the three dimensional flow past a stretching sheet and the homotopy perturbation method an approximate analytical solution is obtained of the steady laminar three dimensional flow for an incompressible viscous fluid past a stretching sheet using the homotopy perturbation method hpm proposed by he the flow is governed by a boundary value problem bvp consisting of a pair of non linear differential equations the solution is simple yet highly accurate and compares favorably with the exact solutions obtained early in the literature the methodology presented in the paper is useful for solving the bvps consisting of more than one differential equation

non similar series solution for boundary layer flow of a third order fluid over a stretching sheet this study deals with the boundary layer flow of a third order fluid induced by a stretching sheet by means of similarity transformation the governing non linear partial differential equation is reduced to a non linear ordinary differential equation the analytical solution of the problem is obtained using homotopy analysis method ham finally the solutions are also compared with the existing results in the literature

decision analysis under ambiguity abstract in selecting the preferred course of action decision makers are often uncertain about one or more probabilities of interest the experimental literature has ascertained that this uncertainty ambiguity might affect decision makers preferences then the decision maker might wish to incorporate ambiguity aversion in the analysis we investigate the modeling ambiguity attitudes in the solution of decision analysis problems through functionals well established in the decision theory literature we obtain the multiple event problems for subjective expected utility smooth ambiguity and maximin decision makers this allows us to establish the conditions under which these alternative decision makers face equivalent problems results for certainty equivalents and risk premia in the presence of both risk and ambiguity aversion are obtained a recent generalization of the classical arrow pratt quadratic approximation allows us to quantify the portions of a premium due to risk plxinsert and to ambiguity aversion the numerical implementation of the objective functions is addressed showing that all functionals can be estimated at no additional burden through monte carlo simulation the well known carter racing case study is addressed quantitatively to demonstrate the findings

probability and time trade off probability and time are integral dimensions of virtually any decision to treat them together we consider the prospect of receiving outcome x with a probability p at time t we define risk and time distance and show that if these two distances are traded off linearly then preferences are characterized by three functions a value function a probability discount rate function and a psychological distance function the concavity of the psychological distance function explains the common ratio and common difference effects a decreasing probability discount rate accounts for the magnitude effect the discount rate and the risk premium depend on the shape of these three functions this paper was accepted by peter wakker decision analysis

a note on a certain boundary layer equation abstract this paper deals with a differential equation of mixing layer the existence of a solution is established by using weyl technique

a smooth model of decision making under ambiguity we propose and axiomatize a model of preferences over acts such that the decision maker prefers act f to act g if and only if e e u f e e u g where e is the expectation operator u is a vn m utility function is an increasing transformation and is a subjective probability over the set of probability measures that the decision maker thinks are relevant given his subjective information a key feature of our model is that it achieves a separation between ambiguity identified as a characteristic of the decision maker s subjective information and ambiguity attitude a characteristic of the decision maker s tastes we show that attitudes towards risk are characterized by the shape of u as usual while attitudes towards ambiguity are characterized by the shape of we also derive x 1 e x as the special case of constant ambiguity aversion ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures this characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by epstein zhang 2001 and ghirardato marinacci 2002 one advantage of this model is that the welldeveloped machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes the model is also distinct from many in the literature on ambiguity in that allows smooth rather than kinked indifference curves this leads to different behavior and improved tractability while still sharing the main features e g ellsberg s paradox etc the maxmin eu model e g gilboa and schmeidler 1989 with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion two illustrative applications to portfolio choice are offered

harmonic wave generation in non linear thermoelasticity by variational iteration method and adomian s method this paper applies the variational iteration method and adomian s decomposition method to solve numerically the harmonic wave generation in a nonlinear one dimensional elastic half space model subjected initially to a prescribed harmonic displacement the results show that the variational iteration method is much easier more convenient and more stable and efficient than adomian decomposition method

a singular nonlinear differential equation arising in the homann flow abstract the existence and uniqueness of a positive solution of the singular nonlinear boundary value problem y 2 y 1 2 1 x 2 y 0 0 x 1 y 0 1 2 and y 1 0 which arises in the homann flow are studied

solution of the falkner skan equation by recursive evaluation of taylor coefficients we present a computational method for the solution of the third order boundary value problem characterized by the well known falkner skan equation on a semi infinite domain numerical treatments of this problem reported in the literature thus far are based on shooting and finite differences while maintaining the simplicity of the shooting approach the method presented in this paper uses a technique known as automatic differentiation which is neither numerical nor symbolic using automatic differentiation a taylor series solution is constructed for the initial value problems by calculating the taylor coefficients recursively the effectiveness of the method is illustrated by applying it successfully to various instances of the falkner skan equation

risk ambiguity and the separation of utility and beliefs we introduce a general model of static choice under uncertainty arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs most of the nonexpected utility models existing in the literature are special cases of it such separation is motivated by the view that tastes are constant whereas beliefs change with new information the model has a simple and natural axiomatization elsewhere forthcoming we show that it can be very helpful in the characterization of a notion of ambiguity aversion as separating utility and beliefs allows us to identify and remove aspects of risk attitude from the decision maker s behavior here we show that the model allows us to generalize several results on the characterization of risk aversion in betting behavior these generalizations are of independent interest as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts

approximate analytical solution for the zakharov kuznetsov equations with fully nonlinear dispersion in this paper variational iteration method vim is used to obtain numerical and analytical solutions for the zakharov kuznetsov equations with fully nonlinear dispersion comparisons with exact solution show that the vim is a powerful method for the solution of nonlinear equations

intuitive approach to the approximate analytical solution for the blasius problem for the blasius problem we propose an approximate analytical solution in the form of a logarithm of the hyperbolic cosine function which satisfies the given boundary conditions and some known properties of the exact solution furthermore adding some hyperbolic tangent functions to this solution we obtain much more accurate approximate solution with the relative error less than 0 16 over the whole region the superiority of the proposed solutions is shown by comparison with the existing approximate analytical solution

on the determination of the steady film profile for a non newtonian thin droplet abstract a shooting method is used to determine a solution to a third order ode modeling the steady profile of a non newtonian thin droplet we compare a direct approach to an iterative approach using a secant method we obtain a nonlinear relationship between the contact angle and the position of the contact line r from this nonlinear relationship we use curve fitting to obtain an empirical law of the form tan r f k where k is the power law coefficient and f is a nonlinear function of k

a study on a boundary layer equation arising in an incompressible fluid in this paper a differential equation of mixing layer that arises in viscous incompressible fluid will be investigated the series solution method will be effectively implemented to a related integro differential equation the condition at infinity will be applied to a related pade approximants of the obtained series solution

numerical solution of the falkner skan equation based on quasilinearization we present two iterative methods for solving the falkner skan equation based on the quasilinearization method we formulate the original problem as a new free boundary value problem the truncated boundary depending on a small parameter is an unknown free boundary and has to be determined as part of solution using a change of variables the free boundary value problem is transformed to a problem defined on 0 1 we apply the quasilinearization method to solve the resulting nonlinear problem then we propose two different iterative algorithms by means of a cubic spline solver numerical results for various instances are compared with those reported previously in the literature the comparisons show the accuracy robustness and efficiency of the presented methodology

on similarity solutions of a boundary layer problem with an upstream moving wall this work deals with the problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream it has previously been shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream in particular it was proved that a solution exists only if this parameter does not exceed a certain critical value and numerical evidence was adduced to show that this solution is nonunique using crocco formulation the present work proves this nonuniqueness also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter

axisymmetric flow due to a stretching sheet with partial slip the steady laminar axisymmetric flow of a newtonian fluid due to a stretching sheet when there is a partial slip of the fluid past the sheet has been investigated the flow is governed by a third order non linear boundary value problem whose exact numerical solution has been obtained non iteratively in terms of the non dimensional slip parameter l a perturbation solution valid for small l and an asymptotic solution valid for large l have been derived finally a solution based upon he s homotopy perturbation method has been developed the latter being analytical is elegant but is sufficiently accurate for all values of l

minimizing variation of production rates in just in time systems a survey abstract in the past several years there has been growing interest in scheduling problems where jobs are penalized both for being early and for being tardy this notable deviation from previous work in which finishing early is generally regarded as being at least as desirable as finishing on time is perceived to be the one that well captures the scheduling dimension of jit production systems a number of excellent surveys on these problems has appeared over the last four years there is however another important scheduling objective in jit production systems which is to minimize variation of rates at which processes supply their outputs these scheduling problems are for example of primary concern in the toyota jit system thus far most research efforts in this area have been focused on minimizing variation of the rate at which different products are being produced on the final multi model assembly line which itself is a supplying process we shall review the results of this research and relate them to the due date based scheduling problems extensions and open problems will also be reviewed schedules that minimize variation of the rate at which different products are being produced on the line do not necessarily minimize variation in the line demand for outputs of processes that supply it few heuristics for the problem of minimizing the variation are available and hardly anything is known on its complexity as wel as exact algorithms to tackle it we shall review a mathematical programming model of the problem and open questions that result from it

a numerical method for solving nth order boundary value problems in this paper we consider the solution of an nth order boundary value problem we solve this problem by changing the problem to a system of two integral differential equations and using the variational iteration method by giving three examples and comparing with the other methods the efficiency of the method will be shown

radiation effects for the blasius and sakiadis flows with a convective surface boundary condition abstract this study aims to analyze the effects of thermal radiation on the laminar boundary layer about a flat plate in a uniform stream of fluid blasius flow and about a moving plate in a quiescent ambient fluid sakiadis flow both under a convective surface boundary condition the resulting similarity energy equation is solved numerically and the variations of dimensionless surface temperature and fluid solid interface characteristics for different values of prandtl number pr radiation parameter nr and parameter a which characterizes our convection processes are graphed and tabulated quite different and interesting behaviours were encountered for a blasius flow compared with a sakiadis flow a comparison with previously published results on special case of the problem shows excellent agreement

exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method the purpose of this study is to introduce a modification of the homotopy perturbation method using laplace transform and pade approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations two test examples are given the coupled nonlinear system of burger equations and the coupled nonlinear system in one dimensional thermoelasticity the results obtained ensure that this modification is capable of solving a large number of nonlinear differential equations that have wide application in physics and engineering

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

the rich domain of ambiguity explored ellsberg and others suggested that decision under ambiguity is a rich empirical domain with many phenomena to be investigated beyond the ellsberg urns we provide a systematic empirical investigation of this richness by varying the uncertain events the outcomes and combinations of both although ambiguity aversion is prevailing we also find systematic ambiguity seeking confirming insensitivity we find that ambiguity attitudes depend on the kind of uncertainty the source but not on the kind of outcomes ambiguity attitudes are closer to rationality ambiguity neutrality for natural uncertainties than for artificial ellsberg urn uncertainties this also appears from the reductions of monotonicity violations and of insensitivity ambiguity attitudes have predictive power across different outcomes and sources of uncertainty with individual specific components our rich domain serves well to test families of weighting functions for fitting ambiguity attitudes we find that two parameter families capt

a second order finite difference method for the falkner skan equation the falkner skan equation arises in the study of laminar boundary layers exhibiting similarity numerical methods reported in the literature thus far are based on shooting methods and finite difference methods obtained by first truncating the semi infinite physical domain of the problem to a finite domain at an unknown finite boundary which is determined as part of the solution by imposing an asymptotic boundary condition at this boundary the method presented in this paper transforms the semi infinite domain without truncating it to a finite domain and without imposing the asymptotic condition this is accomplished by a coordinate transformation which maps the physical domain 0 directly to the computational domain 0 1 the effectiveness of the method is illustrated by applying it successfully to various instances of the falkner skan equation and by demonstrating second order accuracy

a new set of solutions to a singular second order differential equation arising in boundary layer theory abstract the paper studies a boundary value problem of a nonlinear second order differential equation that governs the laminar flow of newtonian and non newtonian fluids it presents a new sufficient condition for the existence of solutions to the boundary value problem

a new solution branch for the blasius equation a shrinking sheet problem in this work a similarity equation of the momentum boundary layer is studied for a moving flat plate with mass transfer in a stationary fluid the solution is applicable to the practical problem of a shrinking sheet with a constant sheet velocity theoretical estimation of the solution domain is obtained it is shown that the solution only exists with mass suction at the wall surface the equation with the associated boundary conditions is solved using numerical techniques greatly different from the continuously stretching surface problem and the blasius problem with a free stream quite complicated behavior is observed in the results it is seen that there are three different solution zones divided by two critical mass transfer parameters f 0 1 1 7028 and f 0 2 1 7324 when f 0f 0 2 there is a terminating point for the solution domain and the terminating point corresponds to a special algebraically decaying solution for the current problem the current results provide a new solution branch of the blasius equation which is greatly different from the previous study and provide more insight into the understanding of the blasius equation

a new algorithm for solving classical blasius equation in this paper a reliable algorithm is employed to investigate the classical blasius equation the algorithm is based mainly on applying the adomian decomposition method to the transformation of the blasius equation the results demonstrate reliability and efficiency of the proposed algorithm

fluid flow over a nonlinearly stretching sheet numerical solutions are obtained for a class of nonlinear third order differential equations arising in fluid flows over a nonlinearly stretching sheet using a similarity transformation which is different from that of the linearly stretching sheet problem furthermore using the schauder theory existence of a solution of the third order differential equation over a large but finite interval is established moreover the analytical solutions are obtained and are compared with the corresponding numerical solutions the results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the effects of nonlinear stretching on the flow characteristics

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

numerical solution of the falkner skan equation using piecewise linear functions we present a finite element method for the solution of the falkner skan equation the method uses a coordinate transformation to map the semi infinite domain of the problem to the unit interval 0 1 by means of a suitable change of variables the transformed third order boundary value problem is further rewritten as a system of differential equations consisting of a second order equation and a first order equation the second order equation is approximated using a galerkin formulation with piecewise linear elements and the first order equation is approximated using a centered difference approximation in the process of the initial transformation a finite computational boundary is introduced this boundary is obtained as part of the computational solution by imposing an additional asymptotic boundary condition the solutions obtained thus are in excellent agreement with those obtained by previous authors

optimal stopping with multiple priors we develop a theory of optimal stopping under knightian uncertainty a suitable martingale theory for multiple priors is derived that extends the classical dynamic programming or snell envelope approach to multiple priors we relate the multiple prior theory to the classical setup via a minimax theorem in a multiple prior version of the classical model of independent and identically distributed random variables we discuss several examples from microeconomics operation research and finance for monotone payoffs the worst case prior can be identified quite easily with the help of stochastic dominance arguments for more complex payoff structures like barrier options model ambiguity leads to stochastic changes in the worst case beliefs

thermal boundary layer problems in a semi infinite flat plate by the differential transformation method this paper investigates the velocity and temperature field in the thermal boundary layer over a semi infinite flat plate the differential transformation method is used to determine some solutions of these velocity and thermal boundary layer problems numerical results for the dimensionless temperature profiles are presented graphically for different values of prandtl number it is found that the results obtained by the present method are in good agreement with those provided by other numerical methods

a finite difference method for the falkner skan equation we present a finite difference method for the solution of the falkner skan equation the method uses a coordinate transformation to map a semi infinite physical domain to the unit interval 0 1 after using a suitable change of variables the transformed third order boundary value problem for this domain is solved using a finite difference scheme the numerical solutions obtained by the present method are in agreement with those obtained by previous authors

a reliable algorithm for solving boundary value problems for higher order integro differential equations the aim of this paper is to present an efficient analytical and numerical procedure for solving boundary value problems for higher order integro differential equations the modified form of adomian decomposition method is found to be fast and accurate the analysis is accompanied by numerical examples the results demonstrate reliability and efficiency of the proposed algorithm

boundary layer flow of a second grade fluid with variable heat flux at the wall we study the boundary layer stagnation flow of a second grade fluid with a prescribed variable heat flux at the wall the flow is assumed to be steady and laminar the governing equations are solved using an iterative central difference approximation method in a non uniform grid domain the effects of the non newtonian nature of the fluid and the heat flux parameter on the thermal boundary layer are also presented

a simple perturbation approach to blasius equation in this paper we couple the iteration method with the perturbation method to solve the well known blasius equation the obtained approximate analytic solutions are valid for the whole solution domain comparison with howarth s numerical solution reveals that the proposed method is of high accuracy the first iteration step leads to 6 8 accuracy and the second iteration step yields the 0 73 accuracy of initial slop

the modified decomposition method and pade approximants for a boundary layer equation in unbounded domain the modified decomposition method is applied for analytic treatment of nonlinear differential equations that appear on boundary layers in fluid mechanics the modified method accelerates the rapid convergence of the series solution dramatically reduces the size of work the obtained series solution is combined with the diagonal pade approximants to handle the boundary condition at infinity

viscous flow over a nonlinearly stretching sheet an analysis is carried out to study the flow and heat transfer characteristics in a viscous fluid over a nonlinearly stretching sheet the equations of conservation of momentum mass and energy which govern the flow and heat transfer are partially decoupled using a similarity transformation which is different from that of the linearly stretching sheet problem however the results for the linearly stretching sheet problem can be obtained as a special case the basic nonlinear differential equation for the velocity field f and the differential equation with variable coefficient for the temperature field q are solved numerically by using a fourth order runge kutta integration scheme the numerical results thus obtained for the flow and heat transfer characteristics are presented by a table and graphs furthermore it is shown that the heat flow is always from the stretching sheet to the fluid

a new algorithm for solving differential equations of lane emden type in this paper a reliable algorithm is employed to investigate the differential equations of lane emden type the algorithm rests mainly on the adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point the proposed framework is applied to a generalization of lane emden equations so that it can be used in differential equations of the same type

rational scaled generalized laguerre function collocation method for solving the blasius equation in this paper we propose a collocation method for solving the blasius equation the blasius equation is a third order nonlinear ordinary differential equation this approach is based on a rational scaled generalized laguerre function collocation method we also present the comparison of this work with some well known results and show that the present solution is accurate

the numerical solution of sixth order boundary value problems by the modified decomposition method a fast and accurate algorithm is developed for the solution of sixth order boundary value problems bvps with two point boundary conditions a modified form of the adomian decomposition method is applied to construct the numerical solution for such problems the scheme is tested on one linear and two nonlinear problems the results demonstrate reliability and efficiency of the algorithm developed

the blasius function computations before computers the value of tricks undergraduate projects and open research problems the blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick semi infinite flat plate the blasius function is the solution to 2 f xxx f f xx 0 on x in 0 infty subject to f 0 f x 0 0 f x infty 1 we use this famous problem to illustrate several themes first although the flow solves a nonlinear partial differential equation pde toepfer successfully computed highly accurate numerical solutions in 1912 his secret was to combine a runge kutta method for integrating an ordinary differential equation ode initial value problem with some symmetry principles and similarity reductions which collapse the pde system to the ode shown above this shows that pde numerical studies were possible even in the precomputer age the truth both a hundred years ago and now is that mathematical theorems and insights are an arithmurgist s best friend and they can vastly reduce the computational burden second we show that special tricks applicable only to a given problem can be as useful as the broad general methods that are the fabric of most applied mathematics courses the importance of particularity in spite of these triumphs many properties of the blasius function f x are unknown we give a list of interesting projects for undergraduates and another list of challenging issues for the research mathematician

new perturbation iteration solutions for bratu type equations perturbation iteration theory is systematically generated for both linear and nonlinear second order differential equations and applied to bratu type equations different perturbation iteration algorithms depending upon the number of taylor expansion terms are proposed using the iteration formulas derived using different perturbation iteration algorithms new solutions of bratu type equations are obtained solutions constructed using different perturbation iteration algorithms are contrasted with each other as well as with numerical solutions it is found that algorithms with more taylor series expansion terms yield more accurate results

numerical solutions of the classical blasius flat plate problem abstract this paper presents a numerical study of the non linear differential equation af ff 0 where a prime denotes differentiation with respect to the similarity variable and a is a parameter for a 1 and a 2 this equation is a form of the blasius relation for the flat plate flow in fluid mechanics several numerical solution are obtained using a runge kutta algorithm for high order initial value problems for 1 a 2

laguerre collocation method for the flow and heat transfer due to a permeable stretching surface embedded in a porous medium with a second order slip and viscous dissipation a numerical method is given for studying the effect of viscous dissipation on the steady flow with heat transfer of newtonian fluid towards a permeable stretching surface embedded in a porous medium with a second order slip the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equations by using similarity variables the proposed method is based on replacement of the unknown function by truncated series of well known laguerre expansion of functions an approximate formula of the derivative is introduced special attention is given to study the convergence analysis and derive an upper bound of the error of the presented approximate formula the introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with laguerre coefficients thus by solving this system of equations the laguerre coefficients are obtained graphically results are shown for non dimensional velocities and temperature the effects of the porous parameter the suction injection parameter eckert number first and second order velocity slip parameter and the prandtl number on the flow and temperature profiles are presented moreover the local skin friction and nusselt numbers are presented a comparison of numerical results is made with the earlier published results under limiting cases

invariant probabilistic sensitivity analysis in evaluating opportunities investors wish to identify key sources of uncertainty we propose a new way to measure how sensitive model outputs are to each probabilistic input e g revenues growth idiosyncratic risk parameters we base our approach on measuring the distance between cumulative distributions risk profiles using a metric that is invariant to monotonic transformations thus the sensitivity measure will not vary by alternative specifications of the utility function over the output to measure separation we propose using either kuiper s metric or kolmogorov smirnov s metric we illustrate the advantages of our proposed sensitivity measure by comparing it with others most notably the contribution to variance measures our measure can be obtained as a by product of a monte carlo simulation we illustrate our approach in several examples focusing on investment analysis situations this paper was accepted by peter wakker decision analysis

on a certain boundary value problem arising in shrinking sheet flows abstract this paper presents an analysis of the boundary value problem resulting from the magnetohydrodynamic mhd viscous flow influenced by a shrinking sheet with suction for the cases of two dimensional m 1 and axisymmetric m 2 shrinking the influences of the parameter m as well as the effects of suction parameter s and hartmann number m 2 on similar entrainment velocity f and flow characteristics are studied to this purpose the resulting nonlinear ordinary differential equation is solved numerically using the 4th order runge kutta method in combination with a shooting procedure the obtained results elucidate reliability and efficiency of the technique from which interesting features between the skin friction coefficient f 0 and the entrainment velocity f as function of the mass transfer parameter s can also be obtained

level schedules for mixed model just in time processes a mixed model manufacturing facility running under a just in time jit production system is controlled by setting the production sequence of the final assembly process this sequence is set to achieve the primary goal of an organization operating under a jit system which is to maintain a constant rate of part usage in this paper a graph theoretic approach is used to determine an optimal solution for this goal for a new nonconvex objective function furthermore it is shown that a schedule always exists such that at all times the deviation of actual production from the desired level of production for every product is never more than one unit

singularly perturbed third order boundary value problem for nonlinear systems abstract this paper deals with the existence of solutions to a singularly perturbed boundary value problem for third order nonlinear differential systems the authors construct an appropriate generalized lower solution upper solution pair a concept that is defined in this paper and employ the method of descent nagumo conditions algebraic boundary layer functions and volterra type integral operator to guarantee the existence of solutions of the problem the uniformly valid asymptotic estimate of the solutions is given as well the differential systems has nonlinear dependence on all over order derivatives of the unknown

finite difference schemes on quasi uniform grids for bvps on infinite intervals abstract the classical numerical treatment of boundary value problems defined on infinite intervals is to replace the boundary conditions at infinity by suitable boundary conditions at a finite point the so called truncated boundary a truncated boundary allowing for a satisfactory accuracy of the numerical solution has to be determined by trial and errors and this seems to be the weakest point of the classical approach on the other hand the free boundary approach overcomes the need for a priori definition of the truncated boundary in fact in a free boundary formulation the unknown free boundary can be identified with a truncated boundary and being unknown it has to be found as part of the solution in this paper we consider a different way to overcome the introduction of a truncated boundary namely non standard finite difference schemes defined on quasi uniform grids a quasi uniform grid allows us to describe the infinite domain by a finite number of intervals the last node of such grid is placed on infinity so that right boundary conditions are taken into account exactly we apply the proposed approach to the falkner skan model and to a problem of interest in foundation engineering the obtained numerical results are found in good agreement with those available in literature moreover we provide a simple way to improve the accuracy of the numerical results using richardson s extrapolation finally we indicate a possible way to extend the proposed approach to boundary value problems defined on the whole real line

hyper heuristic approaches for the response time variability problem we propose two classes for the implementation of hyper heuristic algorithms the first is based on constructive heuristics whereas the second uses improvement methods within the latter class a general framework is designed for the use of local search procedures and metaheuristics as low level heuristics a dynamic scheme to guide the use of these approaches is also devised these ideas are tested on an np hard scheduling problem known as the response time variability problem rtvp an intensive computational experiment shows especially in the second class where the new best results are found the effectiveness of the proposed hyper heuristics

a belief based account of decision under uncertainty we develop a belief based account of decision under uncertainty this model predicts decisions under uncertainty from i judgments of probability which are assumed to satisfy support theory and ii decisions under risk which are assumed to satisfy prospect theory in two experiments subjects evaluated uncertain prospects and assessed the probability of the respective events study 1 involved the 1995 professional basketball playoffs study 2 involved the movement of economic indicators in a simulated economy the results of both studies are consistent with the belief based account but violate the partition inequality implied by the classical theory of decision under uncertainty

application of fixed point method to obtain semi analytical solution to blasius flow and its variation the classical blasius flow and its variation sakiadis flow are investigated by the fixed point method fpm and the semi analytical solutions are obtained different from early perturbation series solutions the present semi analytical solutions are valid in the whole region without using matching procedure moreover these solutions can correctly provide the asymptotic property of the governing equations the comparison of the present results with numerical results is carried out which reveals that fpm is a convenient and effective tool for nonlinear problems

numerical transformation methods blasius problem and its variants blasius problem is the simplest nonlinear boundary layer problem we hope that any approach developed for this epitome can be extended to more difficult hydrodynamics problems with this motivation we review the so called topfer transformation which allows us to find a non iterative numerical solution of the blasius problem by solving a related initial value problem and applying a scaling transformation the applicability of a non iterative transformation method to the blasius problem is a consequence of its partial invariance with respect to a scaling group several problems in boundary layer theory lack this kind of invariance and cannot be solved by non iterative transformation methods to overcome this drawback we can modify the problem under study by introducing a numerical parameter and require the invariance of the modified problem with respect to an extended scaling group involving this parameter then we apply initial value methods to the most recent developments involving variants and extensions of the blasius problem

the optimal homotopy asymptotic method for solving blasius equation starting from the reality that many known methods fail in the attempt to obtain analytic solutions of blasius type equations in this work a new procedure namely optimal homotopy asymptotic method oham is proposed to obtain an explicit analytical solution of the blasius problem comparison with howarth s numerical solution as well as the obtained residual reveals that the proposed method is highly accurate this proves the validity and great potential of the proposed procedure oham as a new kind of powerful analytical tool for nonlinear problems

a new algorithm for calculating two dimensional differential transform of nonlinear functions a new algorithm for calculating the two dimensional differential transform of nonlinear functions is developed in this paper this new technique is illustrated by studying suitable forms of nonlinearity three strongly nonlinear partial differential equations are then solved by differential transform method to demonstrate the validity and applicability of the proposed algorithm the present framework offers a computationally easier approach to compute the transformed function for all forms of nonlinearity this gives the technique much wider applicability

viscous flow and heat transfer over a nonlinearly stretching sheet this paper presents a numerical analysis for flow and heat transfer in a viscous fluid over a nonlinear stretching sheet by employing a novel numerical procedure and two cases are studied namely i the sheet with constant surface temperature cst case and ii the sheet with prescribed surface temperature pst case the governing partial differential equations are converted into highly nonlinear ordinary differential equations by a similarity transformation the variations of dimensionless surface temperature dimensionless surface temperature gradient as well as flow and heat transfer characteristics with the governing parameters are graphed and tabulated

choice based elicitation and decomposition of decision weights for gains and losses under uncertainty this paper reports the results of an experimental parameter free elicitation and decomposition of decision weights under uncertainty assuming cumulative prospect theory utility functions were elicited for gains and losses at an individual level using the tradeoff method subsequently decision weights were elicited through certainty equivalents of uncertain two outcome prospects furthermore decision weights were decomposed using observable choice instead of invoking other empirical primitives as in previous experimental studies the choice based elicitation of decision weights allows for a quantitative study of their characteristics and also allows among other things for the examination of the sign dependence hypothesis for observed choice under uncertainty our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice based subjective probabilities we also find evidence for sign dependence of decision weights

mathematical programming modeling of the response time variability problem the response time variability problem rtvp is a scheduling problem that has recently been defined in the literature the rtvp has a broad range of real life applications from manufacturing to services and information technology a previous study developed a position exchange heuristic to apply to initial sequences for the rtvp and a milp mixed integer linear programming to obtain optimal solutions with a practical limit of 25 units to be scheduled this paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality the contribution of this paper is 4 fold i larger instances can be solved to optimality by the off the shelf standard software ii the new optimal solutions of the rtvp can be used to compare the results of heuristic procedures iii the importance of modeling is demonstrated as well as the huge impact that reformulation redundant constraints and the elimination of symmetries have on the efficiency of milps is clearly established finally iv a challenge to develop a customized optimization algorithm to rival the milp solution efficiency for the rtvp is put forward

he s parameter expanding methods for strongly nonlinear oscillators ji huan he s work on asymptotic techniques is briefly reviewed and his parameter expanding methods including modified lindstedt poincare method and bookkeeping parameter method are discussed in detail some remarkable virtues of the methods are exploited and their applications are illustrated

a new analytical solution branch for the blasius equation with a shrinking sheet a similarity equation of the momentum boundary layer is analytically studied for a moving flat plate with mass transfer in a stationary fluid by a newly developed technique namely homotopy analysis method ham the equation shows its significance for the practical problem of a shrinking sheet with a constant velocity and only admits the existence of the solution with mass suction at the wall surface the present work provides analytically new solution branch of the blasius equation with a shrinking sheet in different solution areas including both multiple solutions and unique solution with the aid of an introduced auxiliary function the analytical results show that quite complicated behavior with three different solution areas controlled by two critical mass transfer parameters exists which agrees well with the numerical techniques and greatly differs from the continuously stretching surface problem and the blasius problem with a free stream the new analytical solution branch of the blasius equation with a shrinking sheet enriches the solution family of the blasius equation and helps to deeply understand the blasius equation