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Applied Mathematics Commons™

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2009

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Articles 61 - 90 of 223

Full-Text Articles in Applied Mathematics

Variational Analysis In Semi-Infinite And Infinite Programming, Ii: Necessary Optimality Conditions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra Jul 2009

Variational Analysis In Semi-Infinite And Infinite Programming, Ii: Necessary Optimality Conditions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5] from our viewpoint of robust Lipschitzian stability. We present meaningful interpretations and practical examples of such models. The main results establish necessary optimality conditions for a broad class of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. …

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On The Rigidity Of The Cotangent Complex At The Prime 2, James M. Turner Jul 2009

On The Rigidity Of The Cotangent Complex At The Prime 2, James M. Turner

University Faculty Publications and Creative Works

In [D. Quillen, On the (co)homology of commutative rings, Proc. Symp. Pure Math. 17 (1970) 65-87; L. Avramov, Locally complete intersection homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology, Annals of Math. 2 (150) (1999) 455-487] a conjecture was posed to the effect that if R → A is a homomorphism of Noetherian commutative rings then the flat dimension, as defined in the derived category of A-modules, of the associated cotangent complex LA / R satisfies: fdA LA / R < ∞ {long rightwards double arrow} fdA LA / R ≤ 2. The aim of this paper is to initiate an approach for solving this conjecture when R has characteristic 2 using simplicial algebra techniques. To that end, we obtain two results. First, we prove that the conjecture can be reframed in terms of certain nilpotence properties for the divided square γ2 and the André operation θ{symbol} as it acts on TorR (A, ℓ), ℓ any residue field of A. Second, we prove the conjecture is valid in two cases: when fdR A < ∞ and when R is a Cohen-Macaulay ring.

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Modeling And Analysis Of Biological Populations, Joan Lubben Jul 2009

Modeling And Analysis Of Biological Populations, Joan Lubben

Department of Mathematics: Dissertations, Theses, and Student Research

Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the long-term trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of non-indigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.

(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where …

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An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron Jul 2009

An Adaptive Method For Calculating Blow-Up Solutions, Charles F. Touron

Mathematics & Statistics Theses & Dissertations

Reactive-diffusive systems modeling physical phenomena in certain situations develop a singularity at a finite value of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use a priori knowledge of the blow-up solution such as monotonicity or self-similarity. For equations where such a priori knowledge is unavailable, ad hoc methods were constructed. The object of this research is to develop a simple and consistent approach to find numerically the blow-up solution without having a priori knowledge or resorting …

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Caching And Visualizing Statistical Analyses, Roger D. Peng, Duncan Temple Lang Jun 2009

Caching And Visualizing Statistical Analyses, Roger D. Peng, Duncan Temple Lang

Johns Hopkins University, Dept. of Biostatistics Working Papers

We present the cacher and CodeDepends packages for R, which provide tools for (1) caching and analyzing the code for statistical analyses and (2) distributing these analyses to others in an efficient manner over the web. The cacher package takes objects created by evaluating R expressions and stores them in key-value databases. These databases of cached objects can subsequently be assembled into “cache packages” for distribution over the web. The cacher package also provides tools to help readers examine the data and code in a statistical analysis and reproduce, modify, or improve upon the results. In addition, readers can easily …

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Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori Jun 2009

Sum Rules And Universality In Electron-Modulated Acoustic Phonon Interaction In A Free-Standing Semiconductor Plate, Shigeyasu Uno, Darryl H. Yong, Nobuya Mori

All HMC Faculty Publications and Research

Analysis of acoustic phonons modulated due to the surfaces of a free-standing semiconductor plate and their deformation-potential interaction with electrons are presented. The form factor for electron-modulated acoustic phonon interaction is formulated and analyzed in detail. The form factor at zero in-plane phonon wave vector satisfies sum rules regardless of electron wave function. The form factor is larger than that calculated using bulk phonons, leading to a higher scattering rate and lower electron mobility. When properly normalized, the form factors lie on a universal curve regardless of plate thickness and material.

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A Space Topologized By Functions From Omega To Omega, Akira Iwasa Jun 2009

A Space Topologized By Functions From Omega To Omega, Akira Iwasa

Computer Science and Mathematics Faculty Publications

No abstract provided.

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Variational Analysis In Semi-Infinite And Infinite Programming, I: Stability Of Linear Inequality Systems Of Feasible Solutions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra Jun 2009

Variational Analysis In Semi-Infinite And Infinite Programming, I: Stability Of Linear Inequality Systems Of Feasible Solutions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems described by parameterized systems of infinitely many linear inequalities in Banach spaces of decision variables indexed by an arbitrary set T. The parameter space of admissible perturbations under consideration is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set is finite, this …

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Finite Sample Properties Of Minimum Kolmogorov-Smirnov Estimator And Maximum Likelihood Estimator For Right-Censored Data, Jerzy Wieczorek Jun 2009

Finite Sample Properties Of Minimum Kolmogorov-Smirnov Estimator And Maximum Likelihood Estimator For Right-Censored Data, Jerzy Wieczorek

Dissertations and Theses

MKSFitter computes minimum Kolmogorov-Smirnov estimators (MKSEs) for several different continuous univariate distributions, using an evolutionary optimization algorithm, and recommends the distribution and parameter estimates that best minimize the Kolmogorov-Smirnov (K-S) test statistic. We modify this tool by extending it to use the Kaplan-Meier estimate of the cumulative distribution function (CDF) for right-censored data. Using simulated data from the most commonly-used survival distributions, we demonstrate the tool's inability to consistently select the correct distribution type with right-censored data, even for large sample sizes and low censoring rates. We also compare this tool's estimates with the right-censored maximum likelihood estimator (MLE). While …

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Sequence Characterization Of Riordan Arrays, Tian-Xiao He, Renzo Sprugnoli Jun 2009

Sequence Characterization Of Riordan Arrays, Tian-Xiao He, Renzo Sprugnoli

Scholarship

In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the A- and Z-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the A- and Z-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtained for the inverse. We also show how the sequence characterization is applied to construct easily a Riordan array. Finally, we give the characterizations relative to some subgroups of the Riordan group, in particular, of …

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Analytical Solution For Nonlinear Gas Dynamic Equation By Homotopy Analysis Method, Hossein Jafari, Changbum Chun, S. Seifi, M. Saeidy Jun 2009

Analytical Solution For Nonlinear Gas Dynamic Equation By Homotopy Analysis Method, Hossein Jafari, Changbum Chun, S. Seifi, M. Saeidy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the Homotopy Analysis Method (HAM) is used to implement the homogeneous gas dynamic equation. The analytical solution of this equation is calculated in form of a series with easily computable components.

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Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey Jun 2009

Modeling And Analysis Of The Spread Of Japanese Encephalitis With Environmental Effects, Ram Naresh, Surabhi Pandey

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear mathematical model for the spread of Japanese Encephalitis, caused by infected mosquito feeding on susceptible human population incorporating demographic and environmental factors is proposed and analyzed. In the modeling process, it is assumed that the growth rates of reservoir animal population and vector mosquito population are enhanced due to environmental discharges caused by human population related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is found that whenever the disease-free equilibrium is locally asymptotically stable, the endemic …

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Linear Stability Of Thermosolutal Convection In A Micropolar Fluid Saturating A Porous Medium, R Reena, U. S. Rana Jun 2009

Linear Stability Of Thermosolutal Convection In A Micropolar Fluid Saturating A Porous Medium, R Reena, U. S. Rana

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, the theoretical investigation of the double-diffusive convection in a micropolar fluid layer heated and soluted from below saturating a porous medium is considered. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been used. For the case of stationary convection, the effect of various parameters like medium permeability, solute gradient and micropolar parameters (i.e., coupling parameter, spin diffusion parameter, micropolar heat conduction parameter and micropolar solute parameter arises due to coupling between spin and solute fluxes) has been analyzed …

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Effects Of Hematocrit On Impedance And Shear Stress During Stenosed Artery Catheterization, V. P. Srivastava, Rati Rastogi Jun 2009

Effects Of Hematocrit On Impedance And Shear Stress During Stenosed Artery Catheterization, V. P. Srivastava, Rati Rastogi

Applications and Applied Mathematics: An International Journal (AAM)

The flow of blood through a stenosed catheterized artery has been studied. To observe the effects of hematocrit, blood has been represented by a two-phase macroscopic model (i.e., a suspension of red cells in plasma). It is found that for any given catheter size, the impedance increases with hematocrit and also for a given hematocrit, the same increases with the catheter size. In the stenotic region, the wall shear stress increases in the upstream of the stenosis throat and decreases in the downstream in an uncatheterized artery but the same possesses an opposite character in the case of a catheterized …

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Variational Iteration Method For Solving Telegraph Equations, Syed T. Mohyud-Din, Muhammad A. Noor, Khalida I. Noor Jun 2009

Variational Iteration Method For Solving Telegraph Equations, Syed T. Mohyud-Din, Muhammad A. Noor, Khalida I. Noor

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the variational iteration method (VIM) for solving telegraph equations, which arise in the propagation of electrical signals along a telegraph line. The suggested algorithm is more efficient and easier to handle as compare to the decomposition method. Numerical results show the efficiency and accuracy of the proposed VIM.

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Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare Jun 2009

Analysis Of Rotating Flow Around A Growing Protein Crystal, Daniel N. Riahi, Charles W. Obare

Applications and Applied Mathematics: An International Journal (AAM)

We consider the problem of steady flow around a growing protein crystal in a medium of its solution in a normal gravity environment. The whole flow system is assumed to be rotating with a constant angular velocity about a vertical axis which is anti-parallel to the gravity vector. Convective flow takes place due to the solute depletion around the growing crystal which leads to a buoyancy driven flow. Such convective flow can produce inhomogeneous solute concentration, which subsequently generate non-uniformities in the crystal’s structure finalizing lower quality protein crystal. Using scaling analysis within a diffusion boundary layer around the crystal, …

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Effect Of Glycocalyx On Red Blood Cell Motion In Capillary Surrounded By Tissue, Rekha Bali, Swati Mishra, P. N. Tandon Jun 2009

Effect Of Glycocalyx On Red Blood Cell Motion In Capillary Surrounded By Tissue, Rekha Bali, Swati Mishra, P. N. Tandon

Applications and Applied Mathematics: An International Journal (AAM)

The aim of the paper is to develop a simple model for capillary tissue fluid exchange system to study the effect of glycocalyx layer on the single file flow of red cells. We have considered the channel version of an idealized Krogh capillary-tissue exchange system. The glycocalyx and the tissue are represented as porous layers with different property parametric values. Hydrodynamic Lubrication theory is used to compute the squeezing flow of plasma within the small gap between the cell and the glycocalyx layer symmetrically surrounded by the tissue. The system of non linear partial differential equations has been solved using …

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A New Approach To Improve Inconsistency In The Analytical Hierarchy Process, Morteza Rahmami, Hamidreza Navidi Jun 2009

A New Approach To Improve Inconsistency In The Analytical Hierarchy Process, Morteza Rahmami, Hamidreza Navidi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new approach based on the generalized Purcell method for solving a system of homogenous linear equations is applied to improve near consistent judgment matrices. The proposed method relies on altering the components of the pairwise comparison matrix in such a way that the resulting sequences of improved matrices approach a consistent matrix. The complexity of the proposed method, together with examples, shows less cost and better results in computation than the methods in practice.

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Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang Jun 2009

Stability Of An Age-Structured Seir Epidemic Model With Infectivity In Latent Period, Xue-Zhi Li, Bin Fang

Applications and Applied Mathematics: An International Journal (AAM)

We study an age-structured SEIR epidemic model with infectivity in the latent period. By using the theory and methods of Differential and Integral Equations, the explicit expression for the basic reproductive number R0 is first derived. It is shown that the disease-free equilibrium is locally and globally asymptotically stable if R0 < 1. It is then proved that only one endemic equilibrium exists if R0 > 1 and its stability conditions are also given.

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Mehler-Fock Transformation Of Ultradistribution, Deshna Loonker, P. K. Banerji Jun 2009

Mehler-Fock Transformation Of Ultradistribution, Deshna Loonker, P. K. Banerji

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the testing function space Z and its dual Z', which is known as ultradistrbution. Some theorems and properties are investigated for the Mehler-Fock transformation and its inverse for the ultradistribution.

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Analytical Solution Of Time-Fractional Advection Dispersion Equation, Tariq O. Salim, Ahmad El-Kahlout Jun 2009

Analytical Solution Of Time-Fractional Advection Dispersion Equation, Tariq O. Salim, Ahmad El-Kahlout

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we get exact solution of the time-fractional advection-dispersion equation with reaction term, where the Caputo fractional derivative is considered of order α ϵ (0,2]. The solution is achieved by using a function transform, Fourier and Laplace transforms to get the formulas of the fundamental solution, which are expressed explicitly in terms of Fox’s H-function by making use of the relationship between Fourier and Mellin transforms. As special cases the exact solutions of time-fractional diffusion and wave equations are also obtained, and the solutions of the integer order equations are mentioned.

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Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang Jun 2009

Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang

Applications and Applied Mathematics: An International Journal (AAM)

Two new families of nonlinear 3-point subdivision schemes for curve design are introduced. The first family is ternary interpolatory and the second family is binary approximation. All these new schemes are circular-invariant, meaning that new vertices are generated from local circles formed by three consecutive old vertices. As consequences of the nonlinear schemes, two new families of linear subdivision schemes for curve design are established. The 3-point linear binary schemes, which are corner-cutting depending on the choices of the tension parameter, are natural extensions of the Lane-Riesenfeld schemes. The four families of both nonlinear and linear subdivision schemes are implemented …

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Adomian Decomposition Method For Solving The Equation Governing The Unsteady Flow Of A Polytropic Gas, M. A. Mohamed Jun 2009

Adomian Decomposition Method For Solving The Equation Governing The Unsteady Flow Of A Polytropic Gas, M. A. Mohamed

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we have discussed a new application of Adomian decomposition method on nonlinear physical equations. The models of interest in physics are considered and solved by means of Adomian decomposition method. The behavior of Adomian solutions and the effects of different values of time are investigated. Numerical illustrations that include nonlinear physical models are investigated to show the pertinent features of the technique.

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A New Hpm For Integral Equations, Hossein Aminikhah, Maziar Salahi Jun 2009

A New Hpm For Integral Equations, Hossein Aminikhah, Maziar Salahi

Applications and Applied Mathematics: An International Journal (AAM)

Homotopy perturbation method is an effective method for obtaining exact solutions of integral equations. However, it might perform poorly on ill-posed integral equations. In this paper, we introduce a new version of the homotopy perturbation method that efficiently solves ill-posed integral equations. Finally, several numerical examples, including a system of integral equations, are presented to demonstrate the efficiency of the new method.

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Effect Of Dust Particles On Rotating Micropolar Fluid Heated From Below Saturating A Porous Medium, R. Reena, U. S. Rana Jun 2009

Effect Of Dust Particles On Rotating Micropolar Fluid Heated From Below Saturating A Porous Medium, R. Reena, U. S. Rana

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the theoretical investigation of the effect of dust particles on a layer of rotating micropolar fluid heated from below saturating a porous medium. A dispersion relation is obtained for a flat fluid layer contained between two free boundaries using a linear stability analysis theory and normal mode analysis. The principle of exchange of stabilities is found to hold true for the micropolar fluid saturating a porous medium heated from below in the absence of dust particles, rotation and micropolar heat conduction parameter. The oscillatory modes are introduced due to the presence of the dust particles and …

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Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen Jun 2009

Closed Knight's Tours With Minimal Square Removal For All Rectangular Boards, Joseph Demaio, Thomas Hippchen

Faculty Articles

A closed knight's tour of a chessboard uses legal moves of the knight to visit every square exactly once and return to its starting position. In 1991 Schwenk completely classified the rectangular chessboards that admit a closed knight's tour. For a rectangular chessboard that does not contain a closed knight's tour, this paper determines the minimum number of squares that must be removed in order to admit a closed knight's tour. Furthermore, constructions that generate a closed tour once appropriate squares are removed are provided.

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Discussing Vocation As A Part Of A Senior Capstone Class, Maria Zack May 2009

Discussing Vocation As A Part Of A Senior Capstone Class, Maria Zack

ACMS Conference Proceedings 2009

Many of us in Christian higher education are seeking ways to help our students discern their own sense of call. At the 2007 ACMS meeting Greg Crow and I participated in a panel on vocation and published a related paper in the Journal of the ACMS. This current paper discusses what has been learned from incorporating some of our ideas into our department's senior capstone course. This has been very meaningful for both the students and the faculty involved.

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Fire! Lessons Learned And Applied To Computer Systems, Kim P. Kihlstrom May 2009

Fire! Lessons Learned And Applied To Computer Systems, Kim P. Kihlstrom

ACMS Conference Proceedings 2009

A wildfire swept through Santa Barbara on November 13, 2008, burning 1940 acres and destroying 230 homes. Nine structures on the Westmont College campus were destroyed as well as fifteen faculty homes near campus. What insights can be drawn from this experience? We will examine some of the lessons that can be applied to the design of intrusion-tolerant computer systems.

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Are Mathematical Entities Real?, Phillip E. Lestmann May 2009

Are Mathematical Entities Real?, Phillip E. Lestmann

ACMS Conference Proceedings 2009

This talk will introduce ontological questions related to mathematics. After surveying the views of Plato and Artistotle, other possible philosophical perspectives will be considered including realism, nominalism, conceptualism, and empiricism with their relative strengths and weaknesses. The discussion will conclude with a possible biblical foundation for mathematical ontology.

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A Career Preparation Course For Students In Mathematics And Computer Science, Donna Pierce, Peter A. Tucker May 2009

A Career Preparation Course For Students In Mathematics And Computer Science, Donna Pierce, Peter A. Tucker

ACMS Conference Proceedings 2009

As professors, we all want our students to succeed, and to be motivated to study. We all get questions from students that can be boiled down to, "What can I do with X degree?" Certainly, a quick answer is to point students to career websites, or to send them to the career services department on campus. However, we want to do better than that. We want students to learn how to investigate these future directions, and to have them think about their future more holistically--not just an effort to find a job. To that end, we have developed a course …

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