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• 101.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Lefschetz Properties of Monomial Ideals with Almost Linear ResolutionIn: Article in journal (Other academic)

We study the WLP and SLP of artinian monomial ideals in S = K[x1, . . . , xn]

via studying their minimal free resolutions. We study the Lefschetz properties of such ideals

where the minimal free resolution of S/I is linear for at least n − 2 steps. We give an

affirmative answer to a conjecture of Eisenbud, Huneke and Ulrich for artinian monomial

ideals with almost linear resolutions.

• 102.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
The Weak Lefschetz Property of Equigenerated Monomial IdealsIn: Article in journal (Other academic)

We determine the sharp lower bound for the Hilbert function in degree d of a

monomial algebra failing the WLP over a polynomial ring with n variables and generated in

degree d. We consider artinian ideals in the polynomial ring with

n variables generated by homogeneous polynomials of degree d invariant under an action of

the cyclic group Z/dZ. We give a complete classification of

such ideals in terms of the WLP depending on the action.

• 103.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Free resolution of powers of monomial ideals and Golod rings2017In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 120, no 1, p. 59-67Article in journal (Refereed)

Let S = Kdbl[x1,⋯, xn] be the polynomial ring over a field Kdbl. In this paper we present a criterion for componentwise linearity of powers of monomial ideals. In particular, we prove that if a squarefree monomial ideal I contains no variable and some power of I is componentwise linear, then I satisfies the gcd condition. For a square-free monomial ideal I which contains no variable, we show that S/I is a Golod ring provided that for some integer s ≥ 1, the ideal Is has linear quotients with respect to a monomial order.

• 104.
KTH, School of Electrical Engineering (EES), Electric Power Systems.
Texas Tech University.
The Feedback Control of Glucose: On the road to type II diabetes2006In: Proceedings of the 45th IEEE Conference on Decision & Control, 2006, p. 685-690Conference paper (Refereed)

This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type H diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates.

• 105.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimization of Production Scheduling in the Dairy Industry2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis presents a case study of mathematical production scheduling optimization applied on Arla Foods AB’s production of dairy products. The scheduling was performed as a possible remedy for problems caused by overcrowded finished goods warehouse. Based on the scheduling, conclusions were made on whether the existing two-shift production is sufficient or if an additional night shift should be introduced. In parallel, an empirical and theoretical analysis on the perceived effects of night shift work on employees was conducted.

For the optimization, mixed integer programming was used to model the production context through a discrete time scheduling lot-sizing model developed in this thesis. The model developed and implemented on Arla Foods AB contributes to the research field through its feature of relatively low complexity enabling scheduling of extensive production systems when applied in industrial contexts where products may be categorized.

The thesis concludes that mathematical production scheduling can solve Arla Foods AB’s production problematics and suggests reallocation of the existing shifts for the purpose of reduced costs and acceptable warehouse levels. This reallocation would incur production during inconvenient hours whereas management remedies reducing negative effects of night shift work are identified.

• 106. Amerik, Ekaterina
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Evidence for the Dynamical Brauer-Manin Criterion2016In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 25, no 1, p. 54-65Article in journal (Refereed)

Let phi: X -> X be a morphism of a variety over a number field K. We consider local conditions and a "Brauer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P is an element of X(K) to be disjoint from a subvariety V subset of X, i.e., for V boolean AND O-phi (P) = empty set. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of points in the intersection V boolean AND O-phi (P); this evidence stems from a probabilistic argument as well as unconditional results in the case of etale maps.

• 107.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges2017In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, Vol. 121, p. 42-71Article in journal (Refereed)

We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, which has so far been known to hold for solutions in areal coordinates only, is stable to perturbations of the coordinate systems. Our proof is based on an analysis of the singular initial value problem for the Einstein vacuum equations in the generalized wave gauge formalism, and provides a framework which we anticipate to be useful for more general spacetimes.

• 108.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Technion Israel Inst Technol, Dept Math.
On the K-divisibility constant for some special finite-dimensional Banach couples2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 360, no 1, p. 130-155Article in journal (Refereed)

We prove new estimates of the K-divisibility constants for some special Banach couples. In particular, we prove that the K-divisibility constant for a couple of the form (U circle plus V, U) where U and V are non-trivial Hilbert spaces equals 2/root 3. We also prove estimates for the K-divisibility constant of the two-dimensional version of the couple (L-2, L-infinity), proving in particular that this couple is not exactly K-divisible. There are also several auxiliary results, including some estimates for relative Calderon constants for finite-dimensional couples.

• 109.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Berezin Transform in Polynomial Bergman Spaces2010In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 63, no 12, p. 1533-1584Article in journal (Refereed)

Fix a smooth weight function Q in the plane, subject to a growth condition from below Let K-m,K-n denote the reproducing kernel for the Hilbert space of analytic polynomials of degree at most n - 1 of finite L-2-norm with respect to the measure e-(mQ) dA Here dA is normalized area measure, and m is a positive real scaling parameter The (polynomial) Berezin measure dB(m,n)(< z0 >) (z) = K-m,K-n(z(0).z(0))(-1) vertical bar K-m,K-n(z.z(0))vertical bar(2)e(-mQ(z)) dA(z) for the point z(0) is a probability measure that defines the (polynomial) Berezin transform B-m,B-n f(z(0)) = integral(C) f dB(m,n)(< z0 >) for continuous f is an element of L-infinity (C). We analyze the semiclassical limit of the Berezin measure (and transform) as m -> +infinity while n = m tau + o(1), where tau is fixed, positive, and real We find that the Berezin measure for z(0) converges weak-star to the unit point mass at the point z(0) provided that Delta Q(z(0)) > 0 and that z(0) is contained in the interior of a compact set f(tau). defined as the coincidence set for an obstacle problem. As a refinement, we show that the appropriate local blowup of the Berezin measure converges to the standardized Gaussian measure in the plane For points z(0) is an element of C\f(tau), the Berezin measure cannot converge to the point mass at z(0) In the model case Q(z) = vertical bar z vertical bar(2), when f(tau) is a closed disk, we find that the Berezin measure instead converges to harmonic measure at z(0) relative to C\f(tau) Our results have applications to the study of the cigenvalues of random normal matrices The auxiliary results include weighted L-2-estimates for the equation partial derivative u = f when f is a suitable test function and the solution u is restricted by a polynomial growth bound at infinity.

• 110. Ameur, Yacin
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
FLUCTUATIONS OF EIGENVALUES OF RANDOM NORMAL MATRICES2011In: Duke mathematical journal, ISSN 0012-7094, E-ISSN 1547-7398, Vol. 159, no 1, p. 31-81Article in journal (Refereed)

In this article, we consider a fairly general potential in the plane and the corresponding Boltzmann-Gibbs distribution of eigenvalues of random normal matrices. As the order of the matrices tends to infinity, the eigenvalues condensate on a certain compact subset of the plane-the "droplet." We prove that fluctuations of linear statistics of eigenvalues of random normal matrices converge on compact subsets of the interior of the droplet to a Gaussian field, and we discuss various ramifications of this result.

• 111. Ameur, Yacin
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Random normal matrices and ward identities2015In: Annals of Probability, ISSN 0091-1798, E-ISSN 2168-894X, Vol. 43, no 3, p. 1157-1201Article in journal (Refereed)

We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the correction to the expectation of the fluctuations, and we show that the potential field of the corrected fluctuations converge on smooth test functions to a Gaussian free field with free boundary conditions on the droplet associated with the potential.

• 112.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Interpolation classes and matrix monotone functions2007In: Journal of operator theory, ISSN 0379-4024, E-ISSN 1841-7744, Vol. 57, no 2, p. 409-427Article in journal (Refereed)

An interpolation function of order n is a positive function -/+ on (0, infinity) such that vertical bar vertical bar -/+ (A)(1/2) T -/+ (A)-(1/2) vertical bar vertical bar <= max(vertical bar vertical bar T vertical bar vertical bar, vertical bar A(1/2)TA(-1/2) vertical bar vertical bar) for all n x ii matrices T and A such that A is positive definite. By a theorem of Donoghue, the class C-n of interpolation functions of order n coincides with the class of functions -/+ such that for each n-subset S = {lambda i}(n)(i=1)of (0,infinity) there exists a positive Pick function h on (0, co) interpolating -/+ at S. This note comprises a study of the classes C-n and their relations to matrix monotone functions of finite order. We also consider interpolation functions on general unital C*-algebras.

• 113.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Equidistributions of mahonian statistics over pattern avoiding permutations2018In: The Electronic Journal of Combinatorics, ISSN 1097-1440, E-ISSN 1077-8926, Vol. 25, no 1, article id #P1.7Article in journal (Refereed)

A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern functions of length at most d. Babson and Ste- ingrímsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over permutations in Sn avoiding a single classical pattern in S3. Tools used include block decomposition, Dyck paths and generating functions.

• 114. Ammann, B.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
The conformal Yamabe constant of product manifolds2013In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 141, no 1, p. 295-307Article in journal (Refereed)

Let (V, g) and (W, h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V × W, g + h) in terms of the conformal Yamabe constants of (V, g) and (W, h).

• 115. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Mass endomorphism, surgery and perturbations2014In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 64, no 2, p. 467-487Article in journal (Refereed)

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

• 116. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Harmonic spinors and local deformations of the metric2011In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 18, no 5, p. 927-936Article in journal (Refereed)

Let (M, g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

• 117. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Low-dimensional surgery and the Yamabe invariant2015In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, E-ISSN 1881-1167, Vol. 67, no 1, p. 159-182Article in journal (Refereed)

Assume that M is a compact n-dimensional manifold and that N is obtained by surgery along a k-dimensional sphere, k <= n - 3. The smooth Yamabe invariants sigma(M) and sigma(N) satisfy sigma(N) >= min(sigma(M), Lambda) for a constant Lambda > 0 depending only on n and k. We derive explicit positive lower bounds for A in dimensions where previous methods failed, namely for (n, k) is an element of {(4, 1), (5, 1), (5, 2), (6, 3), (9, 1), (10, 1)}. With methods from surgery theory and bordism theory several gap phenomena for smooth Yamabe invariants can be deduced.

• 118. Ammann, Bernd
Smooth yamabe invariant and surgery2013In: Journal of differential geometry, ISSN 0022-040X, E-ISSN 1945-743X, Vol. 94, no 1, p. 1-58Article in journal (Refereed)

We prove a surgery formula for the smooth Yamabe invariant sigma(M) of a compact manifold M. Assume that N is obtained from M by surgery of codimension at least 3. We prove the existence of a positive constant Lambda(n), depending only on the dimension n of M, such that sigma(N) >= min{sigma(M), Lambda(n)}.

• 119. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Square-integrability of solutions of the Yamabe equation2013In: Communications in analysis and geometry, ISSN 1019-8385, E-ISSN 1944-9992, Vol. 21, no 5, p. 891-916Article in journal (Refereed)

We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds, which are bounded and L-p for p = 2n/(n -2) are also L-2. This L-p-L-2 implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in our paper [4]. As an application we see that the smooth Yamabe invariant of any two-connected compact seven-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions >= 11.

• 120. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Surgery and harmonic spinors2009In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 220, no 2, p. 523-539Article in journal (Refereed)

Let M he a compact spin manifold with a chosen spin structure. The Atiyah-Singer index theorem implies that for any Riemannian metric on M the dimension of the kernel of the Dirac operator is bounded from below by a topological quantity depending only on M and the spin structure. We show that for generic metrics on M this bound is attained.

• 121. Ammann, Bernd
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Surgery and the Spinorial tau-Invariant2009In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 34, no 10, p. 1147-1179Article in journal (Refereed)

We associate to a compact spin manifold M a real-valued invariant (M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's sigma-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then (N) epsilon min{(M), n}, where n is a positive constant depending only on n=dim M. Various topological conclusions can be drawn, in particular that is a spin-bordism invariant below n. Also, below n the values of cannot accumulate from above when varied over all manifolds of dimension n.

• 122.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
A thesis submitted in fulfilment of the requirements for the degree of Masters of Mathematics2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

An open problem introduced by J. Haglund was to find a bijective proof over Dyck paths that would interchange two of its statistics. This problem was known to be The Symmetry Problem of the q,t-Catalan polynomial and was proven by other means to be true. This project is an attempt to find a bijection, where we provide the bijection's behaviour under certain constrains. Then, we introduce an attempt to translate the problem from Dyck paths to other combinatorial structures. Finally we try to solve a related conjecture, called The Symmetry Problem of parking functions, which generalizes the previous problem. Some results we obtained from The Symmetry Problem of parking functions helped us characterize part of a bijective proof for Dyck paths.

• 123.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
A comparison between different volatility models2011Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
• 124.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Approximate Bayesian Learning of Partition Directed Acyclic Graphs2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Partition directed acyclic graphs (PDAGs) is a model whereby the conditional probability tables (CPTs) are partitioned into parts with equal probability. In this way, the number of parameters that need to be learned can be significantly reduced so that some problems become more computationally feasible. PDAGs have been shown to be connected to labeled DAGs (LDAGs) and the connection is summarized here. Furthermore, a clustering algorithm is compared to an exact algorithm for determining a PDAG. To evaluate the algorithm, we use it on simulated data where the expected result is known.

• 125.
KTH, School of Engineering Sciences (SCI).
Morphisms of Fusion Systems2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

A fusion system on a finite group G with a Sylow p-subgroup P is a category on P with all subgroups of P as objects and group homomorphisms induced by conjugation in G as morphisms and was first introduced by L. Puig around 1990 in order to aid his research in finite group theory. The idea turned out to be fruitful and today, the theory of fusion systems is an active field in mathematics, with applications to topology, representation theory and finite group theory.

In this paper, we will, among other things, see how fusion systems aid in solving problems in finite group theory. We begin with an introduction to the theory with basic examples and then proceed to prove two famous theorems named after Burnside and Frobenius. However, to finish the proof of Frobenius’ theorem, we will require the focal subgroup theorem, whose proof requires transfer theory and is thus discussed. Afterwards, we introduce abstract and saturated fusion systems, in which one disregard the underlying group, and later prove that every fusion system on a finite group is saturated. We end with a discussion of morphisms of fusion systems, utilizing the concept previously developed, and generalize the isomorphism theorems to saturated fusion systems.

The presentation is well adapted for undergraduate students with limited knowledge of group and category theory and no previous knowledge of fusion systems is assumed.

• 126.
KTH, School of Computer Science and Communication (CSC).
Modeling of a Cooling Airflow in an Electric Motor.2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

An electric motor converts electrical to mechanical energy and provides the rotational torque which is converted into linear motion. In some applications the duty is cyclic and the motor is used for both providing driving and breaking torque. In many applications today, the power to weight requirements are continuously increasing which means that the cooling is crucial. One of the major design elements in the cooling system of an electric motor is the fan. Unfortunately the current fan exceeds the noise constraints. The thesis analyses the fan in terms of noise production and performance, and proposes an improved fan design. The computation of the airflow is done with the software COMSOL. In the beginning different design guidelines and noise sources of a fan in general are summarized. Subsequently the concrete simulation procedure in COMSOL is described. After these basic issues are discussed, the different noise sources, namely the broad-band and the tonal noise, are investigated for the current fan and the improved fan design. The analysis of different design-space parameters is also done in terms of performance of the fan, i.e. the actual transported airflow together with the produced pressure difference. In the end, the results of these studies are summarized and the most improved fan design is the outcome of this.

• 127.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Smart Beta Investering Baserad på Makroekonomiska Indikatorer2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis examines the possibility to find a relationship between the Nasdaq Nordea Smart Beta Indices and a series of macroeconomic indicators. This relationship will be used as a signal-value and implemented in a portfolio consisting of all six smart beta indices. To investigate the impact of the signal-value on the portfolio performance, three portfolio strategies are examined with the equally weighted portfolio as a benchmark. The portfolio weights will be re-evaluated monthly and the portfolios examined are the mean-variance portfolio, the mean-variance portfolio based on the signal-value and the equally weighted portfolio based on the signal-value.

In order to forecast the performance of the portfolio, a multivariate GARCH model with time-varying correlations is fitted to the data and three different error-distributions are considered. The performances of the portfolios are studied both in- and out-of-sample and the analysis is based on the Sharpe ratio.

The results indicate that a mean-variance portfolio based on the relationship with the macroeconomic indicators outperforms the other portfolios for the in-sample period, with respect to the Sharpe ratio. In the out-of-sample period however, none of the portfolio strategies has Sharpe ratios that are statistically different from that of an equally weighted portfolio.

• 128.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
A mixed relaxed singular maximum principle for linear SDEs with random coefficientsArticle in journal (Refereed)

We study singular stochastic control of a two dimensional stochastic differential equation, where the first component is linear with random and unbounded coefficients. We derive existence of an optimal relaxed control and necessary conditions for optimality in the form of a mixed relaxed-singular maximum principle in a global form. A motivating example is given in the form of an optimal investment and consumption problem with transaction costs, where we consider a portfolio with a continuum of bonds and where the portfolio weights are modeled as measure-valued processes on the set of times to maturity.

• 129.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Contributions to the Stochastic Maximum Principle2009Doctoral thesis, comprehensive summary (Other academic)

This thesis consists of four papers treating the maximum principle for stochastic control problems.

In the first paper we study the optimal control of a class of stochastic differential equations (SDEs) of mean-field type, where the coefficients are allowed to depend on the law of the process. Moreover, the cost functional of the control problem may also depend on the law of the process. Necessary and sufficient conditions for optimality are derived in the form of a maximum principle, which is also applied to solve the mean-variance portfolio problem.

In the second paper, we study the problem of controlling a linear SDE where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditons for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

The third paper generalizes the second one by adding a singular control process to the SDE. That is, the control is singular with respect to the Lebesgue measure and its influence on the state is thus not continuous in time. In terms of the portfolio problem, this allows us to consider two investment possibilities - bonds (with a continuum of maturities) and stocks - and incur transaction costs between the two accounts.

In the fourth paper we consider a general singular control problem. The absolutely continuous part of the control is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

• 130.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Necessary Optimality Conditions for Two Stochastic Control Problems2008Licentiate thesis, comprehensive summary (Other scientific)

This thesis consists of two papers concerning necessary conditions in stochastic control problems. In the first paper, we study the problem of controlling a linear stochastic differential equation (SDE) where the coefficients are random and not necessarily bounded. We consider relaxed control processes, i.e. the control is defined as a process taking values in the space of probability measures on the control set. The main motivation is a bond portfolio optimization problem. The relaxed control processes are then interpreted as the portfolio weights corresponding to different maturity times of the bonds. We establish existence of an optimal control and necessary conditions for optimality in the form of a maximum principle, extended to include the family of relaxed controls.

In the second paper we consider the so-called singular control problem where the control consists of two components, one absolutely continuous and one singular. The absolutely continuous part of the control is allowed to enter both the drift and diffusion coefficient. The absolutely continuous part is relaxed in the classical way, i.e. the generator of the corresponding martingale problem is integrated with respect to a probability measure, guaranteeing the existence of an optimal control. This is shown to correspond to an SDE driven by a continuous orthogonal martingale measure. A maximum principle which describes necessary conditions for optimal relaxed singular control is derived.

• 131.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
The relaxed general maximum principle for singular optimal control of diffusions2009In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, ISSN 01676911, Vol. 58, no 1, p. 76-82Article in journal (Refereed)

In this paper we study optimality in stochastic control problems where the state process is a stochastic differential equation (SDE) and the control variable has two components, the first being absolutely continuous and the second singular. A control is defined as a solution to the corresponding martingale problem. To obtain existence of an optimal control Haussmann and Suo [U.G. Haussmann, W. Suo, Singular optimal stochastic controls I: Existence, SIAM J. Control Optim. 33 (3) (1995) 916-936] relaxed the martingale problem by extending the absolutely continuous control to the space of probability measures on the control set. Bahlali et al. [S. Bahlali, B. Djehiche, B. Mezerdi, The relaxed stochastic maximum principle in singular optimal control of diffusions, SIAM J. Control Optim. 46 (2) (2007) 427-444] established a maximum principle for relaxed singular control problems with uncontrolled diffusion coefficient. The main goal of this paper is to extend their results to the case where the control enters the diffusion coefficient. The proof is based on necessary conditions for near optimality of a sequence of ordinary controls which approximate the optimal relaxed control. The necessary conditions for near optimality are obtained by Ekeland's variational principle and the general maximum principle for (strict) singular control problems obtained in Bahlali and Mezerdi [S. Bahlali, B. Mezerdi, A general stochastic maximum principle for singular control problems, Electron J. Probab. 10 (2005) 988-1004. Paper no 30]. © 2008 Elsevier B.V. All rights reserved.

• 132.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
The relaxed stochastic maximum principle in singular optimal control of diffusions with controlled diffusion coefficientManuscript (Other academic)
• 133.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
A maximum principle for relaxed stochastic control of linear SDEs with application to bond portfolio optimization2010In: Mathematical Methods of Operations Research, ISSN 1432-2994, E-ISSN 1432-5217, Vol. 72, no 2, p. 273-310Article in journal (Refereed)

We study relaxed stochastic control problems where the state equation is a one dimensional linear stochastic differential equation with random and unbounded coefficients. The two main results are existence of an optimal relaxed control and necessary conditions for optimality in the form of a relaxed maximum principle. The main motivation is an optimal bond portfolio problem in a market where there exists a continuum of bonds and the portfolio weights are modeled as measure-valued processes on the set of times to maturity.

• 134.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
A maximum principle for SDEs of mean-field type2011In: Applied mathematics and optimization, ISSN 0095-4616, E-ISSN 1432-0606, Vol. 63, no 3, p. 341-356Article in journal (Refereed)

We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.

• 135.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Factors affecting the proportion of smartphone usage at Flygresor.se2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Digitization has changed the way people access the internet. Smartphones is soon to be the preferred internet access device leading us into a new generation of e-commerce, namely mobile commerce or m-commerce. The on-going transition, from desktop to smartphone has led to an uprising problem for companies within the area of e-commerce. Visitors coming from a smartphone device tend to not go through with the purchase. With this transition in mind, the thesis aimed to identify the factors that affect the proportion of smartphone visitors on a website, more specifically at the flight comparison site Flygresor.se. The method used was multiple linear regression analysis. To see whether the chosen factors affected the proportion of smartphone transactions or just the proportion of smartphone sessions two regression were performed. One with response variable Sessions and one with response variable Transactions, where Sessions refer to the number of visitors on the website and Transactions refer to the number of visitors moving on to the final booking website. The explanatory variables used were divided into four categories; Marketing, Channels, Season and Other, where the category Other contained the variables Total number of visitors and Amount of MB used per smartphone subscription. The study showed that all categories contained variables with significant impact on both of the response variables. There was only one variable that had different impact on the models, namely the Total number of visitors. The result indicates that smartphone users tend to, in comparison with desktop users, to a less extent continue to the final booking website. Since there were no other variables that only had an impact on Transactions it was assumed that there exist other factors which have a greater impact on smartphone users tendency to finalize a booking.

• 136.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Solving the Train Timetabling Problem by using Rapid Branching2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The topic of this thesis is the implementation of rapid branching to find an integer solution for the train timetabling problem. The techniques that rapid branching are based on are presented. The important aspect of rapid branching are discussed and then the algorithm is applied to some artificial problems. It is shown that rapid branching can be both faster and slower than a standard integer solver depending on the problem instance. For the most realistic set of the examined instances, rapid branching turned out to be faster than the standard integer solver and produce satisficingly high quality solutions.

• 137.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Missing Data in Value-at-Risk Analysis: Conditional Imputation in Optimal Portfolios Using Regression2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

A regression-based method is presented in order toregenerate missing data points in stock return time series. The method usesonly complete time series of assets in optimal portfolios, in which the returnsof the underlying tend to correlate inadequately with each other. The studyshows that the method is able to replicate empirical VaR-backtesting resultswhere all data are available, even when up to 90% of the time series in half ofthe assets in the portfolios have been removed.

• 138.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Counting words avoiding patterns of length three with generating functions2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

The set of 123-avoiding words with exactly r occurrences of each letter was recently enumerated by N. Shar and D. Zeilberger. This paper enumerates more complicated sets of pattern avoiding words, such as those allowing 1, 2, ... or r occurrences of each letter, or those for which the numbers of occurrences of each individual letter follow a repeating sequence. The results are also generalized to apply to all patterns of length three with distinct letters. The generating functions enumerating the words are shown to be algebraic, for all investigated sets of words. A notable number of coefficients for the relevant generating functions have been found and the first few confirmed by independent methods. The asymptotic behaviour of these coefficients has been established as exponential. The employed strategy involves partitioning words into subwords which allow for the construction of equations relating the generating functions.

• 139.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
On Invertibility of the Radon Transform and Compressive Sensing2014Doctoral thesis, comprehensive summary (Other academic)

This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property.

• 140.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Stockholm University.
Stability estimates with a priori bound for the inverse local Radon transformManuscript (preprint) (Other academic)

We consider the inverse problem for the 2-dimensional weighted local Radon transform $R_{m}[f]$, where $f$ is supported in $y\geq x^2$ and $R_{m}[f](\xi,\eta)=\int f(x,\xi x+\eta)m(x,\xi,\eta)dx$ is defined near $(\xi,\eta)=(0,0)$. For weight functions satisfying a certain differential equation we give weak estimates of$f$ in terms of $R_{m}[f]$ for functions $f$ that satisfies an a priori bound.

• 141.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
On the Theorem of Uniform Recovery of Random Sampling Matrices2014In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 3, p. 1700-1710Article in journal (Refereed)

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

• 142.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Locating Multiple Change-Points Using a Combination of Methods2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The aim of this study is to find a method that is able to locate multiple change-points in a time series with unknown properties. The methods that are investigated are the CUSUM and CUSUM of squares test, the CUSUM test with OLS residuals, the Mann-Whitney test and Quandt’s log likelihood ratio. Since all methods are detecting single change-points, the binary segmentation technique is used to find multiple change-points. The study shows that the CUSUM test with OLS residuals, Mann-Whitney test and Quandt’s log likelihood ratio work well on most samples while the CUSUM and CUSUM of squares are not able to detect the location of the change-points. Furthermore the study shows that the binary segmentation technique works well with all methods and is able to detect multiple change-points in most circumstances. The study also shows that the results can, most of the time, be improved by using a combination of the methods.

• 143.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Free boundary problems and global solutions in half spaces2005Doctoral thesis, comprehensive summary (Other scientific)
• 144.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
On the De Giorgi conjecture in half spacesManuscript (preprint) (Other academic)
• 145.
Max Planck Institute, Leipzig.
On the regularity of a free boundary near contact points with a fixed boundary2007In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 232, no 1, p. 285-302Article in journal (Refereed)

We investigate the regularity of a free boundary near contact points with a fixed boundary, with C boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly C 1 up to the fixed boundary. We will also construct some examples of irregular free boundaries.

• 146.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Optimal regularity for the Signorini problem and its free boundary2015In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297Article in journal (Refereed)

We will show optimal regularity for minimizers of the Signorini problem for the Lame system. In particular if (Formula presented.) minimizes (Formula presented.)in the convex set (Formula presented.)where (Formula presented.) say. Then (Formula presented.). Moreover the free boundary, given by (Formula presented.)will be a (Formula presented.) graph close to points where (Formula presented.) is not degenerate. Similar results have been know before for scalar partial differential equations (see for instance [5, 6]). The novelty of this approach is that it does not rely on maximum principle methods and is therefore applicable to systems of equations.

• 147.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
The free boundary near the fixed boundary for the heat equationManuscript (preprint) (Other academic)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Optimal Regularity for the No-Sign Obstacle Problem2013In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 66, no 2, p. 245-262Article in journal (Refereed)

In this paper we prove the optimal C-1,C-1(B-1/2)-regularity for a general obstacle-type problem Delta u = f chi({u not equal 0}) in B-1, under the assumption that f * N is C-1,C-1(B-1), where N is the Newtonian potential. This is the weakest assumption for which one can hope to get C-1,C-1-regularity. As a by-product of the C-1,C-1-regularity we are able to prove that, under a standard thickness assumption on the zero set close to a free boundary point x(0), the free boundary is locally a C-1-graph close to x(0) provided f is Dini. This completely settles the question of the optimal regularity of this problem, which has been the focus of much attention during the last two decades.

• 149.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Optimal regularity for the obstacle problem for the p-Laplacian2015In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 6, p. 2167-2179Article in journal (Refereed)

In this paper we discuss the obstacle problem for the p-Laplace operator. We prove optimal growth results for the solution. Of particular interest is the point-wise regularity of the solution at free boundary points. The most surprising result we prove is the one for the p-obstacle problem: Find the smallest u such thatdiv(|∇u|p-2∇u)≤0,u≥ϕ,in B1, with ϕ∈C1,1(B1) and given boundary datum on ∂B1. We prove that the solution is uniformly C1,1 at free boundary points. Similar results are obtained in the case of an inhomogeneity belonging to L∞. When applied to the corresponding parabolic problem, these results imply that any solution which is Lipschitz in time is C1,1p-1 in the spatial variables.

• 150.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
Optimal regularity for the parabolic no-sign obstacle type problem2013In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, no 4, p. 477-499Article in journal (Refereed)

We study the parabolic free boundary problem of obstacle type Delta u - partial derivative u/partial derivative t = f chi({u not equal 0}). Under the condition that f = H nu for some function nu with bounded second order spatial derivatives and bounded first order time derivative, we establish the same regularity for the solution u. Both the regularity and the assumptions are optimal. Using this result and assuming that f is Dini continuous, we prove that the free boundary is, near so called low energy points, a C-1 graph. Our result completes the theory for this type of problems for the heat operator.

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