bias in utility assessments further evidence and explanations judgments about simple gambles such as those used in utility assessment can generate sizable and systematic bias after hershey and schoemaker hershey j c p j h schoemaker 1985 probability vs certainty equivalence methods in utility measurement are they equivalent management sci 31 1213 1231 we employ both the probability and certainty equivalence methods to explore bias our results show that 1 the direction and degree of bias depend on characteristics of the assessment gamble such as the reference probability and the difference between outcomes 2 presenting subjects with explicit anchors can change the size and direction of the bias and 3 subjects using heuristic response strategies show significantly more bias than those using expectation strategies we also discuss the status of possible explanations for the bias in light of these new results including pe mode reframing random error and anchoring and adjustment

exact solutions to nonlinear nonautonomous space fractional diffusion equations with absorption we analyze a nonlinear fractional diffusion equation with absorption by employing fractional spatial derivatives and obtain some more exact classes of solutions in particular the diffusion equation employed here extends some known diffusion equations such as the porous medium equation and the thin film equation we also discuss some implications by considering a diffusion coefficient d x t d t x theta theta in r and a drift force f k 1 t x k alpha x x alpha 1 in both situations we relate our solutions to those obtained within the maximum entropy principle by using the tsallis entropy

a quantitative measurement of regret theory this paper introduces a method to measure regret theory a popular theory of decision under uncertainty regret theory allows for violations of transitivity and it may seem paradoxical to quantitatively measure an intransitive theory we adopt the trade off method and show that it is robust to violations of transitivity our method makes no assumptions about the shape of the functions reflecting utility and regret it can be performed at the individual level taking account of preference heterogeneity our data support the main assumption of regret theory that people are disproportionately averse to large regrets even when event splitting effects are controlled for the findings are robust similar results were obtained in two measurements using different stimuli the data support the reliability of the trade off method its measurements could be replicated using different stimuli and were not susceptible to strategic responding

bi matching a new preference assessment method to reduce compatibility effects preference models and utility functions are often assessed by eliciting value trade offs among attributes prior research has shown that trade off judgments can be biased in systematic ways for example the attribute which is used as response receives more relative subjective weight i e the so called scale compatibility effects tversky et al tversky a s sattath p slovic 1988 contingent weighting in judgment and choice psych rev 95 371 384 this paper proposes a new procedure to elicit value trade offs called bidimensional matching or bi matching designed to alleviate this effect bi matching differs from traditional trade off judgments in that both attributes are adjusted simultaneously to reach indifference judgments bi matching is compared with simple matching and choice in four experimental studies to measure preferences for lotteries and riskless multiattribute alternatives the main results are 1 bi matching produces trade offs intermediate between those derived from matching on the more important attribute and matching on the less important attribute although closer to the former 2 the trade offs derived from choice reflect more relative weight on the more important dimension than those from bi matching 3 bi matching appears to reduce response error compared to standard matching these results are generally consistent with theoretical predictions we discuss the normative question of which preference assessment method is preferable the current results as a whole and the built in features of the bi matching procedure already position this elicitation method as a worthwhile alternative to traditional methods for helping decision makers introspect and construct their value trade offs

the application of preconditioning in viscous flows a time derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows has been developed the algorithm uses a preconditioning matrix that introduces well conditioned eigenvalues while simultaneously avoiding nonphysical time reversals for viscous flows the resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters at very diffusive flows thereby ensuring rapid convergence for very viscous flows as well as for inviscid flows computational capabilities are demonstrated through computation of a wide variety of problems convergence rates are shown to be accelerated by as much as two orders of magnitudes while providing solutions that are indentical to those obtained without preconditioning method

preconditioned hlle method for flows at all mach numbers a two dimensional preconditioned multigrid navier stokes solver has been developed for all mach number viscous flows for the computation of all mach number flows a local preconditioning technique with a modified reference velocity was used to extend the harten lax van leer einfeldt hlle scheme which has good characteristics for compressible viscous flows the developed methods used to compute several representative steady problems grid refinement and parametric studies are performed to verify the performance the results show that the preconditioned hlle scheme can be successfully applied to a wide variety of flows and that the implicit multigrid solver provides good convergence for the test problems

variational methods in nonextensive tsallis statistics a comparative study abstract in the context of nonextensive tsallis statistics sensible examples are employed in order to compare the variational method proposed in phys rev lett 80 1998 218 with the one in j phys a 26 1993 l893 these examples are such that they can be solved exactly thus a comparison of the exact result with the approximated ones is possible the analysis of these examples indicates that the calculation related to the first variational method is easier to work with than the other method in particular when one is trying to apply the last variational method the calculation of the approximated case can be more cumbersome than solving the exact one

sources of bias in assessment procedures for utility functions utility functions are an important component of normative decision analysis in that they characterize the nature of people s risk taking attitudes in this paper we examine various factors that make it difficult to speak of the utility function for a given person similarly we show that it is questionable to pool risk propensity data across studies for descriptive purposes that differ in the elicitation methods employed the following five sources of bias or indeterminacy are hypothesized and demonstrated first certainty equivalence methods generally yield greater risk seeking than probability equivalence methods second the probability and outcome levels used in reference lotteries induce systematic bias third combining gain and loss domains yields different utility measures than separate examinations of the two domains fourth whether a risk is assumed or transferred away exerts a significant influence on people s preferences in ways counter to expected utility theory finally context or frami

numerical simulations of a transient injection flow at low mach number regime in this paper a transient injection flow at low mach number regime is investigated three different methods are used and analyzed two of them are based on asymptotic models of the navier stokes equations valid for small mach numbers whereas the other is based on the full compressible navier stokes equations with particular care given to the discretization at low mach numbers numerical solutions are computed both with or without the gravity force finally the performance of the solvers in terms of cpu time consumption is investigated and the sensitivity of the solution to some parameters which affect cpu time is also performed

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

perturbation and variational methods in nonextensive tsallis statistics a unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on tsallis entropy is given here in the case of the variational method the bogoliubov inequality is generalized in a very natural way following the feynman proof for the usual statistical mechanics the inequality turns out to be form invariant with respect to the entropic index q the method is illustrated with a simple example in classical mechanics the formalisms developed here are expected to be useful in the discussion of nonextensive systems

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

computations of homogeneous equilibrium two phase flows with accurate and efficient shock stable schemes for accurate and efficient computations of compressible gas liquid two phase mixture flows the ausmpw and roem schemes for which the accuracy efficiency and robustness have been successfully demonstrated in gas dynamics are extended to two phase flows at all speeds from the mixture equations of state a new shock discontinuity sensing term suitably scaled for two phase flows is derived and its performance is validated in addition several numerical difficulties appearing in the development of the two phase ausmpw and roem schemes are analyzed and successfully cured the two phase ausmpw and roem schemes are then efficiently preconditioned for the simulation of all mach number flows by employing the existing ausm or harten lax van leer with contact restoration types of preconditioning strategies various gas liquid two phase flows from highly compressible to nearly incompressible flow conditions are tested the numerical results show the accurate and robust behavior of the proposed schemes for all speeds of two phase flows

making descriptive use of prospect theory to improve the prescriptive use of expected utility this paper proposes a quantitative modification of standard utility elicitation procedures such as the probability and certainty equivalence methods to correct for commonly observed violations of expected utility traditionally decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities however descriptive violations of expected utility bias utility elicitations that such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that under expected utility should have yielded identical utilities as it is not clear how to correct for these biases without further knowledge of their size or nature most utility elicitations still calculate utilities by means of the expected utility formula this paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory it presents quantitative corrections for the probability and certainty equivalence methods if interactive sessions to correct for biases are not possible then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions in an experiment the discrepancies between the probability and certainty equivalence methods are removed by the authors proposal

variational method in generalized statistical mechanics concavity properties of a recently generalized not necessarily extensive entropy enable among others the generalization of the bogolyubov inequality hence of the variational method in equilibrium statistical mechanics

a reconstructed discontinuous galerkin method based on a hierarchical weno reconstruction for compressible flows on tetrahedral grids a reconstructed discontinuous galerkin rdg method based on a hierarchical weno reconstruction termed hweno p 1p 2 in this paper designed not only to enhance the accuracy of discontinuous galerkin methods but also to ensure the nonlinear stability of the rdg method is presented for solving the compressible euler equations on tetrahedral grids in this hweno p 1p 2 method a quadratic polynomial solution p 2 is first reconstructed using a hermite weno reconstruction from the underlying linear polynomial p 1 discontinuous galerkin solution to ensure the linear stability of the rdg method and to improve the efficiency of the underlying dg method by taking advantage of handily available and yet invaluable information namely the derivatives in the dg formulation the stencils used in the reconstruction involve only von neumann neighborhood adjacent face neighboring cells and thus are compact the first derivatives of the quadratic polynomial solution are then reconstructed using a weno reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities thus ensuring the nonlinear stability of the rdg method the developed hweno p 1p 2 method is used to compute a variety of flow problems on tetrahedral meshes to demonstrate its accuracy robustness and non oscillatory property the numerical experiments indicate that the hweno p 1p 2 method is able to capture shock waves within one cell without any spurious oscillations and achieve the designed third order of accuracy one order accuracy higher than the underlying dg method

probability versus certainty equivalence methods in utility measurement are they equivalent certainty equivalence ce and probability equivalence pe methods are the two most frequently used procedures for constructing von neumann morgenstern utility functions in this paper we compare these methods experimentally using a two stage within subject design by asking subjects first for a ce judgment and later for a related pe judgment or vice versa a consistency test is devised which any deterministic expectation model including those allowing probability transformations should meet using four related experiments this consistency test is applied separately to gain and loss questions and to the two sequences of linked equivalence judgments namely ce pe and pe ce the empirical results reveal serious inconsistencies between the ce and pe responses for each of the four experiments the extent of discrepancy depends strongly on the subject s initial risk attitude and whether the gain or loss domain is examined to explain the complex pattern of results the second part of the paper explores several plausible hypotheses the first of these concerns the role of random error in either the responses or the utility function itself it is shown that both can lead to bias although not of a type that could explain our results thereafter shifts in reference points are examined a particular reframing of the pe response mode is postulated in which a pure gamble is psychologically translated into a mixed one leading to increased risk aversion this hypothesis which is also supported by other evidence offers a complete and simple explanation of the results finally several other behavioral hypotheses are examined after developing a weighted average model to simulate them they concern anchoring effects differences in salience between the probability and outcome dimensions strategic misrepresentation regret or rejoice influences and endowment effects although each hypothesis predicts some type of bias none of these five could singly explain the particular pattern of bias observed in general the study demonstrates 1 that serious discrepancies exist between the ce and pe methods of utility measurement 2 that the particular results are incompatible with traditional deterministic choice models 3 how random response errors through propagation can induce systematic biases in the utility function 4 that reframing of the pe mode offers a simple reference shift explanation of the complex findings and 5 how various heuristics and biases can be operationalized and simulated to assess their effects on utility measurement as such this study represents a further step toward a systematic investigation of response mode biases in utility measurement

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

low diffusion flux splitting methods for flows at all speeds methods for extending the advective upwind splitting method ausm family of low diffusion flux splitting schemes to operate effectively at all flow speeds are developed the extensions developed are designed for use with time derivative preconditioning and are based on the idea that the speed of sound should cease to be an important scaling parameter for the diffusive contributions to the interface flux as the mach number becomes small using this criterion alternative definitions for the interface mach numbers are developed and methods for ensuring pressure velocity coupling at low speeds are formulated results are presented for inviscid flows through a channel at various mach numbers developing viscous flow in a two dimensional duct driven cavity flows at various mach and reynolds numbers flow over a backward facing step and hydrogen nitrogen mixing layers

extension of harten lax van leer scheme for flows at all speeds the harten lax and van leer with contact restoration hllc scheme has been modified and extended in conjunction with time derivative preconditioning to compute flow problems at all speeds it is found that a simple modification of signal velocities in the hllc scheme based on the eigenvalues of the preconditioned system is only needed to reduce excessive numerical diffusion at the low mach number the modified scheme has been implemented and used to compute a variety of flow problems in both two and three dimensions on unstructured grids numerical results obtained indicate that the modified hllc scheme is accurate robust and efficient for flow calculations across the mach number range istorically numerical algorithms for the solution of the euler and navier stokes equations are classified as either pressure based or density based solution methods the pressurebased methods originally developed and well suited for incompressible flows are typically based on the pressure correction techniques they usually use a staggered grid and solve the governing equations in a segregated manner the density based methods originally developed and robust for compressible flows use time arching procedures to solve the hyperbolic system of governing equations in a coupled manner in general density based methods are not suitable for efficiently solving low mach number or incompressible flow problems because of large ratio of acoustic and convective timescales at the low speed flow regimes to alleviate this stiffness and associated convergence problems time derivative preconditioning techniques have been developed and used successfully for solving low machnumber and incompressible flows by many investigators including chorin 1 choi and merkle 2 turkel 3 weiss and smith 4 and dailey and pletcher 5 among others such methods seek to modify the time component of the governing equations so that the convergence can be made independent of mach number this is accomplished by altering the acoustic speeds of the system so that all eigenvalues become of the same order and thus condition number remains bounded independent of the mach number of the flows over the last two decades characteristic based upwind methods have established themselves as the methods of choice for prescribing the numerical fluxes for compressible euler equations when these upwind methods are used to compute the numerical fluxes for the preconditioned euler equations solution accuracy at low speeds can be compromised unless the numerical flux formulation is modified to take into account the eigensystem of the precondi

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated