studert: 1)Det er ingen forskjell i hvordan sentrene har utøvet sin rolle som årsak til at noen mister sin status og andre ikke. 2)Årsakene til at noen mister sin status ligger i interne organisasjonsmessige, personalmessige eller økonomiske forhold. 3) ASC’ene og deres oppgaver er ikke særlig godt kjent blant ”brukerne” 4)ASC’ene har et svakt eller lite bevisst forhold til det teoretiske og vitenskapelige grunnlag for spredningsprosesser 5)SC-begrepet oppfattes i liten grad som en organisasjonsmodell på linje med andre organisasjonsmodeller. Data ble samlet inn fra spørreskjemaundersøkelser, skriftlig materiale og intervju. Materialet omfatter alle ”nivåer” i SC-bevegelsen. Alle fem påstander ble styrket av materialet. Studien har ledet til følgende konklusjoner og anbefalinger som forhåpentligvis kan styrke både renommé og effektivitet i SC-bevegelsen og lette arbeidet i ASCene: Organisasjonsteori og organisasjonsspørsmål må i langt større grad settes på dagsorden i bevegelsen. Vekst og utbredelse av SC-”ideén” får for stor plass i forhold til konsolidering. Det forekommer konflikter mellom ASC-arbeidet og andre arbeidsoppgaver. Det gjelder særlig når det gjelder prioriteringen mellom forsking og arbeidet med å utbre SC-modellen. ASCene har ikke tilstrekkelig kapasitet til å følge opp veksten i SC-bevegelsen. Begge disse forhold synes hovedsakelig å bunne i mangel på finansiering og mangel på planmessig utbygging. Mangel på planmessig organisering av bevegelsen er foruroligende. Dersom det ikke blir tatt tak i denne manglende organiseringen, vil det kunne være til hinder for videre utbredelse og i verste fall virke ødeleggende for bevegelsen. Det må også pekes på kvinnenes sterke, til dels dominerende stilling / The international Safe-Community (SC) movement is steadily growing. This study highlights the so-called Affiliate Safe Community Support Centres (ASC) and their role in the movement. The concept of SC is treated as an innovation and an organisational model diffusing according to the theories of Rogers and Røvik. The ASCs are looked upon as ”change agencies” according to these theories. This is a case-study according to Yin of 9 out of 15 ASCs. Three of them have lost their status as ASC, six still have their status. The following five propositions are examined: 1.There are no differences in how the ASCs have executed their role that can explain why some have lost their status and some not. 2.The reason why some have lost their status can be explained by internal organisational, personal or economic conditions. 3.The ASCs and their tasks are not well known by the ”users”. 4.The ASCs have a weak or little conscious relations to the theoretical and scientific foundation of diffusion processes. 5.The SC-concept is to a very little degree considered as an organisational model. Data was collected from surveys and interviews with people at all ”levels” of the SC-movement as well as written material. All five propositions were strengthened by the material. The study leads to the following conclusions and recommendations which hopefully can improve the reputation and efficiency of the SC-movement and ease the work of the ASCs: The ASCs have an important role in the movement, but they are too few to serve an increasing number of SCs. The development of new ASCs should go on simultaneously with the increase of SCs. It is also necessary with a geographical distribution corresponding with the distribution of the SCs. The economy of the ASC-work has a very weak foundation, and this should be taken more seriously. There are conflicts between ASC-work and other tasks. There are no indications that certain models of internal organisation or company construction are more functional than others. Organisational matters are not considered sufficiently important. This is alarming, and may threaten the existence of the whole movement if not taken more seriously. It must be a responsibility of the WHO Collaborating Centre to bring these matters to discussion. There are few other arenas for these discussions than the regional and world-wide conferences. But in addition the institutions teaching SC-issues have a responsibility for taking up these topics in their education programmes. Women have a very strong position in the ASC. But it is not possible from this material to draw conclusions as to whether their position has influenced the priorities or choice of topics in the ASC-work. / <p>ISBN 978-9185721-08-5</p>

Surface plasmon polaritons are non radiative modes which exist at the interface between a dielectric and a metal. They can confine light at sub-wavelength scales. However, their propagation is restricted by the intrinsic losses of the metal which imply a rapid absorption of the mode. The aim of this thesis is the study of the coupling of surface plasmons in metallo-dielectric planar structures. Obtaining the properties of the modes implies the extension of the solutions to the complex plane of propagation constants. The method used consists in determining the poles of the scattering matrix by means of Cauchy's integrals. The first solution to solve the problem of propagation of the surface plasmons consists in coupling these modes to one another. In a symmetric medium, when the thickness of the metallic film becomes thin enough, the coupling between the plasmon modes which exist on each side becomes possible. One of the coupled modes which is created, the so-called long range surface plasmon, has a bigger propagation length than the usual plasmon whereas the other coupled mode, named short range surface plasmon, has a smaller propagation length. We present a configuration which allows the excitation of the long range surface plasmon without the short range mode with a metallic layer deposited on a perfect electric conductor substrate. This excitation can be done in air and allows applications, such as the detection and the characterisation of molecules. Then, we present the coupling between dielectric waveguides, and, in particular, the coupled-mode theory in the case of the transverse magnetic polarisation. We consider also the case of PT symmetric structure. The last part of this work presents the demonstration of the strong coupling regime between a surface plasmon and a guided mode. We demonstrate an increase of the propagation length of the hybrid surface plasmon, which still has the confinement of a surface mode. A linear gain is added in the different layers of the structure. When the gain is added in the layer between both coupled modes allows an enhancement of the propagation lengths of the modes, and more precisely of the hybrid surface plasmon mode, which can propagate at the millimeter scale.

No description available.