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Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set problem. In this thesis we study the k-set packing problem where given a universe U and a collection C of subsets over U, each of cardinality k, one needs to find the maximum collection of mutually disjoint subsets. Local search techniques have proved to be successful in the search for approximation algorithms, both for the unweighted and the weighted version of the problem where every subset in C is associated with a weight and the objective is to maximise the sum of the weights. We make a survey of these approaches and give some background and intuition behind them. In particular, we simplify the algebraic proof of the main lemma for the currently best weighted approximation algorithm of Berman ([Ber00]) into a proof that reveals more intuition on what is really happening behind the math. The main result is a new bound of k/3 + 1 + epsilon on the integrality gap for a polynomially sized LP relaxation for k-set packing by Chan and Lau ([CL10]) and the natural SDP relaxation [NOTE: see page iii]. We provide detailed proofs of lemmas needed to prove this new bound and treat some background on related topics like semidefinite programming and the Lovasz Theta function. Finally we have an extended discussion in which we suggest some possibilities for future research. We discuss how the current results from the weighted approximation algorithms and the LP and SDP relaxations might be improved, the strong relation between set packing and the independent set problem and the difference between the weighted and the unweighted version of the problem.

Door ervaren behandelaren binnen de forensische en algemene psychiatrie is gebrainstormd over hoe empathisch vermogen tot uiting komt in observeerbaar gedrag. Op basis daarvan is een eerste empathieobservatie-instrument ontwikkeld met 120 items, waaruit voor verdere analyse twintig items werden verwijderd op grond van een onvoldoende interbeoordelaar-betrouwbaarheid tussen 118 dubbele beoordelingen. Na analyse van de uitkomsten voor de overgebleven honderd items bij een onderzoeksgroep van 172 personen kon het oorspronkelijk aantal vragen gereduceerd worden tot tien, met nagenoeg dezelfde meetpretentie. Omdat de totale groep proefpersonen bestond uit drie subgroepen: personen zonder psychiatrische problemen, opgenomen psychiatrische patiënten én opgenomen forensisch psychiatrische patiënten, konden we ook een eerste normering vaststellen voor een ‘normaal empathisch vermogen’. Uit de resultaten blijkt dat het instrument duidelijk differentieert tussen personen met en zonder een forensisch psychiatrische achtergrond. It was not I that sinn'd the sin, The ruthless body dragged me in; Though long I strove courageously, The body was too much for me (W. Whitman (1959). The Singer in the Prison. Complete Poetry and Selected Prose.)

llumination optics is an important field in the lighting industry. However, the knowledge is gained merely by experience and stored in the heads of a small group of aging engineers. In practice, optical design for lighting applications is a process of trial and error and thus time-consuming and expensive.

In this report we examine a model for human hearing. The unknown parameters in the model are estimated using experimental data and standard optimisation methods as described in the text. Additionally, we suggest possible improvements to the model as well as proposing a method to use the current model in locating which frequencies are aected in a damaged ear. Keywords: cochlear model, delay dierential equation, parameter es-timation, hearing loss

The point vortex model predicts that a certain configuration of three point vortices leads to a collapse of these vortices to one point. Numerical simulations have been performed to investigate the effect of a finite vortex size on this two-dimensional collapse interaction. The paper presents results obtained with contour dynamics simulations of patches of uniform vorticity, and results obtained with finite difference simulations of vortices with continuous properties. In addition, the effect of viscosity and the presence of impermeable domain boundaries are investigated. The results show that the motion of finite-sized vortices is quite similar to the motion of point vortices as long as the mutual distance between the vortices is larger than their size. When the vortices are closer together their shapes start to deform and the subsequent evolution is different from that of the point vortices, and an actual collapse to one vortex does not take place.

When a beer company replaces its returnable packaging materials, for exam-ple when updating the design of a bottle, it needs to know in advance how much new material will be needed. Dutch beer brewer Heineken submitted the question of estimating the returnable packaging materials to the 2013 Studygroup Mathe-matics with Industry. In this report, we present both stochastic flow models and a queueing model to estimate the amount of returnable packaging material present in the market. Furthermore, we give recommendations on what data to collect, and how to sample this data in an unbiased way in order to increase accuracy of the estimation. Keywords: Modelling, Markov Chain, Stochastic Differential Equation, Queue-ing Theory

A frequently occurring issue in hot rolling of steel is so-called tail pinching. Prominent features of a pinched tail are ripple-like defects and a pointed tail. In this report two algorithms are presented to detect those features accurately in 2D gray scale images of steel strips. The two ripple detectors are based on the second order Gaussian derivative and the Gabor transform, a localized Fourier transform, yielding the so-called rippleness measures. Additionally a parameter called tail length is defined which indicates to what extent the overall shape of the tail deviates from an ideal rectangular shape. These methods are tested on images from the surface inspection system at Tata Hot Strip Mill 2 in IJmuiden, it is shown that by defining a simple criterion in the feature space spanned by these two parameters a given set of strips can correctly be classified into pinched and nonpinched strips. These promising results open the way for the development of an automatic pinch detection system.

We discuss the idea of building a 2 km high mountain in the Netherlands. In this paper, we give suggestions on three important areas for the completion of this project. Issues like location, structure and sustainability are investigated and discussed in detail.

Three mathematical models were formulated to describe the oxygen con-sumption of seeds during germination. These models were fitted to measure-ment data of oxygen consumption curves for individual germinating seeds of Savoy cabbage, barley and sugar beet provided by Fytagoras. The first model builds on a logistic growth model for the increasing population of mitochondria in the embryo during growth. The other two take the anatomy and physiologi-cal properties of the seed into account. One describes the oxygen uptake during the germination phase only. An extension of this model is capable of fitting the complete oxygen consumption curve, including the initial ‘repair’ phase in which the embryonic cells recover from their dormant state before extensive cell division and growth commences. Keywords: Modelling, seed germination, cellular respiration, oxygen transport

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At the European Study Group Mathematics with Industry 2012 in Eindhoven, the Maritime Research Institute Netherlands (MARIN) presented the problem of identifying the response amplitude operator (RAO) for a ship, given input information on the amplitudes of the sea waves and output information on the movement of the ship. We approach the problem from a threefold perspective: a direct least-squares approach, an approach based on truncated Fourier series, and an approach using low-dimensional measures of the RAO. We give a few recommendations for possible further investigations.

The generation by renewables and the loading by electrical vehicle charging imposes severe challenges in the redesign of today’s power supply systems. Indeed, accommodating these emerging power sources and sinks requires traditional power systems to evolve from rigid centralized unidirectional architectures to intelligent decentralized entities allowing a bidirectional power flow. In the case study proposed by ENDINET, we investigate how the penetration of solar panels and of battery charging stations on large scale affects the voltage quality and loss level in a distribution network servicing a residential area in Eindhoven, NL. In our case study we take the average household load during summer and winter into account and consider both a radial and meshed topology of the network. Our study results for both topologies considered in a quantification of the levels of penetration and a strategy for electrical vehicle loading strategy that meet the voltage and loss requirements in the network. Keywords: power systems, load flow computations, distributed generation, electrical vehicle charging

What is propeller efficiency at full scale? This question is asked equally by ship operators and by propeller and propulsion system manufacturers. The question reflects the need to measure propeller efficiency at full physical scale and during regular operation of the vessel. The question has a context: the ship operator wants to reduce the fuel consumption and forecast maintenance; and, the manufacturer wants to improve the design of the propeller and optimize the propulsion system. In this thesis, we work towards an answer by designing methods to determine propeller efficiency at full scale. In accordance to the hydrodynamics community, we define propeller efficiency as the ratio of the power produced to the power consumed. The power produced and the power consumed are the product of thrust and advance velocity, and, of torque and angular velocity, respectively. Thus, propeller efficiency at full physical scale requires full scale measurements of thrust, torque, angular velocity, and advance velocity. Up-to-date, thrust and advance velocity are thought to be the bottlenecks in estimating propeller efficiency at full scale. Recently, a prototype thrust sensor has been developed that seems to have solved the problem of propeller thrust measurements. The remaining bottleneck, the measurement of advance velocity, is a main topic of this thesis. The advance velocity cannot be directly measured on board of a vessel with the current sensor technology. We replace the advance velocity by ship’s speed-through-water up to a factor. This factor is known as the wake fraction. Since the speed-through-water is measurable at full scale, we need to find the wake fraction. For that we apply mathematical modeling in combination with full scale measurements during rigourously defined conditions. The method to determine propeller efficiency at full-scale relies on five principles: mathematical models, design of measurements, identification of parameters, statistical analysis of data, and identification of stationary states. Propeller efficiency at full scale can only be defined when the ship is in a stationary state; also in the practice of propeller model tests and CFD simulations the propeller efficiency is determined under stationary conditions. First, we developed a concept of stationarity of a process; it means that the trend is close to zero, and small oscillations about the trend are allowed. Second, we developed a method that automatically extracts the stationary excerpts from the full scale measurements. The mathematical models that we elaborate on in this thesis are inspired by the classical mathematical models for guidance and control of vessels. In this mathematical environment, relationships between advance velocity, thrust, torque, speed-through-water, and angular velocity are defined on basis of physical laws and empirically established relationships. The mathematical models introduce parameters that are unknown at full physical scale. One of these parameters is the wake fraction. For realistic values of parameters the model mimics the ship behavior. From the measurements we want to obtain the model parameters by estimation. For that, we construct a regression kind of method that minimizes the difference between the measurements data and the output of the mathematical model when we feed it by full scale measurements. Our measurement design includes the functional specification for a data collection system, a list of signals with details on sampling frequency and resolution, a design of propulsion tests, and processing of measurements. The result of that processing is the selection of stationary states and their characteristics. A central piece of the data collection system is the propeller thrust sensor. In fact, this thesis would not have been written as it is without the availability of the thrust sensor. The speed-through-water measured by the speed log is equally important. It is generally known that speed logs are not reliable. Thus, we had to focus on getting a reliable speed-through-water. For this purpose, we designed an algorithm that reconciles the speed-through-water with other measured navigation signals. The combination of mathematical models and propulsion test measurements yields the model parameters. The value of each model parameter is calculated by a mathematical algorithm that needs measurements of stationary or dynamic states as input. The mathematical models structure these algorithms. It is at this stage that the external factors come into play. External factors, for instance, wind, waves, and sea currents, are not explicitly modeled so that their influence is noticeable in the model parameters. For instance, the parameters of the ship resistance force account also for the wind-induced resistance. Consequently, the estimated propeller efficiency at full scale is influenced by the external factors. If our findings were put into practice, the best would be to create a ship-tailored lookup table of reference model parameters and reference propeller efficiency as function of external conditions that would represent the reference states. At predefined time intervals, the reference state would be updated by new propulsion tests. During ship operations the reference model parameters would be used to retrieve the propeller efficiency relative to the selected reference states. At sea, vessels have typical operational profiles that are concentrated at one or two predefined velocities. As a result, the relative propeller efficiency forms clusters of data points. Propeller efficiency is function of state variables connected to ship propulsion and external factors. Under the influence of the state variables the data clusters are more or less densely packed. We use statistical tools to analyze these data clusters. To evaluate the data clusters we introduce the concept of precision that, in our definition, is the normalized standard deviation of the data clusters. Filtering the data clusters based on propulsion state variables increase the precision, i.e., the clusters become more densely packed. The clusters of data points indicate that the external factors account for most of the variations in propeller efficiency. We expect that this is the de facto situation of propeller efficiency at sea. Thus, what is propeller efficiency at full scale? Propeller efficiency is an indicator with values between 0 and 1. This indicator is measured by a sensor: a mathematical algorithm structured by a mathematical model and fed with full-scale measurements. Under specified conditions, this sensor measures the propeller efficiency with high precision. The ship owners and the propeller and propulsion system manufacturers may use the full-scale propeller efficiency to compare different propeller designs at similar conditions, to track long-term changes in propeller efficiency for the maintenance forecast, to optimize fuel consumption as function of external conditions, or to plan the optimal route of the vessel.

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The content of this document is a brief description of the steps taken in the process of designing and writing a simulation program for solving the Maxwell equations using the finite element method (FEM). It covers the theory from the literature by various authors. It deals with the conversion to certain conventions, like the orientation of axis and the time convention for time-harmonic solutions and the non-dimensionalization process. The mathematical foundation is far from complete, but the reader is referred to the literature for the details. The application is the scattering by an object of electromagnetic waves. Part 2 will cover the far-field calculation given the near-field solution obtained by the FEM.

Proposed by Erwin lust (emeritus), Bronx Community College of the City University of New York, New York, NY. Let p be a prime greater than 3. Does there exists a ring with more than one element (not necessarily having a multiplicative identity) such that for all x in the ring, [formula].

In the previous report (part 1), the problem and its governing equations are described and is discarded in this report. The finite element method in part 1, or any other method for that matter, determines the fields in and close to the scatterer (near-field) that is used to construct the fields in the far-field. The goal of part 2 is to find far-field expressions formulated as total fields or the Radar Cross Section (RCS) of the scattered fields. The far-field is calculated from the scatterer problem in the contrast formulation. The scatterer then acts as a radiating object with a known source J. Using Green's function theory, the far-field solution is just the convolution of that source with the fundamental solution G to the Maxwell equation. Without loss of generality, the expressions are formulated in total fields E and H. Again, the time convention for the time-harmonic term exp(-i¿t) is used, but in contrary to part 1, the quantities are in full dimensions, following closely the notation used by Chew, Balanis and others.

The baak is the result of the workshop Partial Differential Equations and Fluid Dynamics that look place at the Mathematics Institute of the University of Warwick. May 21st - 23rd, 2007. It contains ten review and research papers which provide an accessible summary of a wide range of active research topics along with new results.

Structure is an important factor in food. One of the ways to provide structure to foods is by using bubbles and foams. However, they need to be stabilized. One way of doing this is by covering them with microscopic rods. These rods self-assemble at the surface, yielding a stable bubble. The goal of this work is to gain a better understanding into how this self-assembly works using analytical calculations, experiments and simulations.

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Proposed by Marian Tetiva, National College "Gheorghe Rosca Codreanu," Birlad, Romania. Let P be a polynomial of degree n with complex coefficients and with p(0) = 0. Show that for any complex alfa with alfa

Proposed by Yaming Yu, University of California lrvine, lrvine,CA. Let f be the decreasing function on (0, (omega) that satisfies f(x)e-f(x) = xe-x.

The Hamiltonian Hopf bifurcation is described by part of a swallowtail surface. In this short note it is shown that this swallowtail is actually a non-transversally unfolded cusp singularity, and that the swallowtail surface is obtained by folding a cusp along a fold line that is tangent to the cusp and moving along the cusp.

The current on a linear strip or wire solves an equation governed by a linear integral-differential operator that is the composition of the Helmholtz operator and an integral operator with logarithmically singular displacement kernel. We investigate the spectral behavior of this classical operator, particularly because various methods of analysis and solution rely on asymptotic properties of spectra, while no investigations of the spectrum of this operator seem to exist. In our approach, we first consider the composition of the second order differentiation operator and the integral operator with logarithmic displacement kernel. Employing the Weyl-Courant minimax principle and properties of the Cebysev polynomials of the first and second kind, we derive index-dependent bounds for the ordered sequence of eigenvalues of this operator and specify their ranges of validity. Additionally we derive bounds for the eigenvalues of the integral operator with logarithmic kernel. With slight modification our result extends to kernels that are the sum of the logarithmic displacement kernel and a real displacement kernel whose second derivative is square integrable. Employing this extension we derive bounds for the eigenvalues of the integral-differential operator of a linear strip with the complex kernel replaced by its real part. Finally, for specific geometry and frequency settings, we present numerical results for the eigenvalues of the considered operators using Ritz’s methods with respect to finite bases.

Proposed by Oskar Maria Baksalary, Adam Mickiewicz University, Poznan, Poland, and Götz Trenkler, Technische Universität Dortmund, Dortmund,Germany. Let Cn,n denote the set of n x n complex matrices. Determine the shortest interval [a, b] such that if P and Q in Cn,n are nonzero orthogonal projectors, that is, Hermitian idempotent matrices, then all eigenvalues of PQ + QP belong to [a, b].

A fall of the thin jet of viscous fluid onto the moving surface is considered. The jet is described by the effects of elongational viscosity, inertia and gravity. For the model equations we derive the boundary conditions allowing us to show existence for all the parameters, and investigate uniqueness. For the jet fall we distinguish three flow regimes, which are characterized by the convexity of the jet shape, or by an equivalent characterization of the dominant effect in the momentum transfer through the jet cross-section.

In this paper the current distribution in a set of parallel rings and patches, called islands, positioned at the surface of a cylinder, is investigated. The current is driven by an external applied source current. The islands are rectangular pieces of copper (patches) placed in parallel between the rings. The eddy currents in the islands induce currents in the rings that vary in the tangential direction. From the quasi-static Maxwell equations, an integral equation for the current distribution in the strips is derived. The Galerkin method, using global basis functions, is applied to solve this integral equation. It shows fast convergence. The global basis functions are built up of Legendre polynomials in axial direction and 2p-periodic trigonometric functions in tangential direction. The Legendre polynomials efficiently cope with the singularity of the kernel function of the integral equa- tion. Explicit numerical results are shown for three configurations. Besides the current distributions, the resistance and self-inductance of the three systems of rings and islands are computed. The resulting tool can be used in the design of realistic gradient coils. Keywords: MRI-scanning, Eddy currents, Patches, Legendre polynomials, Gradient coils.

Consider a Poisson structure on C8(R3,R) with bracket {, } and suppose that C is a Casimir function. Then {f, g} = is a possible Poisson structure. This confirms earlier observations concerning the Poisson structure for Hamiltonian systems that are reduced to a one degree of freedom system and generalizes the Lie-Poisson structure on the dual of a Lie algebra and the KKS-symplectic form. The fact that the governing reduced Poisson structure is described by one function makes it possible to find a representation, called the energy-momentum representation of the Poisson structure, describing both the singularity of the Poisson structure and the singularity of the energy-momentum mapping and hence the bifurcation of relative equilibria for such systems. It is shown that Hamiltonian Hopf bifurcations are directly related to singularities of Poisson structures of type sl(2).

Proposed by Marian Tetiva, National College "Gheorghe Rosca Codreanu," Barlad, Romallia. Let d be a square-free positive integer greater than 1. Show that there are infinitely many positive integers n such that dn2 + I divides n!.

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Het Amsterdamse All Options is een beursbedrijf dat razendsnel en nuchter handelt in opties. Bij algo-trading laat het bedrijf de handel zelfs geheel over aan computers. All Options heeft nogal wat wiskundigen in dienst, en NAW is uiteraard benieuwd wat zij aan methoden en technieken inzetten. Klaas Landsman (RU), Hans Melissen (TUD) en Wil Schilders (NXP, TU/e) overvielen het bedrijf op 2 juli van dit jaar.

Games, Mathematics, and Decisions. Games have always been loved by mathematicians. Because of their (usually) well-defined rules, games admit a formal analysis, sometimes with surprising results. It is impossible to provide comprehensive coverage in this article. Instead, I will give an overview and focus on the role of variance, which is often overlooked.

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In fabrieksprocessen vind je overal wiskundige fenomenen. Bijvoorbeeld bij de industriiHe productie van polymeermatten. die onder andere gebruikt worden om te voorkomen dat rivierdijken alkalven. Een polymeerdraad valt in vloeibare toestand loodrecht op een horizontaal bewegende band. Op de band vormt de polymeerdraad patronen waalVan de vorm afhankelijk is van de snelheid van de band. De patronen die hierbij ontstaan. blijken te kunnen worden beschreven door Lissajousfiguren, in de elektrotechniek al veellanger bekend. De resultaten van dit onderzoek geven houvast bij het inrichten van het productieproces, bijvoorbeeld om de omzet te verhogen bij constante kwaliteit van de geproduceerde matten.

A uniparametric 4-DOF family of perturbed Hamiltonian oscillators in 1:1:1:1 resonance is studied as a generalization for several models for perturbed Keplerian systems. Normalization by Lie-transforms (only first order is considered here) as well as geometric reduction related to the invariants associated to the symmetries is used based on previous work of the authors. A description is given of the lower dimensional relative equilibria in such normalized systems. In addition bifurcations of relative equilibria corresponding to three dimensional tori are studied in some particular cases where we focus on Hamiltonian Hopf bifurcations and bifurcations in the 3-D van der Waals and Zeeman systems.

We study a hybrid model of Sch¨obel-Zhu-Hull-White-type from a singular-perturbationanalysis perspective. The merit of the paper is twofold: On one hand, we find boundary conditions for the deterministic non-linear degenerate parabolic partial differential equation for the evolution of the stock price. On the other hand, we combine two-scales regular- and singular-perturbation techniques to find an approximate solution to the pricing PDE. The aim is to produce an expression that can be evaluated numerically very fast.

We present two models for the drying of waterborne paints, which consist of non-volatile latex particles suspended in water. One model considers the water and latex density in a layer as a function of time. Water evaporation at the surface represents the drying. This model results in a one-dimensional free boundary problem, which is solved numerically. Extensions to the model are given that describe the stiffening of the paint. A second model is a particle based dynamical simulation where latex particles form a network through which water particles move. A thin slab of the suspension in a threedimensional box is studied. Water particles escaping the slab at the surface represent the drying, progressing network formation the stiffening of the paint. Both models allow for validation with material properties as determined experimentally on real coatings.

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