continuous and discrete latent structure models for item response data relations are examined between latent trait and latent class models for item response data conditions are given for the two latent class and two parameter normal ogive models to agree and relations between their item parameters are presented generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes and methods are presented for relating latent class models to factor models for dichotomized variables results are illustrated using data from the law school admission test previously analyzed by several authors

analysis of the absorbing layers for the weakly compressible lattice boltzmann methods abstract it has been demonstrated that lattice boltzmann methods lbms are very efficient for computational aeroacoustics caa in order to address the issue of absorbing acoustic boundary conditions for lbm three kinds of damping terms are proposed and added to the right hand side of the lbm governing equations according to the classical theory these terms play an important role to damp and minimize the acoustic wave reflections from computational boundaries the corresponding macroscopic equations with the damping terms are recovered for analyzing the macroscopic behaviors of the these damping terms and determining the critical absorbing strength the dissipative and dispersive properties of the proposed absorbing layer terms are then further analyzed considering the linearized lbm equations they are explored in the wave number spaces via the von neumann analysis the related damping strength critical values and the optimal absorbing term are discussed finally some benchmark problems are implemented to assess the theoretical results

finite difference lattice boltzmann method for compressible thermal fluids a splitting method to solve the modeled lattice boltzmann equation the splitting technique permits the boundary conditions for the lattice boltzmann equation to be set as conveniently as those required for the finite difference solution of the navier stokes equations it is shown that the compressible navier stokes equation can be recovered fully from this approach however the formulation requires the solution of a poisson equation governing a secondorder tensor thus constructed the method has no arbitrary constants the proposed method is used to simulate thermalcouette flow aeroacoustics andshockstructureswithanextendedthermodynamicsmodel thesimulations are carried out using a high order finite difference scheme with a two dimensional nine velocity lattice all simulations are performed using a single relaxation time and a set of constants deduced from the derivation it is found that the finite difference lattice boltzmann method is able to correctly replicate viscous effects in thermal couette flows aeroacoustics andshockstructures thesolutionsobtainedareidenticaleithertoanalyticalresults or obtained by solving the compressible navier stokes equations using a direct numerical simulation technique

rasch models for item bundles this paper discusses the application of a class of rasch models to situations where test items are grouped into subsets and the common attributes of items within these subsets brings into question the usual assumption of conditional independence the models are all expressed as particular cases of the random coefficients multinomial logit model developed by adams and wilson this formulation allows a very flexible approach to the specification of alternative models and makes model testing particularly straightforward the use of the models is illustrated using item bundles constructed in the framework of the solo taxonomy of biggs and collis

painleve equations nonlinear special functions the six painleve equations pi pvi were first discovered about a hundred years ago by painleve and his colleagues in an investigation of nonlinear second order ordinary differential equations recently there has been considerable interest in the painleve equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering consequently the painleve equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations despite being nonlinear equations although first discovered from strictly mathematical considerations the painleve equations have arisen in a variety of important physical applications including statistical mechanics plasma physics nonlinear waves quantum gravity quantum field theory general relativity nonlinear optics and fibre optics the painleve equations may be thought of a nonlinear analogues of the classical special functions they possess hierarchies of rational solutions and one parameter families of solutions expressible in terms of the classical special functions for special values of the parameters further the painleve equations admit symmetries under affine weyl groups which are related to the associated backlund transformations in this paper i discuss some of the remarkable properties which the painleve equations possess including connection formulae backlund transformations associated discrete equations and hierarchies of exact solutions in particular the second painleve equation pii is used to illustrate these properties and some of the applications of pii are also discussed

the recurrence coefficients of semi classical laguerre polynomials and the fourth painleve equation we show that the coefficients of the three term recurrence relation for orthogonal polynomials with respect to a semi classical extension of the laguerre weight satisfy the fourth painleve equation when viewed as functions of one of the parameters in the weight we compare different approaches to derive this result namely the ladder operators approach the isomonodromy deformations approach and combining the toda system for the recurrence coefficients with a discrete equation we also discuss a relation between the recurrence coefficients for the freud weight and the semi classical laguerre weight and show how it arises from the backlund transformation of the fourth painleve equation

universal characters integrable chains and the painleve equations abstract the universal character is a generalization of the schur polynomial attached to a pair of partitions see adv math 74 1989 57 we prove that the universal character solves the darboux chain the n periodic closing of the chain is equivalent to the painleve equation of type a n 1 1 consequently we obtain an expression of rational solutions of the painleve equations in terms of the universal characters

on compensation in multidimensional response modeling the issue of compensation in multidimensional response modeling is addressed we show that multidimensional response models are compensatory in their ability parameters if and only if they are monotone in addition a minimal set of assumptions is presented under which the mles of the ability parameters are also compensatory in a recent series of articles beginning with hooker finkelman and schwartzman 2009 in this journal the second type of compensation was presented as a paradoxical result for certain multidimensional response models leading to occasional unfairness in maximum likelihood test scoring first it is indicated that the compensation is not unique and holds generally for any multiparameter likelihood with monotone score functions second we analyze why in spite of its generality the compensation may give the impression of a paradox or unfairness

on the application of the lattice boltzmann method to the investigation of glottal flow the production of voice is directly related to the vibration of the vocal folds which is generated by the interaction between the glottal flow and the tissue of the vocal folds in the current study the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations the numerical investigation is based on the lattice boltzmann method lbm which is an alternative approach within computational fluid dynamics compared to the traditional navier stokes computational fluid dynamics methods the lbm is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator the multiple relaxation time model was used to improve the numerical stability the results obtained with lbm were compared to the results provided by a traditional navier stokes solver and experimental data it was shown that lbm results are satisfactory for all the investigated cases

item selection in multidimensional computerized adaptive testing gaining information from different angles over the past thirty years obtaining diagnostic information from examinees item responses has become an increasingly important feature of educational and psychological testing the objective can be achieved by sequentially selecting multidimensional items to fit the class of latent traits being assessed and therefore multidimensional computerized adaptive testing mcat is one reasonable approach to such task this study conducts a rigorous investigation on the relationships among four promising item selection methods d optimality kl information index continuous entropy and mutual information some theoretical connections among the methods are demonstrated to show how information about the unknown vector can be gained from different perspectives two simulation studies were carried out to compare the performance of the four methods the simulation results showed that mutual information not only improved the overall estimation accuracy but also yielded the smallest conditional mean squared error in most region of in the end the overlap rates were calculated to empirically show the similarity and difference among the four methods

paradoxical results in multidimensional item response theory in multidimensional item response theory mirt it is possible for the estimate of a subject s ability in some dimension to decrease after they have answered a question correctly this paper investigates how and when this type of paradoxical result can occur we demonstrate that many response models and statistical estimates can produce paradoxical results and that in the popular class of linearly compensatory models maximum likelihood estimates are guaranteed to do so in light of these findings the appropriateness of multidimensional item response methods for assigning scores in high stakes testing is called into question

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

measuring latent quantities a distinction is proposed between measures and predictors of latent variables the discussion addresses the consequences of the distinction for the true score model the linear factor model structural equation models longitudinal and multilevel models and item response models a distribution free treatment of calibration and error of measurement is given and the contrasting properties of measures and predictors are examined

constrained least squares estimators of oblique common factors an expression is given for weighted least squares estimators of oblique common factors constrained to have the same covariance matrix as the factors they estimate it is shown that if as in exploratory factor analysis the common factors are obtained by oblique transformation from the lawley rao basis the constrained estimators are given by the same transformation finally a proof of uniqueness is given

from continuous painleve iv to the asymmetric discrete painleve i we examine the discrete equation that is obtained from the schlesinger transformations of the continuous painleve iv equation the use of the schlesinger transformations naturally establishes the lax pair of the discrete equation which is an asymmetric form of d p and has as continuous limit we analyse the transformations of the discrete equation and show that they lead to a self dual description where the discrete equation and the schlesinger s play the same role finally using the relation between and asymmetric d we examine in detail the special solutions of both equations

a study on the fourth q painleve equation a q difference analogue of the fourth painleve equation is proposed its symmetry structure and some particular solutions are investigated

computation of flow noise using source terms in linearized euler s equations an acoustic analogy using linearized euler s equations lee forced with aerodynamic source terms is investigated to computetheacousticfare eld thishybridmethod isappliedto threemodelproblemssimulatedby solving navier stokes equations in this way its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the navier stokes equations the noise radiated by two corotating vortices is studied e rst in a medium at rest and second in a mean sheared e ow with no convection velocity then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated in this case a simplie ed formulation of lee is proposed to prevent the exponential growth of instability waves the acoustic e elds obtained by solving lee are in good agreement with the reference solution this study shows that the source terms introduced into the lee are appropriate for free sheared e ows and that acoustic mean e ow interactions are properly taken into account in the wave operator nomenclature b half width of the monopolar source c sound velocity e f h vectors in linearized euler s equations lee f frequency f0 fundamental frequency of the mixing layer k complex wave number kr ciki m mach number p pressure re reynolds number rc vortex core radius r0 initial half distance between the two vortices s sound source vector in lee si source terms in the momentum equations t period tij lighthill s tensor t time u unknown vector in lee u1 slow stream velocity of the mixing layer u2 rapid stream velocity of the mixing layer u velocity vector u1 u2 v initial tangential velocity of vortices

generalizations of paradoxical results in multidimensional item response theory maximum likelihood and bayesian ability estimation in multidimensional item response models can lead to paradoxical results as proven by hooker finkelman and schwartzman psychometrika 74 3 419 442 2009 changing a correct response on one item into an incorrect response may produce a higher ability estimate in one dimension furthermore the conditions under which this paradox arises are very general and may in fact be fulfilled by many of the multidimensional scales currently in use this paper tries to emphasize and extend the generality of the results of hooker et al by 1 considering the paradox in a generalized class of irt models 2 giving a weaker sufficient condition for the occurrence of the paradox with relations to an important concept of statistical association and by 3 providing some additional specific results for linearly compensatory models with special emphasis on the factor analysis model

coalescence cascades and special function solutions for the continuous and discrete painleve equations we present a systematization of the special function type solutions of continuous and discrete painleve equations our method is to start from and construct its special solutions from the solutions of the hypergeometric equation and by coalescence obtain the lower painleve equations together with their special solutions in the discrete case we study the symmetric one component three point mapping forms of discrete painleve equations starting from d

a generalized speed accuracy response model for dichotomous items we propose a generalization of the speed accuracy response model sarm introduced by maris and van der maas psychometrika 77 615 633 2012 in these models the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled our generalization is similar to that of the one parameter logistic or rasch model to the two parameter logistic or birnbaum model in item response theory an expectation maximization em algorithm for estimating model parameters and standard errors was developed furthermore methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score the presented methods were evaluated in a small simulation study the results of which indicated good parameter recovery and reasonable type i error rates for the residuals finally the methods were applied to two real data sets it was found that the two parameter sarm showed improved fit compared to the one parameter sarm in both data sets

loglinear rasch model tests existing statistical tests for the fit of the rasch model have been criticized because they are only sensitive to specific violations of its assumptions contingency table methods using loglinear models have been used to test various psychometric models in this paper the assumptions of the rasch model are discussed and the rasch model is reformulated as a quasi independence model the model is a quasi loglinear model for the incomplete subgroup score item 1 item 2 itemk contingency table using ordinary contingency table methods the rasch model can be tested generally or against less restrictive quasi loglinear models to investigate specific violations of its assumptions

a new explanation and proof of the paradoxical scoring results in multidimensional item response models in multidimensional item response models paradoxical scoring effects can arise wherein correct answers are penalized and incorrect answers are rewarded for the most prominent class of irt models the class of linearly compensatory models a general derivation of paradoxical scoring effects based on the geometry of item discrimination vectors is given which furthermore corrects an error in an established theorem on paradoxical results this approach highlights the very counterintuitive way in which item discrimination parameters and also factor loadings have to be interpreted in terms of their influence on the latent ability estimate it is proven that despite the error in the original proof the key result concerning the existence of paradoxical effects remains true although the actual relation to the item parameters is shown to be a more complicated function than previous results suggested the new proof enables further insights into the actual mathematical causation of the paradox and generalizes the findings within the class of linearly compensatory models

latent curve analysis as a method for representing development latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth maximum likelihood parameter estimates and associated asymptotic tests follow directly these procedures may be viewed as an alternative to standard repeated measures anova and to first order auto regressive methods as formulated the model encompasses cohort sequential designs and allow for period or practice effects a numerical illustration using data initially collected by nesselroade and baltes is presented

paradoxical results and item bundles hooker finkelman and schwartzman psychometrika 2009 in press defined a paradoxical result as the attainment of a higher test score by changing answers from correct to incorrect and demonstrated that such results are unavoidable for maximum likelihood estimates in multidimensional item response theory the potential for these results to occur leads to the undesirable possibility of a subject s best answer being detrimental to them this paper considers the existence of paradoxical results in tests composed of item bundles when compensatory models are used we demonstrate that paradoxical results can occur when bundle effects are modeled as nuisance parameters for each subject however when these nuisance parameters are modeled as random effects or used in a bayesian analysis it is possible to design tests comprised of many short bundles that avoid paradoxical results and we provide an algorithm for doing so we also examine alternative models for handling dependence between item bundles and show that using fixed dependency effects is always guaranteed to avoid paradoxical results

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

on separable tests correlated priors and paradoxical results in multidimensional item response theory this paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee we demonstrate that when three or more ability dimensions are being used paradoxical results can be induced by using priors in which all abilities are positively correlated where they would not occur if the abilities were modeled as being independent in the case of separable tests we demonstrate the mathematical causes of paradoxical results develop a computationally feasible means to check whether they can occur in any given test and demonstrate a class of prior covariance matrices that can be guaranteed to avoid them

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

numerical simulations of fluid structure interactions in single reed mouthpieces most single reed woodwind instrument models rely on a quasistationary approximation to describe the relationship between the volume flow and the pressure difference across the reed channel semiempirical models based on the quasistationary approximation are very useful in explaining the fundamental characteristics of this family of instruments such as self sustained oscillations and threshold of blowing pressure however they fail at explaining more complex phenomena associated with the fluid structure interaction during dynamic flow regimes such as the transient and steady state behavior of the system as a function of the mouthpiece geometry previous studies have discussed the accuracy of the quasistationary approximation but the amount of literature on the subject is sparse mainly due to the difficulties involved in the measurement of dynamic flows in channels with an oscillating reed in this paper a numerical technique based on the lattice boltzmann method and a finite difference scheme is proposed in order to investigate the characteristics of fully coupled fluid structure interaction in single reed mouthpieces with different channel configurations results obtained for a stationary simulation with a static reed agree very well with those predicted by the literature based on the quasistationary approximation however simulations carried out for a dynamic regime with an oscillating reed show that the phenomenon associated with flow detachment and reattachment diverges considerably from the theoretical assumptions furthermore in the case of long reed channels the results obtained for the vena contracta factor are in significant disagreement with those predicted by theory for short channels the assumption of constant vena contracta was found to be valid for only 40 of the duty cycle

studies on the painlev equations iii second and fourth painlev equations p ii andp iv etude des transformations birationnelles canoniques du systeme de painleve associe a chacune des equations

universal characters and an extension of the kp hierarchy the universal character is a polynomial attached to a pair of partitions and is a generalization of the schur polynomial in this paper we define vertex operators which play roles of raising operators for the universal character by means of the vertex operators we obtain a series of non linear partial differential equations of infinite order called the uc hierarchy we regard it as an extension of the kp hierarchy we investigate also solutions of the uc hierarchy the totality of the space of solutions forms a direct product of two infinite dimensional grassmann manifolds and its infinitesimal transformations are described in terms of the lie algebra

new similarity solutions for the modified boussinesq equation in this paper the author presents some new similarity solutions of the modified boussinesq equation which is a completely integrable soliton equation these new similarity solutions include reductions to the second and fourth painleve equations which are not obtainable using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method which involves no group theoretical techniques

monodromy of certain painleve vi transcendents and reflection groups we study the global analytic properties of the solutions of a particular family of painleve vi equations with the parameters 0 1 2 and 2 2 1 2 with arbitrary 2 we introduce a class of solutions having critical behaviour of algebraic type and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space the analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group we show that the finite orbits of this action correspond to the algebraic solutions of our painleve vi equation and use this result to classify all of them we prove that the algebraic solutions of our painleve vi equation are in one to one correspondence with the regular polyhedra or star polyhedra in the three dimensional space

finite difference lattice boltzmann method applied to acoustic scattering problems this paper reports on an attempt to simulate acoustic waves scattering using a finite difference lattice boltzmann method based on an alternative lattice equilibrium particle distribution function constructed for compressible thermal fluids the studies focus on acoustics scattering by a zero circulation vortex and by an isolated thermal source with no heat gain loss two limiting cases of each type of scattering are examined one is the case of an incoming acoustic wave with a short wavelength and the other has a relatively long wavelength compared with the characteristic dimension of the obstacle these scattering problems have been treated previously using a conventional lattice boltzmann method and a gas kinetic scheme the results showed that these methods were only able to simulate the short wavelength limit case with fair accuracy for the two types of acoustics scattering considered because the present approach is able to recover the compressible navier stokes equations with correct fluid properties the finite difference solution of the proposed alternative modeled lattice boltzmann equation allows the limiting cases of the acoustics scattering problems to be calculated without numerical instability the results thus obtained are in agreement either with analysis or with results obtained from direct aeroacoustics simulations employing the compressible navier stokes equations

modeled boltzmann equation and its application to direct aeroacoustics simulation the bhatnagar gross and krook modeled boltzmann equation has been applied to simulate different fluid dynamics problems with varying degrees of success however its application to direct aeroacoustic computation is less successful one possible reason could be its inability to recover the state equation correctly for a diatomic gas and hence an inaccurate determination of the speed of sound the present study reports on the development of an improved modeled boltzmann equation for aeroacoustics simulation the approach is to modify the maxwellian distribution normally assumed for the equilibrium particle distribution function constraints imposed are the exact recovery of the state equation for a diatomic gas and the euler equations without invoking the small mach number assumption thus formulated a distribution function consisting of the maxwellian distribution plus three other terms that attempt to account for particle particle collisions is obtained a velocity lattice method is used to solve the improved modeled boltzmann equation using an equivalent lattice equilibrium distribution function the simulations are validated against benchmark aeroacoustic problems whose solutions are deduced from a direct numerical simulation of the euler equations the results of the improved modeled boltzmann equation obtained using a smaller computational domain are in excellent agreement with those deduced from direct numerical simulation using a larger computational domain thus verifying the viability and correctness of the modified equilibrium distribution function

one step aeroacoustics simulation using lattice boltzmann method the lattice boltzmann method lbm is a numerical simplification of the boltzmann equation of the kinetic theory of gases that describes fluid motions by tracking the evolution of the particle velocity distribution function based on linear streaming with nonlinear collision if the bhatnagar gross krook bgk collision model is invoked the velocity distribution function in this mesoscopic description of nonlinear fluid motions is essentially linear this intrinsic feature of lbm can be exploited for convenient parallel programming which makes itself particularly attractive for one step aeroacoustics simulations it is shown that the compressible navier stokes equations and the ideal gas equation of state can be correctly recovered by considering the translational and rotational degrees of freedom of diatomic gases in the internal energy and using a multiscale chapman enskog expansion assuming two relaxation times in the bgk model allows the temperature dependence of the first coefficient of viscosity of diatomic gases to be replicated the modified lbm model is solved using a two dimensional 9 discretized and a twodimensional 13 discretized velocity lattices three cases are selected to validate the one step lbm aeroacoustics simulation they are the one dimensional acoustic pulse propagation the circular acoustic pulse propagation and the propagation of acoustic vorticity and entropy pulses in a uniform stream the accuracy of the lbm is established by comparing with direct numerical simulation dns results obtained by solving the governing equations using a finite difference scheme the tests show that the proposed lbm and the dns give identical results thus suggesting that the lbm can be used to simulate aeroacoustics problems correctly

determinant structure of the rational solutions for the painleve iv equation rational solutions for the painleve iv equation are investigated by hirota bilinear formalism it is shown that the solutions in one hierarchy are expressed by 3 reduced schur functions and those in another two hierarchies by casorati determinants of the hermite polynomials or by a special case of the schur polynomials

on the sampling theory roundations of item response theory models item response theory it models are now in common use for the analysis of dichotomous item responses this paper examines the sampling theory foundations for statistical inference in these models the discussion includes some history on the stochastic subject versus the random sampling interpretations of the probability in irt models the relationship between three versions of maximum likelihood estimation for irt models estimating versus estimating predictors irt models and loglinear models the identifiability of irt models and the role of robustness and bayesian statistics from the sampling theory perspective

connection between quantum systems involving the fourth painleve transcendent and k step rational extensions of the harmonic oscillator related to hermite exceptional orthogonal polynomial the purpose of this communication is to point out the connection between a 1d quantum hamiltonian involving the fourth painleve transcendent piv obtained in the context of second order supersymmetric quantum mechanics and third order ladder operators with a hierarchy of families of quantum systems called k step rational extensions of the harmonic oscillator and related with multi indexed xm1 m2 mk hermite exceptional orthogonal polynomials of type iii the connection between these exactly solvable models is established at the level of the equivalence of the hamiltonians using rational solutions of the fourth painleve equation in terms of generalized hermite and okamoto polynomials we also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving darboux crum and krein adler supercharges their zero modes and the corresponding energies these results will demonstrate and clarify the relation observed for a particular case in previous papers

determinant structure of the rational solutions for the painleve ii equation two types of determinant representations of the rational solutions for the painleve ii equation are discussed by using the bilinear formalism one of them is a representation by the devisme polynomials and another one is hankel determinant representation they are derived from the determinant solutions of the kp hierarchy and toda lattice respectively

the fourth painleve equation and associated special polynomials in this article rational solutions and associated polynomials for the fourth painleve equation are studied these rational solutions of the fourth painleve equation are expressible as the logarithmic derivative of special polynomials the okamoto polynomials the structure of the roots of these okamoto polynomials is studied and it is shown that these have a highly regular structure the properties of the okamoto polynomials are compared and contrasted with those of classical orthogonal polynomials further representations are given of the associated rational solutions in the form of determinants through schur functions

the third painleve equation and associated special polynomials in this paper we are concerned with rational solutions algebraic solutions and associated special polynomials with these solutions for the third painleve equation piii these rational and algebraic solutions of piii are expressible in terms of special polynomials defined by second order bilinear differential difference equations which are equivalent to toda equations the structure of the roots of these special polynomials is studied and it is shown that these have an intriguing highly symmetric and regular structure using the hamiltonian theory for piii it is shown that these special polynomials satisfy pure difference equations fourth order bilinear differential equations as well as differential difference equations further representations of the associated rational solutions in the form of determinants through schur functions are given

modeled boltzmann equation and its application to shock capturing simulation a modified equilibrium distribution function for the bhatnagar gross krook type modeled boltzmann equation has recently been proposed the function was deduced using acoustics scaling to normalize the equation and allowed a correct recovery of similarly normalized euler equations it is a combination of a maxwellian distribution plus three other terms that are moments of particle velocity the lattice counterpart of the modified equilibrium distribution function also led to an exact recovery of the euler equations therefore there is no mach number limitation in the entire approach this lattice counterpart was able to replicate aeroacoustics problems involving vorticity acoustic and entropy acoustic interactions correctly and the simulations were carried out using a finite difference lattice boltzmann method employing only a two dimensional nine velocity lattice thus formulated the numerical scheme has no arbitrary constants and all calculations were carried out using one single relaxation time and a set of constants derived from the analysis this paper investigates the validity and extent of the formulation to capture shocks and resolve contact discontinuity and expansion waves in one and two dimensional riemann problems the simulations are carried out using the same two dimensional nine velocity lattice and identical set of constants and relaxation time they are compared with theoretical results and those obtained by solving the euler equations directly using harten s first order numerical scheme good agreement is obtained for all test cases however the modified equilibrium distribution function is not suitable for shock structure simulation for that an exact recovery of the navier stokes equations is required

special polynomials associated with rational solutions of the fifth painleve equation in this paper special polynomials associated with rational and algebraic solutions of the fifth painleve equation pv are studied these special polynomials defined by second order bilinear differential difference equations which are equivalent to toda equations the structure of the zeroes of these special polynomials which involve a parameter is investigated and it is shown that these have an intriguing symmetric and regular structure for large negative values of the parameter the zeroes have an approximate triangular structure as the parameter increases the zeroes coalesce for certain values and eventually for large positive values of the parameter the zeroes also have an approximate triangular structure though with the orientation reversed in fact the interaction of the zeroes is solitonic in nature since the same pattern reappears with its orientation reversed

sound reflection at the open end of axisymmetric ducts issuing a subsonic mean flow a numerical study abstract this paper investigates the reflection of sound waves as they propagate toward the open end of ducts issuing a cold subsonic mean flow in a stagnant fluid the investigations are conducted by using a relatively new one step numerical technique known as the lattice boltzmann method the results obtained in terms of end correction l and magnitude of the pressure reflection coefficient r for an unflanged pipe model are in very good agreement with theoretical predictions and experimental data for the range of mach numbers m 0 15 and helmholtz numbers ka 1 5 simulations carried out for a similar pipe terminated by circular horns of different curvature radii show that r is independent of the horn geometry for strouhal numbers sr 0 4 sr 0 ka m for situations in which m 0 the amplification of the reflection coefficient magnitude that is r 1 is normally 20 percent higher than that observed for an unflanged pipe issuing an equal mach number flow furthermore the amplification maxima is found to occur always at sr 0 2 regardless of whether the pipe is unflanged or terminated by different circular horns conversely the results for the end correction are strongly dependent on the horn curvature for the low strouhal number limit the dimensionless end correction measured at the junction between the horn and the pipe with radius a becomes l a 0 31 for a horn whose curvature radius is 2 a and l a 0 62 for a horn with curvature radius equal to 4 a

stochastic order in dichotomous item response models for fixed adaptive and multidimensional tests dichotomous irt models can be viewed as families of stochastically ordered distributions of responses to test items this paper explores several properties of such distributions in particular it is examined under what conditions stochastic order in families of conditional distributions is transferred to their inverse distributions from two families of related distributions to a third family or from multivariate conditional distributions to a marginal distribution the main results are formulated as a series of theorems and corollaries which apply to dichotomous irt models one part of the results holds for unidimensional models with fixed item parameters the other part holds for models with random item parameters as used for example in adaptive testing or for tests with multidimensional abilities