Applied Mathematics

Stringent emission regulations combined with customer demands for improved fuel economy and performance have forced the automotive industry to consider more advanced powertrain configurations than standard port-fuel injected gasoline engines. Modern state-of-the-art powertrain systems may combine several power sources (internal combustion engines, electric motors, fuel cells, etc.) and various exhaust aftertreatment devices (catalytic converters, lean NOx traps, particulate filters, etc.) in addition to conventional engine subsystems such as turbochargers and exhaust gas recirculation. The determination of the way in which these systems need to be operated to meet driver's torque demand, performance and fuel economy expectations while satisfying federal emission regulations is a complex and a multiobjective optimal control problem. This paper reviews some of the approaches to this problem in the context of two case studies

Coherent-population-trapping resonances within the degenerate two-level system of the F=2→F'=1 transition of the 87 Rb D1 line were investigated in an uncoated Rb vapor cell by means of level-crossing-type experiments. Tuning over the two-photon resonance is achieved sweeping a magnetic field around zero value. The influence of transverse magnetic fields on the amplitude and the width of the resonances, recorded in fluorescence and absorption, were investigated in the cases of excitation with linear, circular, and elliptical laser light polarization. A theoretical analysis was performed for the case of linearly polarized excitation, the results of which are in good agreement with the experiment.

We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations. A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two non-standard formulations, that numerous FV schemes, including

Conventional skew upwind differencing (SUD) substantially reduces numerical diffusion but produces oscillations for convection-dominated jlows. The present study describes a modified skew upwind weighted differencing (SUWD) scheme which produces less numerical diffusion and oscillations than SUD. The convected quantity at a cell face is approximated by a weighted average of two quantities. These two quantities are obtained by using linear interpolation at two successive locations upstream of the resultant velocity vector at the cell face. Three laminar flow test cases are used to evaluate the scheme. Comparison of the results obtained by SUD and SUWD schemes are presented.

A common observation is that large groups of oscillatory biological units often have the ability to synchronize. A paradigmatic model of such behavior is provided by the Kuramoto model, which achieves synchronization through coupling of the phase dynamics of individual oscillators, while each oscillator maintains a different constant inherent natural frequency. Here we consider the biologically likely possibility that the oscillatory units may be capable of enhancing their synchronization ability by adaptive frequency dynamics. We propose a simple augmentation of the Kuramoto model which does this. We also show that, by the use of a previously developed technique [Ott and Antonsen, Chaos 18, 037113 (2008)], it is possible to reduce the resulting dynamics to a lower dimensional system for the macroscopic evolution of the oscillator ensemble. By employing this reduction, we investigate the dynamics of our system, finding a characteristic hysteretic behavior and enhancement of the qual...

The goal of this paper is the development of control algorithms for the management of an automated warehouse system. As usual, the implementation of a control algorithm requires three preliminary steps: development of a reliable model; design of control procedures according to some optimality criteria; validation of these control procedures. As for modelling, a new level in the control architecture, namely an optimizer system, is introduced which performs real-time optimization thus simplifying the low-level control and improving the overall performance. In this context, the role of a detailed model of the whole warehouse is discussed and such a model is built up by using the colored timed Petri nets framework. As for control, we propose two control algorithms, derived under the simplifying continuity assumption of the rack locations, to optimize the operations of the cranes (moving within the aisles of the warehouse) and the operations of the shuttle (moving on a straight line placed between the aisles and the picking/refilling area), respectively. To evaluate the performance of the proposed control algorithms we define three different cost indices. As for the validation, extensive simulations are performed on the model in order to prove the effectiveness of the proposed control algorithms. A further validation of the algorithms has been performed on a test bed in order to take into account communication delays and computation times. Finally, the proposed architecture and control algorithms have been applied to a real plant. r

In the present work, experimental and numerical studies for the hydrodynamics in a gassolid tapered fluidized bed have been carried out. The experimental results obtained by carrying out experiments in a tapered fluidized bed for glass bead (spherical) of 2.0 mm and dolomite (non-spherical particles) of 2.215 mm in diameter, were compared with the computational fluid dynamics (CFD) simulation results, using a commercial CFD software package, Fluent. The gas-solid flow was simulated using the Eulerian-Eulerian model and applying the kinetic theory of granular flow for solid particles. The Gidaspow drag model was used to calculate the gas-solid momentum exchange coefficients. Pressure drops predicted by the CFD simulations agreed reasonably well with experimental measurements for both types (spherical and non-spherical) of particles. Good agreement was also obtained between experimental and CFD predicted bed expansion ratios for both types of particles. Present study provides a useful basis for further works on the CFD of tapered fluidized bed.

We use a dynamical systems approach to model the origin of bargaining conventions and report the results of a symmetric bargaining game experiment. Our experiment also provides evidence on the psychological salience of symmetry and efficiency. The observed behavior in the experiment was systematic, replicable, and roughly consistent with the dynamical systems approach. For instance, we do observe unequal-division conventions emerging in colmnunities of sylnmetricaily endowed subjects.

The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one sense or another are made up of infinitely many line segments, with specific attention to the "infinite staircase" and to the Koch snowflake, for both of which we develop explicit formulas for the mapping function and explain how one can use standard mathematical software to generate corresponding graphics. We also discuss a number of open questions suggested by these considerations, some of which are related to differentials on hyperelliptic surfaces of infinite genus.

This paper investigates which events of World War II (WWII) the US investors (at that time) considered as turning points (structural breaks) of the war. The empirical study employs daily Dow Jones industrial average stock index and volatility from January 1939 to December 1945 and applies structural shift oriented test to determine endogenously the structural breaks during the WWII period. Results show that the majority of the wartime events (on and off the battlefield) labelled important by historians did result in structural breaks in both price movement and stock returns volatility (risk). These results have major implications for investors of the present and future. 1 Tsiakas is able to show that events during trading and non-trading hours both have substantial effect on both stock price and volatility. During wartime, events can take place during trading and non-trading hours. 2 According to Mazouz et al. (2009) investors under-react to both positive and negative shocks, irrespective of the magnitude of the shocks.

We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method. We prove strong convergence theorem under some parameters. The results in this paper unify and generalize some well-known results in the literature.

We develop simple models that can be used to predict the forces of impact that occur during the injection molding process involving a magnesium alloy. We model the impact of the injection molding screw tip on the molten material entering the mold, and the impact of the piston flange on the machine housing, which can occur when the amount of material that has been injected into the mold is insufficient to completely fill the mold. We consider the effects due to the elasticity of the molten material and machine parts, those due to the presence of a thin film of hydraulic fluid between the piston flange and machine housing, the variation of the viscosity of the hydraulic fluid, and those due to the leakage of molten metal past the screw tip.

Coincidence, Chaos and All That Math Jazz presents selected mathematical concepts in an appealing, non-intimidating and amusing manner. Its aim is not mathematical entertainment, but rather to show math at its counter-intuitive best and to vanquish math anxiety. It addresses the ubiquity of mathematics in our everyday world-a subject much talked about, and recently discussed in Turin in an aptly-named and well-attended lecture by Alberto Conte, "The Explosion of Mathematics." Mathematics is present where we expect it and can see itcryptology, computer technology, in art and architecture-and where we don't expect it and can't see it: in the advanced technology of cell phones, in traffic control, in genetics. Mathematicians are delighted, and justly so, by the attention given to mathematics and mathematicians in the popular media, reflecting the "sex appeal" of mathematics as presented in movies such as "Good Will Hunting" and "A Beautiful Mind" and in books such as The Da Vinci Code. Coincidence, Chaos and All That Math Jazz is similar in concept to Math and the Mona Lisa, reviewed in vol.

Unto Others (UO) is an important book for all with a genuine interest in evolutionary biology, and right on target for everyone interested in human behavior. It is also of great relevance for those interested in the effects of the global human population increase, and the interaction of population and environment, aspects which will be emphasized in this review. UO is a truly interdisciplinary exploration of the paradox of explaining the existence of both the egoistic (i.e., selfish) and the altruistic (unselfish) behaviors and motives. UO draws upon data and arguments from biology, philosophy, psychology, and anthropology.

In this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(1) (1995) 2) for the condition number of a matrix as a function of the determinant, the Frobenius norm and of k singular values. If no singular value is known it is possible to derive an upper bound for the condition number applying lower and upper bounds for the product of a subset of singular values.

In this paper, we review decision support models for the design of global supply chains, and assess the fit between the research literature in this area and the practical issues of global supply chain design. The classification scheme for this review is based on ongoing and emerging issues in global supply chain management and includes review dimensions for (1) decisions addressed in the model, (2) performance metrics, (3) the degree to which the model supports integrated decision processes, and (4) globalization considerations. We conclude that although most models resolve a difficult feature associated with globalization, few models address the practical global supply chain design problem in its entirety. We close the paper with recommendations for future research in global supply chain modeling that is both forward-looking and practically oriented.

This article addresses the question of validating the homogeneous Lanchestrian square law of attrition by the use of historical data (and by extension, other attrition models). Validating an attrition model means testing that model against reality. In this case, Lanchester's square law is tested against the data from the Inchon-Seoul campaign of the Korean War. The data are examined using three analysis techniques: linear regression, the Akaike Information Criterion (AIC), and Bozdogan's Consistent AIC (CAIC). The data do not fit the assumption of a single, constant coefficient, homogeneous square law battle. The data do fit a set of three such battles (a new one every six or seven days); however, the data fit three constantcasualty-model battles just as well. The homogeneous Lanchester square law cannot be regarded as a proven attrition algorithm for warfare; however, the square law cannot be regarded as disproved either. Data on more battles are required to validate the square law or any other proposed attrition law. Q 1995 John Wiley & Sons, Inc.* Attrition is a euphemism for killing, wounding, destroying, or otherwise rendering hors de combat enemy personnel or equipment. Attrition is at the heart of every general discussion of warfare. Regardless of claims of prior or parallel discovery, Lanchester's equations for attrition provided the origin for modeling of attrition in the United States. Attrition models are referred to as extensions of the Lanchester "laws" or as replacements to those equations. Lanchester proposed that attrition could be mathematically modeled and stated his thoughts on the matter. With the advent of computers, models of warfare have become required in the decision process for research, development, and acquisition of weapons systems, for force mix decisions, and often for operational plans development. Decision makers realize that computer model results are factors for consideration rather than final answers; however, the model results still carry considerable weight in the decision processes.

Let ϕ denote Euler's phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n x such that q ∤ ϕ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Extended Riemann Hypothesis, the prime k-tuples conjecture and a conjecture of Ihara about the distribution of these Euler-Kronecker constants cannot be all true.

This paper considers the strategic routing of a fleet of unmanned combat aerial vehicles (UCAVs) to service a set of predetermined targets from a prior surveillance mission. Targets are characterized by their priority or importance level, and minimum and maximum service levels that, respectively, represent the lower bound of munitions for destruction and upper bound of munitions to limit collateral damage. Additional constraints to be respected are the payload capacities of the (possibly heterogeneous) UCAV fleet and the range based on fuel capacity and payload transported. The vital aspect of this paper is the integrated optimal utilization of available resources-weaponry and flight time-while allocating targets to UCAVs and sequencing them to maximize service to targets based on their criticality.

A natural way to model dynamic systems under uncertainty is to use fuzzy initial value problems (FIVPs) and related uncertain systems. In this paper, we express the fuzzy Laplace transform and then some of its well-known properties are investigated. In addition, an existence theorem is given for fuzzy-valued function which possess the fuzzy Laplace transform. Consequently, we investigate the solutions of FIVPs and the solutions in state-space description of fuzzy linear continuous-time systems under generalized H-differentiability as two new applications of fuzzy Laplace transforms. Finally, some examples are given to show the efficiency of the proposed method.

his unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of modern numerical algorithms and scientific computing. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. It covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithms, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, to nonlinear curve-fitting and swarm optimization. Especially suitable for undergraduates and graduates in computational mathematics, numerical algorithms, and scientific computing, it can be used as a textbook and/or reference book.

This paper describes a quantitative methodology for deriving optimal exploration target zones based on a probabilistic mineral prospectivity map. The methodology is demonstrated in the Rodalquilar mineral district in Spain. A subset of known occurrences of mineral deposits of the type sought were considered discovered and then used as training data, and a map of distances to faults/fractures and three band ratio images of hyperspectral data were used as layers of spatial evidence in weights-of-evidence (WofE) modeling of mineral prospectivity in the study area. A derived posterior probability map of mineral deposit occurrence showing non-violation of the conditional independence assumption and having the highest prediction rate was then input to an objective function in simulated annealing in order to derive a set of optimal exploration focal points. Each optimal exploration focal point represents a pixel or location within a circular neighborhood of pixels with high posterior probability of mineral deposit occurrence. Buffering of each optimal exploration focal point, based on proximity analysis, results in optimal exploration target zones, many of which coincide spatially with at least one of the occurrences of mineral deposit of the type sought in the subset of cross-validation (i.e., presumed undiscovered) mineral deposits of the type sought. The results of the study show usefulness of the proposed methodology for objective delineation of optimal exploration target zones based on a probabilistic mineral prospectivity map.

This paper presents a process for the estimation of tire-road forces, vehicle sideslip angle and wheel cornering stiffness. The method uses measurements (yaw rate, longitudinal/lateral accelerations, steering angle and angular wheel velocities) only from sensors which can be integrated or have already been integrated in modern cars. The estimation process is based on two blocks in series: the first block contains a sliding-mode observer whose principal role is to calculate tire-road forces, while in the second block an extended Kalman filter estimates sideslip angle and cornering stiffness. More specifically, this study proposes an adaptive tire-force model that takes variations in road friction into account. The paper also presents a study of convergence for the sliding-mode observer. The estimation process was applied and compared to real experimental data, in particular wheel force measurements. Experimental results show the accuracy and potential of the estimation process.

This paper addresses a highly challenging scheduling problem faced in multi-head beam-type surface mounting devices (SMD) machines. An integrated mathematical model is formulated aiming to balance workloads over multiple heads as well as improving the traveling speed of the robotic arm by incorporating the appropriateness factors in the model to evaluate the compatibility of component-nozzle pairs. The proposed model is a bi-objective mixed integer nonlinear programming one, which is first converted into a linearized model and then directly solved by using the augmented epsilon constraint method for small problem instances. As the model is turned out to be NP-hard, we also develop a Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to solve the model for medium and large-sized problem instances. The parameters of the proposed MOPSO are tuned by using the Taguchi Method and corresponding numerical results are provided. (S.A. Torabi), [email protected] (M. Hamedi), [email protected] (J. Ashayeri).

A new deterministic numerical formulation named DisPar-k based on particle displacement probability distribution for Markov processes was developed to solve advection-diffusion problems in a one-dimensional discrete spatial grid. DisPar-k is an extension of DisPar, and the major difference is the possibility of establishing a number of consecutive particle destination nodes. This was achieved by solving an algebraic linear system where the particle displacement distribution moments are known parameters taken from the Gaussian distribution. The average was evaluated by an analogy between the Fokker-Planck and the transport equations, being the variance Fickian. The particle displacement distribution is used to predict deterministic mass transfers between domain nodes. Mass conservation was guaranteed by the distribution concept. It was shown that, for linear conditions, the accuracy order is proportional to the number of particle destination nodes. DisPar-k showed to be very sensible to physical discontinuities in the transport parameters ͑water depth, dispersion, and velocity͒, showing that this type of problem can only be disguised by introducing numerical dispersion ͑i.e., changing the Fickian variance͒.

Cube attack is strong cryptanalytic technique. In literature, it is applied mainly on Trivium and Grain. However, cube attack can be applied to any symmetric cipher, stream or block if a generic tool is available. In this paper we present a parallel implementation of cube attack using openMP. The tool is tested on 8-core standard machines and 1024 node cluster. Trivium is tested using this tool and the result shows that tool successfully attacks up to 720 round of Trivium on 1024 node cluster with 42 cores used. The tool provides simple interface to incorporate any symmetric cipher and to change heuristic to generate cubes.

In this paper, a synergy of advanced signal processing and soft computing strategies is applied in order to identify different types of human brain tumors, as a help to confirm the histological diagnosis of experts and consequently to facilitate the decision about the correct treatment or the necessity of an operation. A computational tool has been developed that merges, on the one hand, wavelet transform to reduce the size of the biomedical spectra and to extract the main features, and on the other hand, Support Vector Machine and Neural Networks to classify them. The influence of some of the configuration parameters of each of those soft computing techniques on the clustering is analyzed. These two methods and another one based on medical knowledge are compared. The classification results obtained by these computational tools are promising specially taking into account that medical knowledge has not been considered and that the number of samples of each class is very low in some cases.

Mukherjee and Chakraborti 1 proposed a single distribution-free (nonparametric) Shewhart-type chart based on the Lepage 2 statistic for simultaneously monitoring both the location and the scale parameters of a continuous distribution when both of these parameters are unknown. In the present work, we consider a single distribution-free CUSUM chart, based on the Lepage 2 statistic, referred to as the CUSUM-Lepage (denoted by CL) chart. The proposed chart is distribution-free (nonparametric) and therefore, the in control (denoted IC) properties of the chart remain invariant and known for all continuous distributions. Control limits are tabulated for implementation of the proposed chart in practice. The IC and out of control (denoted OOC) performance properties of the chart are investigated through simulation studies in terms of the average, the standard deviation, the median and some percentiles of the run length distribution. Detailed comparison with a competing Shewhart-type chart is presented. Several existing CUSUM charts are also considered in the performance comparison. The proposed CL chart is found to perform very well in the location-scale models. We also examine the effect of the choice of the reference value (k) of CUSUM chart on the performance of the CL chart. The proposed chart is illustrated with a real data set. Summary and conclusions are presented.

We focus on integrable systems with two degrees of freedom that are integrable in the Liouville sense and are obtained as real and imaginary parts of a polynomial (or entire) complex fimction in two complex variables. We propose definitions of the actions for such systems (which are not of the Arnol'd-Liouville type). We show how to compute the actions from a complex Hamilton-3acobi equation and apply these techniques to several examples including those recently considered in relation to perturbations of the Ruijsenaars-Schneider system. These examples introduce the crucial problem of the semiclassical approach to the corresponding quantum systems.

Most watermarking methods introduced that require concealment is less detectable or undetectable, while others exist that are based on the types of concealment that do not require an indiscernibility. It is within this framework and to ensure the security, at storage and transmission of digital data, we propose in this work, a new crypto-watermarking method using symmetrical injection of noise on architecture of multilayer neural networks performed to compression images. Our crypto-watermarking algorithm provides a good compression ratio and a progressive transmission, which reduces the bandwidth. As regards the time necessary for the operations of dissimilation, it may vary depending on the degree of security.