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.

Solving the Vehicle Routing Problem with Genetic ALgorithm and Simulated Annealing

This Thesis Work will concentrate on a very interesting problem, the Vehicle Routing Problem (VRP). In this problem, customers or cities have to be visited and packages have to be transported to each of them, starting from a basis point on the map. The goal is to solve the transportation problem, to be able to deliver the packages-on time for the customers,-enough package for each Customer,-using the available resources- and – of course - to be so effective as it is possible.Although this problem seems to be very easy to solve with a small number of cities or customers, it is not. In this problem the algorithm have to face with several constraints, for example opening hours, package delivery times, truck capacities, etc. This makes this problem a so called Multi Constraint Optimization Problem (MCOP). What’s more, this problem is intractable with current amount of computational power which is available for most of us. As the number of customers grow, the calculations to be done grows exponential fast, because all constraints have to be solved for each customers and it should not be forgotten that the goal is to find a solution, what is best enough, before the time for the calculation is up. This problem is introduced in the first chapter: form its basics, the Traveling Salesman Problem, using some theoretical and mathematical background it is shown, why is it so hard to optimize this problem, and although it is so hard, and there is no best algorithm known for huge number of customers, why is it a worth to deal with it. Just think about a huge transportation company with ten thousands of trucks, millions of customers: how much money could be saved if we would know the optimal path for all our packages.Although there is no best algorithm is known for this kind of optimization problems, we are trying to give an acceptable solution for it in the second and third chapter, where two algorithms are described: the Genetic Algorithm and the Simulated Annealing. Both of them are based on obtaining the processes of nature and material science. These algorithms will hardly ever be able to find the best solution for the problem, but they are able to give a very good solution in special cases within acceptable calculation time.In these chapters (2nd and 3rd) the Genetic Algorithm and Simulated Annealing is described in details, from their basis in the “real world” through their terminology and finally the basic implementation of them. The work will put a stress on the limits of these algorithms, their advantages and disadvantages, and also the comparison of them to each other.Finally, after all of these theories are shown, a simulation will be executed on an artificial environment of the VRP, with both Simulated Annealing and Genetic Algorithm. They will both solve the same problem in the same environment and are going to be compared to each other. The environment and the implementation are also described here, so as the test results obtained.Finally the possible improvements of these algorithms are discussed, and the work will try to answer the “big” question, “Which algorithm is better?”, if this question even exists.

Alternativa förpackningsmaterial och konstruktioner för »Hackman tools«-serien

Choosing a new plastic material for a container includes several different steps. In this case,the Finnish company Hackman needed a new type of packaging material for theircutlery- and kitchentool series »Hackman tools«. The project was carried out in cooperationwith the design agency Ytterborn & Fuentes, which has Hackman as a client.Several different demands were put on the material in order to fulfill as many of the clientswishes as possible. The most urgent problem with the existing container was the difficultysfor the customer to clearly see the contents in the container. Because of this problemthe customer tried to open the container in the shop. To avoid this from happening,Hackman wanted a more transparent plastic material that still fulfilled all other necessaryproperties such as strength, viscosity, printability, sealability and exhaustion strength.The final result and recommendation of a polypropylen-plastic (Evacast) was based ondetailed studies of packaging plastics and their properties as well as discussions with plasticconvertersand suppliers. The recommended plastic is avaliable in several different modelsthat fulfill all demands on material properties, environmental aspects, cost aspects and transparency.Apart from the material problem the project also included drafting some sketches and ideason new construction solutions for the container. The construction of the exsisting containerwas also a problem because of its complexity. As a result of the change of material it has beenpossible to simplify the construction.

Spanning Tree Approach On The Snow Cleaning Problem

Snow cleaning is one of the important tasks in the winter time in Sweden. Every year government spends huge amount money for snow cleaning purpose. In this thesis we generate a shortest road network of the city and put the depots in different place of the city for snow cleaning. We generate shortest road network using minimum spanning tree algorithm and find the depots position using greedy heuristic. When snow is falling, vehicles start work from the depots and clean the snow all the road network of the city. We generate two types of model. Models are economic model and efficient model. Economic model provide good economical solution of the problem and it use less number of vehicles. Efficient model generate good efficient solution and it take less amount of time to clean the entire road network.

Use Multilevel Graph Partitioning Scheme to solve traveling salesman problem

The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.