Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: the Infinite Horizon Case

We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period.

Periodic Table of Elements

An essential tool for chemistry students. Presentation of the table in which elements are assigned a symbol and shows the atomic number of each element.

Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts

En este documento está desarrollado un modelo de mercado financiero basado en movimientos aleatorios con tiempo continuo, con velocidades constantes alternantes y saltos cuando hay cambios en la velocidad. Si los saltos en la dirección tienen correspondencia con la dirección de la velocidad del comportamiento aleatorio subyacente, con respecto a la tasa de interés, el modelo no presenta arbitraje y es completo. Se construye en detalle las estrategias replicables para opciones, y se obtiene una presentación cerrada para el precio de las opciones. Las estrategias de cubrimiento quantile para opciones son construidas. Esta metodología es aplicada al control de riesgo y fijación de precios de instrumentos de seguros.

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: umbrella motion in NH3

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH3 it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described

Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

Analysis and Simulation of Transverse Random Fracture of Long Fibre Reinforced Composites

La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits. El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen. Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents. Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. II: Changing ENSO regimes

Integrations of a fully-coupled climate model with and without flux adjustments in the equatorial oceans are performed under 2×CO2 conditions to explore in more detail the impact of increased greenhouse gas forcing on the monsoon-ENSO system. When flux adjustments are used to correct some systematic model biases, ENSO behaviour in the modelled future climate features distinct irregular and periodic (biennial) regimes. Comparison with the observed record yields some consistency with ENSO modes primarily based on air-sea interaction and those dependent on basinwide ocean wave dynamics. Simple theory is also used to draw analogies between the regimes and irregular (stochastically forced) and self-excited oscillations respectively. Periodic behaviour is also found in the Asian-Australian monsoon system, part of an overall biennial tendency of the model under these conditions related to strong monsoon forcing and increased coupling between the Indian and Pacific Oceans. The tropospheric biennial oscillation (TBO) thus serves as a useful descriptor for the coupled monsoon-ENSO system in this case. The presence of obvious regime changes in the monsoon-ENSO system on interdecadal timescales, when using flux adjustments, suggests there may be greater uncertainty in projections of future climate, although further modelling studies are required to confirm the realism and cause of such changes.

U.K. HiGEM: The New U.K. High-Resolution Global Environment Model—Model Description and Basic Evaluation

This article describes the development and evaluation of the U.K.’s new High-Resolution Global Environmental Model (HiGEM), which is based on the latest climate configuration of the Met Office Unified Model, known as the Hadley Centre Global Environmental Model, version 1 (HadGEM1). In HiGEM, the horizontal resolution has been increased to 0.83° latitude × 1.25° longitude for the atmosphere, and 1/3° × 1/3° globally for the ocean. Multidecadal integrations of HiGEM, and the lower-resolution HadGEM, are used to explore the impact of resolution on the fidelity of climate simulations. Generally, SST errors are reduced in HiGEM. Cold SST errors associated with the path of the North Atlantic drift improve, and warm SST errors are reduced in upwelling stratocumulus regions where the simulation of low-level cloud is better at higher resolution. The ocean model in HiGEM allows ocean eddies to be partially resolved, which dramatically improves the representation of sea surface height variability. In the Southern Ocean, most of the heat transports in HiGEM is achieved by resolved eddy motions, which replaces the parameterized eddy heat transport in the lower-resolution model. HiGEM is also able to more realistically simulate small-scale features in the wind stress curl around islands and oceanic SST fronts, which may have implications for oceanic upwelling and ocean biology. Higher resolution in both the atmosphere and the ocean allows coupling to occur on small spatial scales. In particular, the small-scale interaction recently seen in satellite imagery between the atmosphere and tropical instability waves in the tropical Pacific Ocean is realistically captured in HiGEM. Tropical instability waves play a role in improving the simulation of the mean state of the tropical Pacific, which has important implications for climate variability. In particular, all aspects of the simulation of ENSO (spatial patterns, the time scales at which ENSO occurs, and global teleconnections) are much improved in HiGEM.

Periodic Reordering

For many networks in nature, science and technology, it is possible to order the nodes so that most links are short-range, connecting near-neighbours, and relatively few long-range links, or shortcuts, are present. Given a network as a set of observed links (interactions), the task of finding an ordering of the nodes that reveals such a range-dependent structure is closely related to some sparse matrix reordering problems arising in scientific computation. The spectral, or Fiedler vector, approach for sparse matrix reordering has successfully been applied to biological data sets, revealing useful structures and subpatterns. In this work we argue that a periodic analogue of the standard reordering task is also highly relevant. Here, rather than encouraging nonzeros only to lie close to the diagonal of a suitably ordered adjacency matrix, we also allow them to inhabit the off-diagonal corners. Indeed, for the classic small-world model of Watts & Strogatz (1998, Collective dynamics of ‘small-world’ networks. Nature, 393, 440–442) this type of periodic structure is inherent. We therefore devise and test a new spectral algorithm for periodic reordering. By generalizing the range-dependent random graph class of Grindrod (2002, Range-dependent random graphs and their application to modeling large small-world proteome datasets. Phys. Rev. E, 66, 066702-1–066702-7) to the periodic case, we can also construct a computable likelihood ratio that suggests whether a given network is inherently linear or periodic. Tests on synthetic data show that the new algorithm can detect periodic structure, even in the presence of noise. Further experiments on real biological data sets then show that some networks are better regarded as periodic than linear. Hence, we find both qualitative (reordered networks plots) and quantitative (likelihood ratios) evidence of periodicity in biological networks.

Abrupt climate change: ice sheets and oceans in action

Large temperature variations on land, in the air, and at the ocean surface, and highly variable flux of ice-rafted debris (IRD) delivered to the North Atlantic Ocean show that rapid climate fluctuations took place during the last glacial period. These quasi-periodic, high-amplitude climate variations followed a sequence of events recognized as a rapid warming, followed by a phase of gradual cooling, and terminating with more rapid cooling and increased flux of IRD to the north Atlantic Ocean. Each cycle lasted ˜1500 years, and was followed by an almost identical sequence. These cycles are referred to as Dansgaard/Oechger cycles (D/O cycles), and approximately every fourth cycle culminated in a more pronounced cooling with a massive discharge of IRD into the north Atlantic Ocean over an interval of ˜500 years. These massive discharges of IRD are known as Heinrich layers. “Heinrich events” are thus characterized as a rapid transfer of IRD from a “source,” the bed of the Laurentide Ice Sheet (LIS), to a “sink,” the North Atlantic.

A bow-form burrow and its sedimentological and palaeoecological significance

A deep-tier, bow-form burrow with a long apertural neck, and several different types of infill is described from Upper Jurassic shelfal carbonates of Saudi Arabia, Miocene pelagic packstones and wackestones of Malta, and Lower Cretaceous shoreface sands and mudrocks of southern England. The two most commonly observed types of infill are a coarse-grained infill, referred to as Glyphichnus-mode (formed by sediment entering the burrow following breakage of the apertural neck), and a laminated, muddy infill, referred to as Cylindrichnus-mode, which is considered to represent passive, drought filling through a complete burrow. The type of infill and aspects of preservation show that these burrows can be used to assess the style of sedimentation, particularly steady aggradation versus periodic erosion. At present the bow-form burrow is not assigned to a specific ichnotaxon.

The application of ichnofabrics towards bridging the dichotomy between siliciclastic and carbonate shelf facies: examples from the Upper Jurassic Fulmar Formation (UK) and the Jubaila Formation (Saudi Arabia)

An initial study of the ichnofabrics of the Upper Jurassic (Kimmeridgian) Jubaila Formation of Saudi Arabia shows that the ichnofabrics are closely matched to the relatively well-described ichnofabrics of the contemporary Fulmar Formation of the UK Continental Shelf (North Sea), in respect of the lower shoreface/offshore transition facies to offshore facies. The ichnology and ichnofabrics of the Lower Jubaila Formation show that deposition took place on an open-marine platform on the Arabian craton subject to periodic storm activity, but under a persisting equilibrium between sediment accumulation and subsidence. This is consistent with the moderately deep-marine foraminiferal assemblages and the presence of calcareous nannofossils. Cyclicity is absent, though storm beds may be grouped, in contrast with the genetic sequences present in the rift and halokinetic scenario of the North Sea. In contrast with the siliciclastic setting hardgrotinds (with Gastrochaenolites), more common firmground omission surfaces, and micritic mudstones with Chondrites and Zoophycos are notable features of the carbonate facies. In siliciclastic successions (parasequences) the latter ichnotaxa are generally regarded as having been deposited in rather deeper water, but in the carbonate Jubaila Formation are interpreted as being associated with local areas of lower turbulence. Likewise, the hardgrounds and firmgrounds, which have not been traced laterally, are tentatively regarded to be of local significance.

Modelling monsoons: understanding and predicting current and future behaviour

The global monsoon system is so varied and complex that understanding and predicting its diverse behaviour remains a challenge that will occupy modellers for many years to come. Despite the difficult task ahead, an improved monsoon modelling capability has been realized through the inclusion of more detailed physics of the climate system and higher resolution in our numerical models. Perhaps the most crucial improvement to date has been the development of coupled ocean-atmosphere models. From subseasonal to interdecadal time scales, only through the inclusion of air-sea interaction can the proper phasing and teleconnections of convection be attained with respect to sea surface temperature variations. Even then, the response to slow variations in remote forcings (e.g., El Niño—Southern Oscillation) does not result in a robust solution, as there are a host of competing modes of variability that must be represented, including those that appear to be chaotic. Understanding the links between monsoons and land surface processes is not as mature as that explored regarding air-sea interactions. A land surface forcing signal appears to dominate the onset of wet season rainfall over the North American monsoon region, though the relative role of ocean versus land forcing remains a topic of investigation in all the monsoon systems. Also, improved forecasts have been made during periods in which additional sounding observations are available for data assimilation. Thus, there is untapped predictability that can only be attained through the development of a more comprehensive observing system for all monsoon regions. Additionally, improved parameterizations - for example, of convection, cloud, radiation, and boundary layer schemes as well as land surface processes - are essential to realize the full potential of monsoon predictability. A more comprehensive assessment is needed of the impact of black carbon aerosols, which may modulate that of other anthropogenic greenhouse gases. Dynamical considerations require ever increased horizontal resolution (probably to 0.5 degree or higher) in order to resolve many monsoon features including, but not limited to, the Mei-Yu/Baiu sudden onset and withdrawal, low-level jet orientation and variability, and orographic forced rainfall. Under anthropogenic climate change many competing factors complicate making robust projections of monsoon changes. Absent aerosol effects, increased land-sea temperature contrast suggests strengthened monsoon circulation due to climate change. However, increased aerosol emissions will reflect more solar radiation back to space, which may temper or even reduce the strength of monsoon circulations compared to the present day. Precipitation may behave independently from the circulation under warming conditions in which an increased atmospheric moisture loading, based purely on thermodynamic considerations, could result in increased monsoon rainfall under climate change. The challenge to improve model parameterizations and include more complex processes and feedbacks pushes computing resources to their limit, thus requiring continuous upgrades of computational infrastructure to ensure progress in understanding and predicting current and future behaviour of monsoons.

Ground deformation at Soufriere Hills Volcano, Montserrat during 1998-2000 measured by radar interferometry and GPS

We examine the motion of the ground surface on the Soufriere Hills Volcano, Montserrat between 1998 and 2000 using radar interferometry (InSAR). To minimise the effects of variable atmospheric water vapour on the InSAR measurements we use independently-derived measurements of the radar path delay from six continuous GPS receivers. The surfaces providing a measurable inter-ferometric signal are those on pyroclastic flow deposits, mainly emplaced in 1997. Three types of surface motion can be discriminated. Firstly, the surfaces of thick, valley-filling deposits subsided at rates of 150-120 mm/year in the year after emplacement to 50-30 mm/year two years later. This must be due to contraction and settling effects during cooling. The second type is the near-field motion localised within about one kilometre of the dome. Both subsidence and uplift events are seen and though the former could be due to surface gravitational effects, the latter may reflect shallow (< 1 km) pressurisation effects within the conduit/dome. Far-field motions of the surface away from the deeply buried valleys are interpreted as crustal strains. Because the flux of magma to the surface stopped from March 1998 to November 1999 and then resumed from November 1999 through 2000, we use InSAR data from these two periods to test the crustal strain behaviour of three models of magma supply: open, depleting and unbalanced. The InSAR observations of strain gradients of 75-80 mm/year/krn uplift during the period of quiescence on the western side of the volcano are consistent with an unbalanced model in which magma supply into a crustal magma chamber continues during quiescence, raising chamber pressure that is then released upon resumption of effusion. GPS motion vectors agree qualitatively with the InSAR displacements but are of smaller magnitude. The discrepancy may be due to inaccurate compensation for atmospheric delays in the InSAR data. (c) 2005 Elsevier B.V. All rights reserved.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.