On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

Smart histogram analysis applied to the skull-stripping problem in T1-weighted MRI

In this paper we address the "skull-stripping" problem in 3D MR images. We propose a new method that employs an efficient and unique histogram analysis. A fundamental component of this analysis is an algorithm for partitioning a histogram based on the position of the maximum deviation from a Gaussian fit. In our experiments we use a comprehensive image database, including both synthetic and real MRI. and compare our method with other two well-known methods, namely BSE and BET. For all datasets we achieved superior results. Our method is also highly independent of parameter tuning and very robust across considerable variations of noise ratio.

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

A knapsack problem as a tool to solve the production planning problem in small foundries

According to recent research carried out in the foundry sector, one of the most important concerns of the industries is to improve their production planning. A foundry production plan involves two dependent stages: (1) determining the alloys to be merged and (2) determining the lots that will be produced. The purpose of this study is to draw up plans of minimum production cost for the lot-sizing problem for small foundries. As suggested in the literature, the proposed heuristic addresses the problem stages in a hierarchical way. Firstly, the alloys are determined and, subsequently, the items that are produced from them. In this study, a knapsack problem as a tool to determine the items to be produced from furnace loading was proposed. Moreover, we proposed a genetic algorithm to explore some possible sets of alloys and to determine the production planning for a small foundry. Our method attempts to overcome the difficulties in finding good production planning presented by the method proposed in the literature. The computational experiments show that the proposed methods presented better results than the literature. Furthermore, the proposed methods do not need commercial software, which is favorable for small foundries. (C) 2010 Elsevier Ltd. All rights reserved.

Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.

Molecular chemistry and the missing mass problem in planetary nebulae

Context. Detections of molecular lines, mainly from H-2 and CO, reveal molecular material in planetary nebulae. Observations of a variety of molecules suggest that the molecular composition in these objects differs from that found in interstellar clouds or in circumstellar envelopes. The success of the models, which are mostly devoted to explain molecular densities in specific planetary nebulae, is still partial however. Aims. The present study aims at identifying the influence of stellar and nebular properties on the molecular composition of planetary nebulae by means of chemical models. A comparison of theoretical results with those derived from the observations may provide clues to the conditions that favor the presence of a particular molecule. Methods. A self-consistent photoionization numerical code was adapted to simulate cold molecular regions beyond the ionized zone. The code was used to obtain a grid of models and the resulting column densities are compared with those inferred from observations. Results. Our models show that the inclusion of an incident flux of X-rays is required to explain the molecular composition derived for planetary nebulae. We also obtain a more accurate relation for the N(CO)/N(H-2) ratio in these objects. Molecular masses obtained by previous works in the literature were then recalculated, showing that these masses can be underestimated by up to three orders of magnitude. We conclude that the problem of the missing mass in planetary nebulae can be solved by a more accurate calculation of the molecular mass.

Trans-Planckian problem in the healthy extension of Horava-Lifshitz gravity

Planck scale physics may influence the evolution of cosmological fluctuations in the early stages of cosmological evolution. Because of the quasiexponential redshifting, which occurs during an inflationary period, the physical wavelengths of comoving scales that correspond to the present large-scale structure of the Universe were smaller than the Planck length in the early stages of the inflationary period. This trans-Planckian effect was studied before using toy models. The Horava-Lifshitz (HL) theory offers the chance to study this problem in a candidate UV complete theory of gravity. In this paper we study the evolution of cosmological perturbations according to HL gravity assuming that matter gives rise to an inflationary background. As is usually done in inflationary cosmology, we assume that the fluctuations originate in their minimum energy state. In the trans-Planckian region the fluctuations obey a nonlinear dispersion relation of Corley-Jacobson type. In the "healthy extension" of HL gravity there is an extra degree of freedom which plays an important role in the UV region but decouples in the IR, and which influences the cosmological perturbations. We find that in spite of these important changes compared to the usual description, the overall scale invariance of the power spectrum of cosmological perturbations is recovered. However, we obtain oscillations in the spectrum as a function of wave number with a relative amplitude of order unity and with an effective frequency which scales nonlinearly with wave number. Taking the usual inflationary parameters we find that the frequency of the oscillations is so large as to render the effect difficult to observe.

The cutting stock problem in the wood industry

This thesis proposes a solution for board cutting in the wood industry with the aim of usage minimization and machine productivity. The problem is dealt with as a Two-Dimensional Cutting Stock Problem and specific Combinatorial Optimization methods are used to solve it considering the features of the real problem.

On the flavor problem in strongly coupled theories

rnThis thesis is on the flavor problem of Randall Sundrum modelsrnand their strongly coupled dual theories. These models are particularly wellrnmotivated extensions of the Standard Model, because they simultaneously address rntherngauge hierarchy problem and the hierarchies in the quarkrnmasses and mixings. In order to put this into context, special attention is given to concepts underlying therntheories which can explain the hierarchy problem and the flavor structure of the Standard Model (SM). ThernAdS/CFTrnduality is introduced and its implications for the Randall Sundrum model withrnfermions in the bulk andrngeneral bulk gauge groups is investigated. It will be shown that the differentrnterms in the general 5D propagator of a bulk gauge field can be related tornthe corresponding diagrams of the strongly coupled dual, which allows for arndeeperrnunderstanding of the origin of flavor changing neutral currents generated by thernexchange of the Kaluza Klein excitations of these bulk fields.rnIn the numerical analysis, different observables which are sensitive torncorrections from therntree-levelrnexchange of these resonances will be presented on the basis of updatedrnexperimental data from the Tevatron and LHC experiments. This includesrnelectroweak precision observables, namely corrections to the S and Trnparameters followed by corrections to the Zbb vertex, flavor changingrnobservables with flavor changes at one vertex, viz. BR (Bd -> mu+mu-) and BR (Bs -> mu+mu-), and two vertices,rn viz. S_psiphi and |eps_K|, as well as bounds from direct detectionrnexperiments. rnThe analysis will show that all of these bounds can be brought in agreement withrna new physics scale Lambda_NP in the TeV range, except for the CPrnviolating quantity |eps_K|, which requires Lambda_NP= Ord(10) TeVrnin the absencernof fine-tuning. The numerous modifications of the Randall Sundrum modelrnin the literature, which try to attenuate this bound are reviewed andrncategorized.rnrnSubsequently, a novel solution to this flavor problem, based on an extendedrncolor gauge group in the bulk and its thorough implementation inrnthe RS model, will be presented, as well as an analysis of the observablesrnmentioned above in the extended model. This solution is especially motivatedrnfromrnthe point of view of the strongly coupled dual theory and the implications forrnstrongly coupled models of new physics, which do not possess a holographic dual,rnare examined.rnFinally, the top quark plays a special role in models with a geometric explanation ofrnflavor hierarchies and the predictions in the Randall-Sundrum model with andrnwithout the proposed extension for the forward-backward asymmetryrnA_FB^trnin top pair production are computed.

Methodological issues in quantifying the magnitude of the tuberculosis problem in a prison population

SETTING: Correctional settings and remand prisons. OBJECTIVE: To critically discuss calculations for epidemiological indicators of the tuberculosis (TB) burden in prisons and to provide recommendations to improve study comparability. METHODS: A hypothetical data set illustrates issues in determining incidence and prevalence. The appropriate calculation of the incidence rate is presented and problems arising from cross-sectional surveys are clarifi ed. RESULTS: Cases recognized during the fi rst 3 months should be classifi ed as prevalent at entry and excluded from any incidence rate calculation. The numerator for the incidence rate includes persons detected as having developed TB during a specifi ed period of time subsequent to the initial 3 months. The denominator is persontime at risk from 3 months onward to the end point (TB or end of the observation period). Preferably, entry time, exit time and event time are known for each inmate to determine person-time at risk. Failing that, an approximation consists of the sum of monthly head counts, excluding prevalent cases and those persons no longer at risk from both the numerator and the denominator. CONCLUSIONS: The varying durations of inmate incarceration in prisons pose challenges for quantifying the magnitude of the TB problem in the inmate population. Recommendations are made to measure incidence and prevalence.

Metaheuristics for the Order Batching Problem in Manual Order Picking Systems

In manual order picking systems, order pickers walk or drive through a distribution warehouse in order to collect items which are requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders are combined into (more substantial) picking orders of limited size. The Order Batching Problem considered in this paper deals with the question of how a given set of customer orders should be combined such that the total length of all tours is minimized which are necessary to collect all items. The authors introduce two metaheuristic approaches for the solution of this problem: the first one is based on Iterated Local Search; the second on Ant Colony Optimization. In a series of extensive numerical experiments, the newly developed approaches are benchmarked against classic solution methods. It is demonstrated that the proposed methods are not only superior to existing methods but provide solutions which may allow distribution warehouses to be operated significantly more efficiently.

A Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains

We present a new model formulation for a multi-product lot-sizing problem with product returns and remanufacturing subject to a capacity constraint. The given external demand of the products has to be satisfied by remanufactured or newly produced goods. The objective is to determine a feasible production plan, which minimizes production, holding, and setup costs. As the LP relaxation of a model formulation based on the well-known CLSP leads to very poor lower bounds, we propose a column-generation approach to determine tighter bounds. The lower bound obtained by column generation can be easily transferred into a feasible solution by a truncated branch-and-bound approach using CPLEX. The results of an extensive numerical study show the high solution quality of the proposed solution approach.