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  • 1. Acker, A.
    et al.
    Henrot, A.
    Poghosyan, M.
    Shahgholian, Henrik
    KTH, Superseded Departments, Mathematics.
    The multi-layer free boundary problem for the p-Laplacian in convex domains2004In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 6, no 1, p. 81-103Article in journal (Refereed)
    Abstract [en]

    The main result of this paper concerns existence of classical solutions to the multi-layer Bernoulli free boundary problem with nonlinear joining conditions and the p-Laplacian as governing operator. The present treatment of the two-layer case involves technical refinements of the one-layer case, studied earlier by two of the authors. The existence treatment of the multi-layer case is largely based on a reduction to the two-layer case, in which uniform separation of the free boundaries plays a key role.

  • 2. Aleman, A.
    et al.
    Beliaev, Dmitri
    KTH, Superseded Departments, Mathematics.
    Hedenmalm, Håkan
    KTH, Superseded Departments, Mathematics.
    Real zero polynomials and Pólya-Schur type theorems2004In: Journal d'Analyse Mathematique, ISSN 0021-7670, E-ISSN 1565-8538, Vol. 94, p. 49-60Article in journal (Refereed)
  • 3.
    Alfredsson, Patrik
    KTH, Superseded Departments, Mathematics.
    On the optimization of support systems1997Doctoral thesis, monograph (Other scientific)
  • 4.
    Almér, Stefan
    et al.
    KTH, Superseded Departments, Mathematics.
    Jönsson, Ulf
    KTH, Superseded Departments, Mathematics.
    Kao, Chung-Yao
    KTH, Superseded Departments, Mathematics.
    Mari, Jorge
    Global stability analysis of DC-DC converters using sampled-data modeling2004In: PROCEEDINGS OF THE 2004 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2004, p. 4549-4554Conference paper (Refereed)
    Abstract [en]

    The paper presents stability analysis of a class of pulse-width modulated (PWM) systems which incorporates many different DC-DC converters. Two types of pulse-width modulation (digital and analog control) are considered. A procedure is developed for systematic search for Lyapunov functions. The state space is partitioned in such a way that stability is verified if a set of coupled Linear Matrix Inequalities (LMIs) is feasible. Global stability is considered as well as the computation of local regions of attraction.

  • 5.
    Altafini, Claudio
    KTH, Superseded Departments, Mathematics.
    Geometric control methods for nonlinear systems and robotic applications2001Doctoral thesis, monograph (Other scientific)
  • 6.
    Altafini, Claudio
    KTH, Superseded Departments, Mathematics.
    Redundant robotic chains on Riemannian submersions2004In: IEEE transactions on robotics and automation, ISSN 1042-296X, Vol. 20, no 2, p. 335-340Article in journal (Refereed)
    Abstract [en]

    The main scope of this paper is to introduce the notion of Riemannian submersion for the modeling and control of certain types of redundant robotic chains. in the robotics literature, the redundant case is normally treated only in numerical terms, as the need to resort to pseudoinversion techniques is usually considered a barrier to the use of analytic or geometric methods. Using Riemannian submersions, however, we can single out a particular type of inverse, the horizontal lift, with distinguished properties with respect to the infinitely many possible others. Quite remarkably, for a wide class of robotic chains, characterized by the vanishing of the curvature tensor, such horizontal lift coincides with the curve obtained from the Moore-Penrose pseudoinverse of the Jacobian.

  • 7.
    Altafini, Claudio
    et al.
    KTH, Superseded Departments, Mathematics.
    Speranzon, Alberto
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Wahlberg, Bo
    KTH, Superseded Departments, Signals, Sensors and Systems.
    A feedback control scheme for reversing a truck and trailer vehicle2001In: IEEE transactions on robotics and automation, ISSN 1042-296X, Vol. 17, no 6, p. 915-922Article in journal (Refereed)
    Abstract [en]

    A control scheme is proposed for stabilization of backward driving along simple paths for a miniaturized vehicle composed of a truck and a two-axle trailer. The paths chosen are straight lines and arcs of circles. When reversing, the truck and trailer under examination can be modeled as an unstable nonlinear system with state and input saturations. The simplified goal of stabilizing along a trajectory (instead of a point) allows us to consider a system with controllable linearization. Still, the combination of instability and saturations makes the task impossible with a single controller. In fact, the system cannot be driven backward from all initial states because of the jack-knife effects between the parts of the multibody vehicle; it is sometimes necessary to drive forward to enter into a specific region of attraction. This leads to the use of hybrid controllers. The scheme has been implemented and successfully used to reverse the radio-controlled vehicle.

  • 8. Aluffi, P.
    et al.
    Faber, Carel
    KTH, Superseded Departments, Mathematics.
    Linear orbits of arbitrary plane curves2000In: The Michigan mathematical journal, ISSN 0026-2285, E-ISSN 1945-2365, Vol. 48, p. 1-37Article in journal (Refereed)
  • 9. Aluffi, P.
    et al.
    Faber, Carel
    KTH, Superseded Departments, Mathematics.
    Plane curves with small linear orbits II2000In: International Journal of Mathematics, ISSN 0129-167X, Vol. 11, no 5, p. 591-608Article in journal (Refereed)
    Abstract [en]

    The linear orbit of a plane curve of degree d is its orbit in p(d(d+3)/2) under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of curves supported on unions of lines. Together with the results of [3], this encompasses the enumerative geometry of all plane curves with small linear orbit. This information will serve elsewhere as an ingredient in the computation of the degree of the orbit closure of an arbitrary plane curve.

  • 10. Andersson, Lars
    et al.
    Dahl, Mattias
    KTH, Superseded Departments, Mathematics.
    scalar curvature rigidity for asymptotically locally hyperbolic manifolds1998In: Annals of Global Analysis and Geometry, ISSN 0232-704X, E-ISSN 1572-9060, Vol. 16, p. 1-27Article in journal (Refereed)
    Abstract [en]

    Rigidity results for asymptotically locally hyperbolic manifoldswith lower bounds on scalar curvature are proved using spinor methodsrelated to the Witten proof of the positive mass theorem. The argument isbased on a study of the Dirac operator defined with respect to the Killingconnection. The existence of asymptotic Killing spinors is related to thespin structure on the end. The expression for the mass is calculated andproven to vanish for conformally compact Einstein manifolds with conformalboundary a spherical space form, giving rigidity. In the 4-dimensional case,the signature of the manifold is related to the spin structure on the end andexplicit formulas for the relevant invariants are given.

  • 11.
    Andersson, Lars
    et al.
    KTH, Superseded Departments, Mathematics.
    Dahl, Mattias
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Howard, Ralph
    Boundary and lens rigidity of Lorentzian surfaces1996In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 348, p. 2307-2329Article in journal (Refereed)
    Abstract [en]

    Let g be a Lorentzian metric on the plane ℝ2 that agrees with the standard metric g0 = -dx2 + dy2 outside a compact set and so that there are no conjugate points along any time-like geodesic of (ℝ2, g). Then (ℝ2, g) and (ℝ2, g0) are isometric. Further, if (M*, g*) and (M*, p*) are two dimensional compact time oriented Lorentzian manifolds with space-like boundaries and so that all time-like geodesies of (M, g) maximize the distances between their points and (M, g) and (M*, g*) are "boundary isometric", then there is a conformal diffeomorphism between (M, g) and (M*, g*) and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

  • 12.
    Andréasson, Fredrik
    KTH, Superseded Departments, Mathematics.
    Higher order differentials and generalized Cartan-de Rham complexes2003Doctoral thesis, monograph (Other scientific)
  • 13.
    Andréasson, Fredrik
    KTH, Superseded Departments, Mathematics.
    Jet bundles and Weierstrass points1999Licentiate thesis, monograph (Other scientific)
  • 14.
    Aniansson, Jockum
    KTH, Superseded Departments, Mathematics.
    Some integral representations in real and complex analysis1999Doctoral thesis, comprehensive summary (Other scientific)
  • 15. Apushkinskaya, D. E.
    et al.
    Ural’Tseva, N. N.
    Shahgholian, Henrik
    KTH, Superseded Departments, Mathematics.
    Lipschitz property of the free boundary in the parabolic obstacle problem2004In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 15, no 3, p. 375-391Article in journal (Refereed)
    Abstract [en]

    A parabolic obstacle problem with zero constraint is considered. It is proved, without any additional assumptions on a free boundary, that near the fixed boundary where the homogeneous Dirichlet condition is fulfilled, the boundary of the noncoincidence set is the graph of a Lipschitz function.

  • 16.
    Armerin, Fredrik
    KTH, Superseded Departments, Mathematics.
    Aspects of cash-flow valuation2004Doctoral thesis, monograph (Other academic)
    Abstract [en]

    This thesis consists of five papers. In the first two papers we consider a general approach to cash flow valuation, focusing on dynamic properties of the value of a stream of cash flows. The third paper discusses immunization theory, where old results are shown to hold in general deterministic models, but often fail to be true in stochastic models. In the fourth paper we comment on the connection between arbitrage opportunities and an immunized position. Finally, in the last paper we study coherent and convex measure of risk applied to portfolio optimization and insurance.

  • 17.
    Armerin, Fredrik
    KTH, Superseded Departments, Mathematics.
    On cash flow valuation2002Licentiate thesis, monograph (Other scientific)
    Abstract [en]

    A fundamental fact in finance and economics is that moneyhas a time value, meaning that if we want to value an amount ofmoney we get at some future date we should discount the amountfrom the future date back to today. When facing a stream ofcash flows occurring at di®erent times we discount each ofthe cash flows using suitable discount rates and then sum thecontributions. This sum of discounted cash flows defines thevalue today of this stream. Most future cash flows that appearin models in finance and economics are assumed to be stochastic(nondefaultable bonds being a counter example). To be able tovalue these stochastic cash flows we also have to takeexpectations. In some cases even the discount rate should bemodelled as a stochastic object. The purpose of the two papersin this licentiate thesis (’On the Valuation of Cash Flows–Discrete Time Models’and’On the Valuation ofCash Flows–Continuous Time Models’) is to establishgeneral properties of the value process. As time passes twothings happen. Firstly, the cash flows that are realised are nomore parts of the value and secondly, the information we canuse to determine the expected cash flows and discount ratesincreases.

    The two papers consider discrete time models and continuoustime models respectively.Of course any continuous time modelis necessarily an idealisation. Thus one could argue from amodelling point of view that we should use discrete timemodels. The main reason for using continuous time models isthat we have the powerful machinery of stochastic calculus athand. Discrete time models are mostly used in practice whenvaluing a firm or a project, while the continuous time settingis more frequently used in thoretical approaches to valuation.Most of the results are parallelled in the two papers. Adi®erence is that we discuss some convergence results forthe value in discrete time which do not occur in the continuoustime paper. The reason for not including this in the continuoustime paper is because we find it a more important question indiscrete time. On the other hand the Brownian models incontinuous time, where the Martingale Representation Theorem isan important tool, make the analysis much more transparent.

    In both papers we first define the underlying objects: thediscount process and the cash flow process. We then define,using these two processes, the value process (i.e. the expecteddiscounted value of the cash flow stream). We show that thediscounted value tends to zero almost surely, and that thereare three equivalent ways of writing the value process, each ofwhich has its own merits. We also extend this result to thecase when the cash flow process and the value process areevaluated at a stopping time. The first paper, on discrete timemodels, then continues by showing examples from finance,economics, and insurance where the discounted value processplays an important role. Finally we present two propositionswith necessary conditions for the value process to convergealmost surely. The second paper, on continuous time models,discusses some properties of the local dynamics of the valueprocess and then continues with Brownian models. We show thatthe value process can equivalently be expressed as a solutionto a forward-backward stochastic di®erential equation.Finally we show that under some additional assumptions there isa one-to-one correspondance between the cash flow process andthe value process. We also investigate the inverse problem offinding a cash flow process generating a given value processand discuss applications to real options.

  • 18.
    Arnlind, Joakim
    KTH, Superseded Departments, Mathematics.
    Eigenvalue dynamics and membrane solutions2004Licentiate thesis, comprehensive summary (Other scientific)
  • 19.
    Arnlind, Joakim
    et al.
    KTH, Superseded Departments, Mathematics.
    Hoppe, Jens
    KTH, Superseded Departments, Mathematics.
    Eigenvalue Dynamics off the Calogero-Moser system2004In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 68, no 2, p. 121-129Article in journal (Refereed)
    Abstract [en]

    By finding N(N-1)/2 suitable conserved quantities, free motions of real symmetric N x N matrices X(t), with arbitrary initial conditions, are reduced to nonlinear equations involving only the eigenvalues of X-in contrast to the rational Calogero-Moser system, for which [X(0), X(0)] has to be purely imaginary, of rank one.

  • 20.
    Arnlind, Joakim
    et al.
    KTH, Superseded Departments, Mathematics.
    Hoppe, Jens
    KTH, Superseded Departments, Mathematics.
    Theisen, Stefan
    Albert Einstein Inst.
    Spinning Membranes2004In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 599, no 1-2, p. 118-128Article in journal (Refereed)
    Abstract [en]

    We present new solutions of the classical equations of motion of bosonic (matrix-)membranes. Those relating to minimal surfaces in spheres provide spinning membrane solutions in AdS(p) X S-q, as well as in flat space-time. Nontrivial reductions of the BMN matrix model equations are also given.

  • 21.
    Aspenberg, Magnus
    KTH, Superseded Departments, Mathematics.
    The Collet-Eckmann condition for rational functions on the Riemann sphere2004Doctoral thesis, monograph (Other scientific)
  • 22.
    Avasjö, Agneta
    KTH, Superseded Departments, Mathematics.
    Automata and growth functions of Coxeter groups2004Licentiate thesis, monograph (Other scientific)
    Abstract [en]

    The aim of this thesis is to study, in some detail,properties of growth functions and geodesic growth functionsfor Coxeter groups. To do this, we use the fact that allCoxeter groups, which can be defined by some simple rules on apresentation by generators and relators, are described byformal languages which satisfy rather strong finitaryconditions. By connecting the context of groups with that offormal languages and constructing finite state automata for thelanguages N(G, S) and L(G, S) we make explicit algorithmiccomputations of the corresponding growth functions of the groupG.

    As a test-case we choose the subclass of triangle groups,which are defined in a purely geometric way as groups generatedby reflections with respect to the sides of a triangle. Thetheorems and the methods shown are however valid for allCoxeter groups. The construction of the automatons is based ona representation of a Coxeter group by linear transformationsacting on a vector space. The key notion here is that of a rootsystem. We demonstrate that the growth series and the growthseries of geodesics associated with a Coxeter system can bothbe given by rational expressions.

    Triangle groups (except for a finite number) are naturallyorganized into a few infinite series, and we were able toperform our computations for these infinite series, with one orseveral parameter tending to infinity. We give graphicalrepresentations of the constructed automata as well as resultsof numerical computations of the corresponding growthfunctions.

  • 23. Averbuch, A. Z.
    et al.
    Meyer, F.
    Strömberg, Jan-Olov
    KTH, Superseded Departments, Mathematics.
    Coifman, R.
    Vassiliou, A.
    Low bit-rate efficient compression for seismic data2001In: IEEE Transactions on Image Processing, ISSN 1057-7149, E-ISSN 1941-0042, Vol. 10, no 12, p. 1801-1814Article in journal (Refereed)
    Abstract [en]

    Compression is a relatively new introduced technique for seismic data operations. The main drive behind the use of data compression in seismic data is the very large size of seismic data acquired. Some of the most recent acquired marine seismic data sets exceed 10 Tbytes, and in fact there are currently seismic surveys planned with a volume of around 120 Tbytes. Thus, the need to compress these very large seismic data riles is imperative. Nevertheless, seismic data are quite different from the typical images used in image processing and multimedia applications. Some of their major differences are the data dynamic range exceeding 100 dB in theory, very often it is data with extensive oscillatory nature, the x and y directions represent different physical meaning, and there is significant amount of coherent noise which is often present in seismic data. Up to now some of the algorithms used for seismic data compression were based on some form of wavelet or local cosine transform. while using a uniform or quasiuniform quantization scheme and they finally employ a Huffman coding scheme. Using this family of compression algorithms we achieve compression results which are acceptable to geophysicists, only at low to moderate compression ratios. For higher compression ratios or higher decibel quality, significant compression artifacts are introduced in the reconstructed images, even with high-dimensional transforms. The objective of this paper is to achieve higher compression ratio, than achieved with the wavelet/uniform quantization/Huffman coding family of compression schemes, with a comparable level of residual noise. The goal is to achieve above 40 dB in the decompressed seismic data sets. Several established compression algorithms are reviewed, and some new compression algorithms are introduced. All of these compression techniques are applied to a good representation of seismic data sets, and their results are documented in this paper. One of the conclusions is that adaptive multiscale local cosine transform with different windows sizes performs well on all the seismic data sets and outperforms the other methods from the SNR point of view. All the described methods cover wide range of different data sets. Each data set will have his own best performed method chosen from this collection. The results were performed on four different seismic data sets. Special emphasis was given to achieve faster processing speed which is another critical issue that is examined in the paper. Some of these algorithms are also suitable for multimedia type compression.

  • 24. Avgustinovich, S. V.
    et al.
    Heden, Olof
    KTH, Superseded Departments, Mathematics.
    Solov'eva, F. I.
    The classification of some perfect codes2004In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 31, no 3, p. 313-318Article in journal (Refereed)
    Abstract [en]

    Perfect 1-error correcting codes C in Z(2)(n), where n = 2(m) - 1, are considered. Let [C] denote the linear span of the words of C and let the rank of C be the dimension of the vector space [C]. It is shown that if the rank of C is n - m + 2 then C is equivalent to a code given by a construction of Phelps. These codes are, in case of rank n - m + 2, described by a Hamming code H and a set of MDS-codes D-h; h is an element of H, over an alphabet with four symbols. The case of rank n - m + 1 is much simpler: Any such code is a Vasil'ev code.

  • 25. Baik, J.
    et al.
    Deift, P.
    Johansson, Kurt
    KTH, Superseded Departments, Mathematics.
    On the distribution of the length of the second row of a young diagram under Plancherel measure2000In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 10, no 4, p. 702-731Article in journal (Refereed)
  • 26. Baladi V,
    et al.
    Benedicks, Michael
    KTH, Superseded Departments, Mathematics.
    Maume-Deschamps V,
    Almost sure rates of mixing for I.I.D. unimodal maps (vol 35, pg 117, 2002)2003In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 36, no 2, p. 319-322Article in journal (Refereed)
    Abstract [en]

    The definition of the return time (p. 117) and the beginning of the proof of Proposition 8.3 of our paper in Vol. 35 of Ann. Scient. Ec. Norm. Sup. (2002) are not correct. We give an amended version which shows that none of the statements are affected. We take this opportunity to correct some other mistakes (without consequences), e.g. in Sublemma 7.2(3) and Lemma 7.10. Published by Editions scientifiques et medicales Elsevier SAS

  • 27. Baladi, V.
    et al.
    Benedicks, Michael
    KTH, Superseded Departments, Mathematics.
    Maume-Deschamps, V.
    Almost sure rates of mixing for i.i.d. unimodal maps2002In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, E-ISSN 1873-2151, Vol. 35, no 1, p. 77-126Article in journal (Refereed)
    Abstract [en]

    It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure. Young and Keller-Nowicki proved exponential decay of its correlation functions. Benedicks and Young [8], and Baladi and Viana [4] studied stability of the density and exponential rate of decay of the Markov chain associated to i.i.d. small perturbations. The almost sure statistical proper-ties of the sample stationary measures of i.i.d. itineraries are more difficult to estimate than the averaged statistics. Adapting to random systems, on the one hand partitions associated to hyperbolic times due to Alves [I], and on the other a probabilistic coupling method introduced by Young [26] to study rates of mixing, we prove stretched exponential upper bounds for the almost sure rates of mixing.

  • 28. Baladi, V.
    et al.
    Benedicks, Michael
    KTH, Superseded Departments, Mathematics.
    Maume-Deschamps, V.
    Decay of random correlation functions for unimodal maps2000In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 46, no 2-Jan, p. 15-26Article in journal (Refereed)
    Abstract [en]

    Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps f(a) (x) = a - x(2) admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing f(a), Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations f + omega (t), with f = f(a) or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and omega (t) chosen independently and identically in [-epsilon, epsilon]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure mu (omega), of almost every itinerary.

  • 29. Balinsky, A.
    et al.
    Laptev, Ari
    KTH, Superseded Departments, Mathematics.
    Sobolev, A. V.
    Generalized Hardy inequality for the magnetic Dirichlet forms2004In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 116, no 4-Jan, p. 507-521Article in journal (Refereed)
    Abstract [en]

    We obtain lower bounds for the magnetic Dirichlet form in dimensions d greater than or equal to 2. For d = 2 the results generalize a well known lower bound by the magnetic field strength: we replace the actual magnetic field B by an non-vanishing effective field which decays outside the support of B as dist( x, supp B)(-2). In the case d greater than or equal to 3 we establish that the magnetic form is bounded from below by the magnetic field strength, if one assumes that the field does not vanish and its direction is slowly varying.

  • 30. Bauer, T.
    et al.
    Di Rocco, Sandra
    KTH, Superseded Departments, Mathematics.
    Szemberg, T.
    Generation of jets on K3 surfaces2000In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 146, no 1, p. 17-27Article in journal (Refereed)
    Abstract [en]

    Let L be an ample line bundle on a K3 surface X. We give sharp bounds on n such that the global sections of nL simultaneously generate k-jets on X.

  • 31.
    Bauer, Thomas
    et al.
    Fachbereich Mathematik und Informatik, Philipps-Universität, Hans-Meerwein-Strasse, Lahnberge, 35032, MARBURG, GERMANY.
    Di Rocco, Sandra
    KTH, Superseded Departments, Mathematics.
    Szemberg, Tomasz
    Department of Mathematics, Krakow Pedagogical Academy, ul. Podchorazych 2, 30-084, KRAKOW, POLAND.
    Cyclic coverings and higher order embeddings of algebraic varieties2001In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 353, no 3, p. 877-891Article in journal (Refereed)
    Abstract [en]

    In the present paper we study higher order embeddings in the context of cyclic coverings. Analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor, we provide criteria for its pull-back to define an embedding of given order. We show that the obtained criteria are sharp. Finally, we apply them to various - sometimes seemingly unrelated-problems in algebraic geometry.

  • 32.
    Benedicks, Michael
    et al.
    KTH, Superseded Departments, Mathematics.
    Viana, M.
    Solution of the basin problem for Henon-like attractors2001In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 143, no 2, p. 375-434Article in journal (Refereed)
    Abstract [en]

    For a large class of non-uniformly hyperbolic attractors of dissipative diffeomorphisms, we prove that there are no holes in the basin of attraction: stable manifolds of points in the attractor fill-in a full Lebesgue measure subset. Then, Lebesgue almost every point in the basin is generic for the SRB (Sinai-Ruelle-Bowen) measure of the attractor. This solves a problem posed by Sinai and by Ruelle, for this class of systems.

  • 33.
    Benedicks, Michael
    et al.
    KTH, Superseded Departments, Mathematics.
    Young, L. S.
    Markov extensions and decay of correlations for certain Henon maps2000In: Astérisque, ISSN 0303-1179, no 261, p. 13-56Article in journal (Refereed)
    Abstract [en]

    Henon maps for which the analysis in [BC2] applies are considered. Sets with good hyperbolic properties and nice return structures are constructed and their return time functions are shown to have exponentially decaying tails. This sets the stage for applying the results in [Y]. Statistical properties such as exponential decay of correlations and central limit theorem are proved.

  • 34.
    Bertilsson, Daniel
    KTH, Superseded Departments, Mathematics.
    On Brennan's conjecture in conformal mapping1999Doctoral thesis, monograph (Other scientific)
  • 35. Besana, G. M.
    et al.
    Di Rocco, Sandra
    KTH, Superseded Departments, Mathematics.
    On polarized surfaces of low degree whose adjoint bundles are not spanned2002In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, E-ISSN 1881-1167, Vol. 54, no 2, p. 329-340Article in journal (Refereed)
    Abstract [en]

    Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to be the only examples in degree three. Two classes of examples in degree four are presented, one of which is shown to characterize regular such pairs. A Reider-type theorem is obtained in which the assumption on the degree of L is removed.

  • 36. Besana, G. M.
    et al.
    Di Rocco, Sandra
    KTH, Superseded Departments, Mathematics.
    Lanteri, A.
    Peculiar loci of ample and spanned line bundles2003In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 112, no 2, p. 197-219Article in journal (Refereed)
    Abstract [en]

    The bad locus and the rude locus of an ample and base point free linear system on a smooth complex projective variety are introduced and studied. Polarized surfaces of small degree, or whose degree is the square of a prime, with nonempty bad loci are completely classified. Several explicit examples are offered to describe the variety of behaviors of the two loci.

  • 37.
    Bjerklöv, Kristian
    KTH, Superseded Departments, Mathematics.
    Dynamical Properties of Quasi-periodic Schrödinger Equations2003Doctoral thesis, comprehensive summary (Other academic)
  • 38.
    Björner, Anders
    KTH, Superseded Departments, Mathematics.
    Face numbers of Scarf complexes2000In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 24, no 3-Feb, p. 185-196Article in journal (Refereed)
    Abstract [en]

    Let A be a (d + 1) x d real matrix whose row vectors positively span R-d and which is generic in the sense of Barany and Scarf [BS1]. Such a matrix determines a certain infinite d-dimensional simplicial complex Sigma, as described by Barany et al. [BHS]. The group Z(d) acts on Sigma with finitely many orbits. Let f(i) be the number of orbits of (i + 1)-simplices of Sigma. The sequence f = (f(0), f(1),..., f(d-1)) is the f-vector of a certain triangulated (d - 1)-ball T embedded in Sigma. When A has integer entries it is also, as shown by the work of Peeva and Sturmfels [PS], the sequence of Betti numbers of the minimal free resolution of k[x(1),...,x(d+1)]/I, where I is the lattice ideal determined by A. In this paper we study relations among the numbers f(i). It is shown that f(0), f(1),..., f([(d-3)/2]) determine the other numbers via linear relations, and that there are additional nonlinear relations. In more precise (and more technical) terms, our analysis shows that f is linearly determined by a certain M-sequence (g(0), g(1),..., g([(d-1)/2])). namely, the g-vector of the (d - 2)-sphere bounding T. Although T is in general not a cone over its boundary, it turns out that its f-vector behaves as if it were.

  • 39.
    Björner, Anders
    KTH, Superseded Departments, Mathematics.
    Nerves, fibers and homotopy groups2003In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 102, no 1, p. 88-93Article in journal (Refereed)
    Abstract [en]

    Two theorems are proved. One concerns coverings of a simplicial complex Delta by subcomplexes. It is shown that if every t-wise intersection of these subcomplexes is (k - t + 1)-connected, then for jless than or equal tok there are isomorphisms pi(j)(Delta) congruent to pi(j)(N) of homotopy groups of Delta and of the nerve X of the covering. The other concerns poset maps f : P --> Q. It is shown that if all fibers f(-1)(Q(less than or equal toq)) are k-connected, then f induces isomorphisms of homotopy groups pi(j)(P) congruent to pi(j)(Q), for all jless than or equal tok.

  • 40.
    Björner, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH, Superseded Departments (pre-2005), Mathematics.
    Goodarzi, A.
    On codimension one embedding of simplicial complexes2017In: A Journey through Discrete Mathematics: A Tribute to Jiri Matousek, Springer International Publishing , 2017, p. 207-219Chapter in book (Other academic)
    Abstract [en]

    We study d-dimensional simplicial complexes that are PL embeddable in Rd+1. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic approach to deriving upper bounds for the number of top-dimensional faces of such complexes, particularly in low dimensions.

  • 41.
    Björner, Anders
    et al.
    KTH, Superseded Departments, Mathematics.
    Hultman, Axel
    KTH, Superseded Departments, Mathematics.
    A note on blockers in posets2004In: Annals of Combinatorics, ISSN 0218-0006, E-ISSN 0219-3094, Vol. 8, no 2, p. 123-131Article in journal (Refereed)
    Abstract [en]

    The blocker A* of an antichain A in a finite poset P is the set of elements minimal with the property of having with each member of A a common predecessor. The following is done: (1) The posets P for which A** = A for all antichains are characterized.(2) The blocker A* of a symmetric antichain in the partition lattice is characterized.(3) Connections with the question of finding minimal size blocking sets for certain set families are discussed.

  • 42.
    Björner, Anders.
    et al.
    KTH, Superseded Departments, Mathematics.
    Lutz, F. H.
    Simplicial manifolds, bistellar flips and a 16-vertex triangulation of the Poincare homology 3-sphere2000In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 9, no 2, p. 275-289Article in journal (Refereed)
    Abstract [en]

    We present a computer program based on bistellar operations that provides a useful too I for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16-vertex triangulation of the Poincare homology 3-sphere; we construct an infinite series of non-FL d-dimensional spheres with d + 13 vertices for d greater than or equal to 5; and we show that ifa d-manifold, with d greater than or equal to 5, admits any triangulation on n vertices, it admits a noncombinatorial triangulation on n + 12 vertices.

  • 43.
    Björner, Anders.
    et al.
    KTH, Superseded Departments, Mathematics.
    Wachs, M. L.
    Geometrically constructed bases for homology of partition lattices of types A, B and D2004In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 11, no 2Article in journal (Refereed)
    Abstract [en]

    We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the splitting basis for the homology of the partition lattice given in [20], thus answering a question asked by R. Stanley. More explicitly, the following general technique is presented and utilized. Let A be a central and essential hyperplane arrangement in R-d. Let R-1,..., R-k be the bounded regions of a generic hyperplane section of A. We show that there are induced polytopal cycles rho(Ri) in the homology of the proper part LA of the intersection lattice such that {rho(Ri)}(i=1,...,k) is a basis for (H) over tilde (d-2)((L) over bar (A)). This geometric method for constructing combinatorial homology bases is applied to the Coxeter arrangements of types A, B and D, and to some interpolating arrangements.

  • 44. Blank, Ivan
    et al.
    Shahgholian, Henrik
    KTH, Superseded Departments, Mathematics.
    Boundary Regularity and Compactness for Overdetermined Problems2003In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 2, no 4, p. 787-802Article in journal (Refereed)
    Abstract [en]

    Let D be either the unit ball B-1(0) or the half ball B-1(+)(0), let f be a strictly positive and continuous function, and let u and Omega subset of D solve the following overdetermined problem: Delta u (x) = chi(Omega) (x) f (x) in D, 0 is an element of partial derivative Omega, u = vertical bar del u vertical bar = 0 in Omega(c), where chi(Omega) denotes the characteristic function of Omega, Omega(c) denotes the set D\Omega, and the equation is satisfied in the sense of distributions. When D = B-1(+)(0), then we impose in addition that u(x) 0 {(x', x(n))vertical bar x(n) = 0} We show that a fairly mild thickness assumption on Omega(c) will ensure enough compactness on it to give us "blow-up" limits, and we show how this compactness leads to regularity of partial derivative Omega. In the case where f is positive and Lipschitz, the methods developed in Caffarelli, Karp, and Shahgholian (2000) lead to regularity of partial derivative Omega under a weaker thickness assumption.

  • 45.
    Blomqvist, Anders
    et al.
    KTH, Superseded Departments, Mathematics.
    Fanizza, Giovanna
    KTH, Superseded Departments, Mathematics.
    Nagamune, Ryozo
    Mittag-Leffler Institute.
    Computation of bounded degree Nevanlinna-Pick interpolants by solving nonlinear equations2003In: 42nd IEEE Conference on Decision and Control: Maui, HI, DEC 09-12, 2003, 2003, p. 4511-4516Conference paper (Refereed)
    Abstract [en]

    This paper provides a procedure for computing scalar real rational Nevanlinna-Pick interpolants of a bounded degree. It applies to a wider class of interpolation problems and seems numerically more reliable than previous, optimization-based, procedures. It is based on the existence and the uniqueness of the solution guaranteed by Georgiou's proof of bijectivity of a map between a class of nonnegative trigonometric polynomials and a class of numerator/denominator polynomial pairs of interpolants. Further analysis of this map suggests a numerical continuation method for determining the interpolant from a system of nonlinear equations. A numerical example illustrates the reliability of the proposed procedure.

  • 46.
    Bodell, Josefin
    KTH, Superseded Departments, Mathematics.
    Cost of searching: probabilistic analysis of the self-organizing move-to-front and move -to-root sorting rules1997Doctoral thesis, monograph (Other scientific)
    Abstract [en]

    Consider two (or more) users who request records in adatabase independently and with different frequencies. On arequest, the user's probability of calling a certain record iseither constant or changes deterministically in time. One userhas priority over the other(s) and rearranges the recordsaccording to seff-organizing rules.

    Extending the model to include not just constant but alsotime-dependent request probabilities allows us to treat a widerclass of situations naturally arising in applications. Theintroduction of several users provides means to model morecomplex systems such as e.g. cach-hierarchies.

    Assuming a finite number of records, the low-priority user'stransient and stationary/long-term search cost distribution(including mean, variance and generating function) is derivedwhen the self-organizing rule ismove-to-frontresp.move-to-root.

    For move-to-front with constant request probabilities, ratesof convergence to stationarity are considered and some examplesfor standard distributions are given.

    As the number of records tends to infinity, the transientresp. long-term search cost as a fraction of the total numberof records (under some regularity assumptions) converges indistribution. The asymptotic distribution function is derivedfor move-to-front assuming deterministically time-dependentrequest probabilities. Also, some stochastic ordering resultsallowing us to decide which low-priority user requestprobability distribution yields the better asymptotic searchcost fraction are given. Taking the request probabilitydistributions to be constant in time, the results stillapply.

    All results for the low-priority user reduce to analogousones for the high-priority one when all users are taken to beidentical. In particular, we recapture the probability functionfor move-to-root with uniform request probabilities.Numerically, we find that the 'worst' set of requestprobabilities, maximizing the expected search cost, closelyresembles the uniform which justifies the interest in thisspecial case.

    Keywords and phrases:Poisson embedding, self-organizingsearch, move-to-front, move-to-root, coupling, search cost,caching.

  • 47.
    Boij, Mats
    KTH, Superseded Departments, Mathematics.
    Artin level modules2000In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 226, no 1, p. 361-374Article in journal (Refereed)
    Abstract [en]

    We introduce level modules and show that these form a natural class of modules over a polynomial ring. We prove that there exist compressed level modules, i.e., level modules with the expected maximal Hilbert function, given socle type and the number of generators. We also show how to use the theory of level modules to compute minimal free resolutions of the coordinate ring of points from the back, which reveals new examples where random sets of points fail to satisfy the minimal resolution conjecture.

  • 48. Boman, J.
    et al.
    Strömberg, Jan-Olov
    KTH, Superseded Departments, Mathematics.
    Novikov's inversion formula for the attenuated radon transform - A new approach2004In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 14, no 2, p. 185-198Article in journal (Refereed)
    Abstract [en]

    We study the inversion of weighted Radon transforms in two dimensions, R-rho f (L) = f(L) f((.)) rho (L, (.)) ds, where the weight function rho (L, x), L a line and x is an element of L, has a special form. It was an important breakthrough when R. G. Novikov recently gave an explicit formula for the inverse of R-rho When rho has the form (1.2); in this case R-rho is called the attenuated Radon transform. Here. we prove similar results,for a somewhat larger class of rho using completely different and quite elementary methods.

  • 49. Borichev, A.
    et al.
    Hedenmalm, Håkan
    KTH, Superseded Departments, Mathematics.
    Volberg, A.
    Large Bergman spaces: invertibility, cyclicity, and subspaces of arbitrary index2004In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 207, no 1, p. 111-160Article in journal (Refereed)
    Abstract [en]

    In a wide class of weighted Bergman spaces, we construct invertible non-cyclic elements. These are then used to produce z-invariant subspaces of index higher than one. In addition, these elements generate non-trivial bilaterally invariant subspaces in anti-symmetrically weighted Hilbert spaces of sequences.

  • 50.
    Bortolin, Gianantonio
    KTH, Superseded Departments, Mathematics.
    On Modelling and Estimation of Curl and Twist in Multi-Ply Paperboard2002Licentiate thesis, monograph (Other scientific)
    Abstract [en]

    This thesis describes a grey-box model for the dimensionalstability properties (i.e. curl and twist) of the carton boardproduced at AssiDomän Frövi paper mill in Sweden.AssiDomän Frövi AB is one of Sweden major cartonboard manufacturer, and produces some 350000 ton of board peryear.

    Curl is defined as the departure from a at form, and it mayseriously affect the processing of the paper. For this reason,customers impose quite restrictive limits on the allowedcurvatures of the board. So, it is becoming more and moreimportant to be able to produce a carton board with a curlwithin certain limits. Due to the economic significance of thecurl problem, much research has been performed to find sheetdesign and processing strategies to eliminate or reducecurl.

    The approach we used to tackle this problem is based ongrey-box modelling. The reasons for such an approach is thatthe physical process is very complex and nonlinear. The inuenceof some inputs is not entirely understood, and besides itdepends on a number of unknown parameters andunmodelled/unmesurable disturbances.

    One of the main part of the model is based on classicallaminate theory which is used to model the dimensionalstability of multi-ply board. The main assumption is that eachlayer is considered as an homogeneous elastic medium.

    The model is then complemented with a sub-model forunmodelled/umeasurable disturbances which are described asstates of a dynamical system, and estimated by means of anextended Kalman filter.

    The simulated curvatures show a general agreement with themeasurements. However, the prediction errors are too large forthe model to be used in an effective way, and a bigger efforthas to be carried out in order to improve the physicalsub-models.

    A chapter of this thesis discusses the modelling of thewet-end part of the paper machine with Dymola, a modelling toolfor simulation of large systems based on Modelica language.

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