Coherent states of a particle in a magnetic field and the Stieltjes moment problem

A solution to a version of the Stieltjes moment. problem is presented. Using this solution, we construct a family of coherent states of a charged particle in a uniform magnetic field. We prove that these states form an overcomplete set that is normalized and resolves the unity. By the help of these coherent states we construct the Fock-Bergmann representation related to the particle quantization. This quantization procedure takes into account a circle topology of the classical motion. (C) 2009 Elsevier B.V. All rights reserved.

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.

Approximation algorithms and hardness results for the clique packing problem

For a fixed family F of graphs, an F-packing in a graph G is a set of pairwise vertex-disjoint subgraphs of G, each isomorphic to an element of F. Finding an F-packing that maximizes the number of covered edges is a natural generalization of the maximum matching problem, which is just F = {K(2)}. In this paper we provide new approximation algorithms and hardness results for the K(r)-packing problem where K(r) = {K(2), K(3,) . . . , K(r)}. We show that already for r = 3 the K(r)-packing problem is APX-complete, and, in fact, we show that it remains so even for graphs with maximum degree 4. On the positive side, we give an approximation algorithm with approximation ratio at most 2 for every fixed r. For r = 3, 4, 5 we obtain better approximations. For r = 3 we obtain a simple 3/2-approximation, achieving a known ratio that follows from a more involved algorithm of Halldorsson. For r = 4, we obtain a (3/2 + epsilon)-approximation, and for r = 5 we obtain a (25/14 + epsilon)-approximation. (C) 2008 Elsevier B.V. All rights reserved.

Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

A Bayesian Semiparametric Approach for Solving the Discrete Calibration Problem

In this article, we introduce a semi-parametric Bayesian approach based on Dirichlet process priors for the discrete calibration problem in binomial regression models. An interesting topic is the dosimetry problem related to the dose-response model. A hierarchical formulation is provided so that a Markov chain Monte Carlo approach is developed. The methodology is applied to simulated and real data.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

An eigenvalue problem for the biharmonic operator on Z(2)-symmetric regions

In this work we show that the eigenvalues of the Dirichlet problem for the biharmonic operator are generically simple in the set Of Z(2)-symmetric regions of R-n, n >= 2, with a suitable topology. To accomplish this, we combine Baire`s lemma, a generalised version of the transversality theorem, due to Henry [Perturbation of the boundary in boundary value problems of PDEs, London Mathematical Society Lecture Note Series 318 (Cambridge University Press, 2005)], and the method of rapidly oscillating functions developed in [A. L. Pereira and M. C. Pereira, Mat. Contemp. 27 (2004) 225-241].

Bjorling problem for timelike surfaces in the Lorentz-Minkowski space

We solve the Bjorling problem for timelike surfaces in the Lorentz-Minkowski space through a split-complex representation formula obtained for this kind of surface. Our approach uses the split-complex numbers and natural split-holomorphic extensions. As applications, we show that the minimal timelike surfaces of revolution as well as minimal ruled timelike surfaces can be characterized as solutions of certain adequate Bjorling problems in the Lorentz-Minkowski space. (C) 2010 Elsevier Inc. All rights reserved.

Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

New classes of spatial central configurations for the n+3-body problem

In this paper, we show the existence of new families of spatial central configurations for the n + 3-body problem, n >= 3. We study spatial central configurations where n bodies are at the vertices of a regular n-gon T and the other three bodies are symmetrically located on the straight line that is perpendicular to the plane that contains T and passes through the center of T. The results have simple and analytic proofs. (c) 2010 Elsevier Ltd. All rights reserved.

Stacked central configurations for the spatial six-body problem

In this paper we show the existence of three new families of stacked spatial central configurations for the six-body problem with the following properties: four bodies are at the vertices of a regular tetrahedron and the other two bodies are on a line connecting one vertex of the tetrahedron with the center of the opposite face. (c) 2009 Elsevier B.V. All rights reserved.

Genus i historieundervisningen : Problem och möjligheter ur ett gymnasielärarperspektiv

Syftet med den här uppsatsen har varit, dels att undersöka ett antal historielärares förståelse av och attityd till användandet av begreppet genus i historieundervisningen på gymnasiet, dels att analysera vad jämställdhetsmålen i gymnasieskolans styrdokument egentligen säger om be-greppet genus och om detta bör tolkas som ett direktiv att implementera genus i historieun-dervisningen. Undersökningen genomfördes i två steg. Gymnasieskolans styrdokument; skollagen, lä-roplanen för de frivilliga skolformerna samt ämnesbeskrivning och kursplaner för historia A, B och C, närlästes och analyserades utifrån en genusteoretisk grund. Därefter intervjuades sex utvalda gymnasielärare i historia kring begreppet genus i teori och praktik. Resultatet analyse-rades och kategoriserades därefter så att lärarnas genusmedvetenhet och attityd till användan-de av genus i historieundervisningen gick att identifiera.Styrdokumentsgranskningen visade att styrdokumenten idag inte säger någonting expli-cit om användandet av ett genusperspektiv i historieundervisningen men att skollagens och läroplanens jämställdhetsdirektiv vilar på en genusteoretisk grund och därmed indirekt kräver ett genusperspektiv i den konkreta undervisningen. Dokumentens formuleringar kräver en god kunskap kring begreppen jämställdhet och genus för att kunna förstås. Utan den kunskapen riskerar avsaknaden av ett explicit uttalat genusbegrepp att legitimera en historieundervisning utan genusperspektiv.Intervjuresultatet visade att genusmedvetenheten bland de utvalda lärarna var låg och att förekomsten av ett genusperspektiv i den egna undervisningen avgjordes av lärarens eget in-tresse för frågan. Attityden till användandet av ett genusperspektiv i historieundervisningen på gymnasiet kunde hos de flesta tolkas som positiv i teorin men i praktiken omgärdad av en rad förhindrande omständigheter såsom omedvetenhet, tids- och utrymmesbrist, metodbrist och historiedidaktiskt förhållningssätt.

Amning : Duration, problem och skäl till att sluta : En retrospektiv studie av mammors erfarenheter

Syftet med uppsatsen var att relatera amningstidens längd till amningsproblem och kvinnors upplevelse av sin amning samt att kartlägga orsaker till delvis amning och upphörande av amning. Studiens design var en deskriptiv, retrospektiv korrelationsstudie med kvantitativ ansats. Materialet till studien hämtades från redan utförda intervjuer. Populationen bestod av 250 kvinnor i åldrarna 19-46 år varav 103 var förstföderskor och 147 omföderskor.Resultatet av studien har visat att tiden för enbart amning och den totala amningstidens längd varierade. De kvinnor som var positiva till amningen hade en längre amningsperiod än de kvinnor som var negativa till amningen. Anledningarna till att kvinnorna upphörde med den exklusiva amningen var främst medveten tillvänjning till annan kost än bröstmjölk. Det näst vanligaste skälet var enligt rekommendation från BVC att börja ge smakportioner, och det näst, näst vanligaste skälet var relaterat till barnet, nämligen hungrigt barn. Skälen till att avsluta amningen var jämnt fördelade mellan mor- och barn-relaterade orsaker. Bland barn-relaterade orsaker var barnets ointresse för bröstet det klart dominerande skälet till avslutad amning och bland mammorna en medveten avvänjning. Under BB-tiden var det varannan mamma som led av problem med amningen. Det vanligaste problemet var fel sugteknik hos barnet och det näst vanligaste problemet var såriga bröstvårtor. Under barnets första vecka efter hemgång var det såriga bröstvårtor som var det största problemet. Under BVC-tiden var det mjölkstockning som var det vanligast förekommande problemet tätt följt av såriga bröstvårtor. Majoriteten av mödrarna hade upplevt sin amning som positiv, en mysig och värdefull tid. Men många hade även negativa upplevelser såsom känsla av bundenhet och stress.