the reduction of binary fuzzy relations and its applications this paper introduces the concept of t reduction of binary fuzzy relations and establishes its properties it presents an approach to providing the one valued restoration of any boundary transitive and t asymmetric binary fuzzy relation by its t reduction a theoretical basis for this approach is established showing that t reduction is the smallest fuzzy relation whose t transitive closure coincides with the given binary fuzzy relation and where an nxn fuzzy relation on a finite universe with cardinality n can be represented by n 1 values this approach opens up an original way for constructing the membership functions of certain binary fuzzy relations important examples for the application of this concept are given

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

the cutting of compositions this paper investigates the cutability of the fuzzy relational compositions the sup t composition the triangular compositions of bandler and kohout and their improved versions the theoretical and practical importance of fuzzy cuts is illustrated by means of a careful selection of results from the fuzzy literature some new potential properties of fuzzy implications operators and triangular norms that play an important role in this cutability study are introduced and discussed extensively the paper concludes with a study of the fuzzy cutability of the sup t composition

a multidimensional gas kinetic bgk scheme for hypersonic viscous flow this paper concerns the development and application of a gas kinetic scheme based on the bhatnagar gross krook bgk model for the navier stokes equations in the study of hypersonic viscous flow firstly we extend the gas kinetic navier stokes solver k xu a gas kinetic bgk scheme for the navier stokes equations and its connection with artificial dissipation and godunov method j comput phys 171 2001 289 335 by implementing a multidimensional particle propagation mechanism in the flux evaluation where the gradients of flow variables in both normal and tangential directions of a cell interface are explicitly included with the construction of a time averaged flux function an implicit bgk scheme with lu sgs method is constructed the main purpose of the current research is to pave the way to extend the current approach directly to the flow computation with unstructured mesh where the flow gradients in both parallel and perpendicular directions around a cell interface can be explicitly taken into account in a viscous flow computation in the numerical parts we concentrate on the computation of heat flux in laminar hypersonic viscous flows where complicated flow phenomena i e shock boundary layer interaction flow separation and viscous inviscid interaction will be encountered the cases studied include the type iv shock shock interaction around a circular cylinder and hypersonic flow passing through a double cone geometry in the hypersonic viscous flow in comparison with the capturing of velocity and pressure fields the accurate computation of stress and heat flux bears large difficulties in all cases studied here the heat fluxes obtained across body surfaces have good agreement with the experimental measurements

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

a lattice boltzmann scheme for incompressible multiphase flow and its application in simulation of rayleigh taylor instability in this paper we propose a new lattice boltzmann scheme for simulation of multiphase flow in the nearly incompressible limit the new scheme simulates fluid flows based on distribution functions the interfacial dynamics such as phase segregation and surface tension are modeled by incorporating molecular interactions the lattice boltzmann equations are derived from the continuous boltzmann equation with appropriate approximations suitable for incompressible flow the numerical stability is improved by reducing the effect of numerical errors in calculation of molecular interactions an index function is used to track interfaces between different phases simulations of the two dimensional rayleigh taylor instability yield satisfactory results the interface thickness is maintained at 3 4 grid spacings throughout simulations without artificial reconstruction steps

on the existence and construction of t transitive closures in this paper it is shown that any fuzzy relation r on an arbitrary universe x has a t transitive closure the triangular norm t involved is not subject to any conditions this existential result can be turned into an explicit expression in the case of a left continuous triangular norm t furthermore this continuity restriction vanishes in the case of a finite universe x in that case the explicit expression can also be operationalized

experimental study of compressible turbulent mixing layers compressible turbulent mixing layers have been investigated experimentally using pressure mesurements schlieren photographs and velocity measurements with a two component laser doppler velocimeter system seven mixing layer cases were examined with relative mach numbers ranging from 0 40 to 1 97 which spans the region of significant compressibility effects both the spatial development and similarty of the mixing layers were considered

fast solving method of fuzzy relational equation and its application to lossy image compression reconstruction a fast solving method of the solution for max continuous t norm composite fuzzy relational equation of the type g i j r sup t spl square a sub i sup t spl square b sub j i 1 2 i j 1 2 j where a sub i spl isin f x x x sub 1 x sub 2 x sub m bj spl isin f y y y sub 1 y sub 2 y sub n r spl isin f x spl times y and spl square max continuous t norm composition is proposed it decreases the computation time ijmn l t p to jm i n l p where l t and p denote the computation time of min t norm and relative pseudocomplement operations respectively by simplifying the conventional reconstruction equation based on the properties of t norm and relative pseudocomplement the method is applied to a lossy image compression and reconstruction problem where it is confirmed that the computation time of the reconstructed image is decreased to 1 335 6 the compression rate being 0 0351 and it achieves almost equivalent performance for the conventional lossy image compression methods based on discrete cosine transform and vector quantization

a study of methods of choosing the smoothing parameter in image restoration by regularization the method of regularization is portrayed as providing a compromise between fidelity to the data and smoothness with the tradeoff being determined by a scalar smoothing parameter various ways of choosing this parameter are discussed in the case of quadratic regularization criteria they are compared algebraically and their statistical properties are comparatively assessed from the results of all extensive simulation study based on simple images

emitter waveform estimation in array signal processing this paper considers the problem of estimating the signal waveforms from the noisy data obtained with an array of receiving sensors the maximum likelihood ml waveform estimate derived under the assumption that the signals are deterministic is compared with the minimum mean square error linear mmsel estimate derived under the assumption of stochastic signals when the signals are assumed to be random the mmsel estimate has by construction a smaller mse than the ml estimate a ridge type extension of the mmsel estimate is shown to still possess smaller mse than the ml estimate under a reasonable condition even if the signals are assumed to be deterministic a numerical study provides more quantitative insights into the performance of several waveform estimators including those mentioned above

a third order gas kinetic cpr method for the euler and navier stokes equations on triangular meshes abstract a third order accurate gas kinetic scheme based on the correction procedure via reconstruction cpr framework is developed for the euler and navier stokes equations on triangular meshes the scheme combines the accuracy and efficiency of the cpr formulation with the multidimensional characteristics and robustness of the gas kinetic flux solver comparing with high order finite volume gas kinetic methods the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes unlike the traditional cpr method where the inviscid and viscous terms are treated differently the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model in addition the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation achieving high order accuracy in both space and time within a single step numerical tests with a wide range of flow problems from nearly incompressible to supersonic flows with strong shocks for both inviscid and viscous problems demonstrate the high accuracy and efficiency of the present scheme

on identification in fuzzy systems and its applications in control problems abstract the problem of identification in fuzzy systems described by the use of fuzzy equation is considered the identification method and its performance index is also presented the formal procedure of the identification algorithm is illustrated by means of a numerical example the possibility of using the proposed algorithm for the solution of a control problem is given as well

comparison of the generalized riemann solver and the gas kinetic scheme for inviscid compressible flow simulations the generalized riemann problem grp scheme for the euler equations and gas kinetic scheme gks for the boltzmann equation are two high resolution shock capturing schemes for fluid simulations the difference is that one is based on the characteristics of the inviscid euler equations and their wave interactions and the other is based on the particle transport and collisions the similarity between them is that both methods can use identical muscl type initial reconstructions around a cell interface and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time dependent flux function although both methods have been applied successfully to the inviscid compressible flow computations their performances have never been compared since both methods use the same initial reconstruction any difference is solely coming from different underlying mechanism in their flux evaluation therefore such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances since grp is so faithfully solving the inviscid euler equations the comparison can be also used to show the validity of solving the euler equations itself the numerical comparison shows that the grp exhibits a slightly better computational efficiency and has comparable accuracy with gks for the euler solutions in 1d case but the gks is more robust than grp for the 2d high mach number flow simulations the gks is absent from the shock instability and converges to the steady state solutions faster than the grp the grp has carbuncle phenomena likes a cloud hanging over exact riemann solvers the grp and gks use different physical processes to describe the flow motion starting from a discontinuity one is based on the assumption of equilibrium state with infinite number of particle collisions and the other starts from the non equilibrium free transport process to evolve into an equilibrium one through particle collisions the different mechanism in the flux evaluation deviates their numerical performance through this study we may conclude scientifically that it may not be valid to use the euler equations as governing equations to construct numerical fluxes in a discretized space with limited cell resolution to adapt the navier stokes ns equations is not valid either because the ns equations describe the flow behavior on the hydrodynamic scale and have no any corresponding physics starting from a discontinuity this fact alludes to the consistency of the euler and navier stokes equations with the continuum assumption and the necessity of a direct modeling of the physical process in the discretized space in the construction of numerical scheme when modeling very high mach number flows the development of numerical algorithm is similar to the modeling process in deriving the governing equations but the control volume here cannot be shrunk to zero

on the multidimensional gas kinetic bgk scheme this paper concerns the performance difference among the multidimensional md gas kinetic bgk scheme the corresponding quasi one dimensional q1d extension and the directional splitting ds scheme with kinetic boundary conditions the md scheme includes tangential slopes in the flux calculation which are absent in a q1d or ds method in spite of taking more computational time the md scheme is found to be able to capture the characteristics of rarefied flow having a boundary with curvature or a nonuniform temperature such as the inverted velocity distribution in rarefied cylindrical couette flow and the weak flow field induced by the temperature gradient of a body where the q1d fails the md scheme can also yield clearly better results in high speed microchannel flow and power law fluid flow between concentric rotating cylinders when compared with direct simulation monte carlo studies and analytic solutions in the low reynolds number flow around a naca0012 airfoil case the md scheme and the q1d method predict wall heat flux distribution with obvious difference the ds method predicts results nearly identical to those from q1d in these steady flow cases except that it can hardly give reasonable solutions in power law fluid case with viscous exponential factor away from unity correct prediction of the stress and the wall temperature gradient is considered responsible for this better performance in simulations of the scalar convection diffusion equation it is found that the inclusion of tangential slopes in the flux computation can clearly improve the temporal accuracy of the scheme in this case the ds scheme also shows good performance the present study suggests caution in adopting of the q1d extension or ds method in multidimensional flow when it is sensitive to the accuracy of stress or wall variable gradient calculations it is better to use the md scheme for high performance simulation

additive decomposition of fuzzy pre orders fuzzy pre orders reflexive and min transitive fuzzy relations constitute an important class of fuzzy relations by means of an indifference generator a fuzzy pre order can be decomposed additively into two parts an indifference relation and a strict preference relation when using a frank t norm as indifference generator we fully characterize the transitivity of these parts only in case the minimum operator is used as generator both parts are min transitive the transitivity of the indifference relation is determined by the frank t norms while the transitivity of the strict preference relation is determined by transforms of the nilpotent minimum t norm

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

a formal study of linearity axioms for fuzzy orderings abstract this contribution is concerned with a detailed investigation of linearity axioms for fuzzy orderings different existing concepts are evaluated with respect to three fundamental correspondences from the classical case linearizability of partial orderings intersection representation and one to one correspondence between linearity and maximality as a main result we obtain that it is virtually impossible to simultaneously preserve all these three properties in the fuzzy case if we do not require a one to one correspondence between linearity and maximality however we obtain that an implication based definition appears to constitute a sound compromise in particular if ukasiewicz type logics are considered

special properties closures and interiors of crisp and fuzzy relations this paper offers optimal definitions of the special properties which relations on a set may possess and which combine to define the classically important types of preorders both kinds of orders tolerances and equivalences the useful concept of local properties is introduced the definitions are shown to unify in a highly convenient way fuzzy and crisp considerations the concepts of closure and interior of a relation with respect to a property are defined necessary and sufficient conditions for the full existence of specific closures and interiors are given and formulae for all of them are presented and validated a widely important area of application of the closure and interior operators is discussed finally fast algorithms are given for the computer calculation of the more troublesome closures and a standardized procedure for the analysis of local orders is presented

unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement this paper describes a unified flow solver ufs for rarefied and continuum gas flows the ufs separates the rarefied and continuum flow domains and selects appropriate solvers to combine the efficiency of continuum models with the accuracy of kinetic models the direct numerical solution of the boltzmann transport equation is used in rarefied regions while kinetic schemes of continuum fluid dynamics are used elsewhere using similar computational techniques for the kinetic and continuum solvers and employing intelligent domain decomposition algorithms attain the efficiency and numerical stability of the ufs solutions of test problems are presented to illustrate the capabilities of the ufs for high and low speed flows it is shown that the ufs can dynamically adapt the computational mesh and automatically introduce and remove kinetic patches to provide significant savings by limiting molecular scale solutions only to the regions where they are needed

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

application of gas kinetic scheme with kinetic boundary conditions in hypersonic flow this work focuses on the application of the gas kinetic scheme based on the bhatnagar gross krook particle collision model in the hypersonic flow simulations kinetic boundary conditions with different accommodation coefficients are constructed and implemented in the scheme the numerical study is based on a laminar shock wave boundary layer interaction in a mach 10 flow passing through a hollow cylinder flare model the grid independent numerical results agree well with experimental measurements the utilization of the kinetic slip boundary condition is necessary to improve the agreement between the current results experimental measurements as well as direct simulation monte carlo solutions the effect of the variation of the accommodation coefficient on the flow solutions is quantitatively evaluated

on the construction of kinetic schemes a general method for the construction of kinetic schemes of evolutionary equations is illustrated with the simple example of the linear advection equation where the role of the collision effect is clarified theoretically and numerically the application to the compressible euler equation and navier stokes equation is explained the theoretical backgrounds of the existing kinetic schemes such as the pullin scheme for the euler equation and chou baganoff scheme and modified prendergast xu scheme for the navier stokes equation are unified and their intrinsic errors are revealed

a compressible navier stokes flow solver with scalar transport this paper concerns the extension of the gas kinetic scheme for the compressible navier stokes equations to the flow calculation with interfaces and mixing the objective of the current research targets mainly on the accurate capturing of navier stokes diffusive interfaces where the thickness can be resolved by the cell size firstly a new bgk ns scheme coupling with the level set type scalar function transport is constructed even though the scalar function is directly incorporated into the gas distribution function and it evolves according to the gas kinetic equation it likes more or less a color function which has no direct contribution for the time evolution of conservative flow variables such as mass momentum and energy due to the coupling of the scalar function into the gas kinetic formulation the governing equations for the scalar function turns out to be an advection diffusion equations and the diffusive coefficient can be controlled by the particle collision time which makes the current scheme suitable for the gas mixing problems with a controllable diffusion coefficients however for the non mixing or sharp interface problems such as the interface between gas and liquid the current method can be used as a scheme similar to the level set method where the interface location can be identified with a fixed level set value such as q 0 the current method is applied to a few examples from the simple square wave propagation and diffusion to the 3d rayleigh taylor instability the supersonic mixing layer and the shock helium bubble interaction case show clearly the convergence of the current navier stokes solver for the flow problems with mixing of components and interface once the interface thickness can be well resolved by the cell size in the case of shock hitting sf6 cylinder the computation predicts the experimental measure very well in the current scheme the schmidt number can be freely chosen according to the physical reality