logic based fuzzy networks a study in system modeling with triangular norms and uninorms the ultimate challenges of system modeling concern designing accurate yet highly transparent and user centric models we have witnessed a plethora of neurofuzzy architectures which are aimed at addressing these two highly conflicting requirements this study is concerned with the design and the development of transparent logic networks realized with the aid of fuzzy neurons and fuzzy unineurons the construction of networks of this form requires a formation of efficient interfaces that constitute a conceptually appealing bridge between the model and the real world experimental environment in which the model is to be used in general the interfaces are constructed by invoking some form of granulation of information and binary boolean discretization in particular we introduce a new discretization environment that is realized by means of particle swarm optimization pso and data clustering implemented by the k means algorithm the underlying structure of the network is optimized by invoking a combination of the pso and the mechanisms of conventional gradient based learning we discuss various optimization strategies by considering boolean as well as fuzzy data coming as the result of discretization of original experimental data and then involving several learning strategies we elaborate on the interpretation aspects of the network and show how those could be strengthened through efficient pruning we also show how the interpreted network leads to a simpler and more accurate logic description of the experimental data a number of experimental studies are included

robust trajectory tracking for a class of hybrid systems an internal model principle approach this paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events switching systems parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes to deal with the hybrid nature of the system and the possible discontinuities of its solutions at switching times a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed the innovative design of the discrete time dynamics of the compensator guarantees the robust existence of a steady state response giving zero tracking error in the controlled output and local convergence to it

synchronization of impacting mechanical systems with a single constraint abstract this paper addresses the synchronization problem of mechanical systems subjected to a single geometric unilateral constraint the impacts of the individual systems induced by the unilateral constraint generally do not coincide even if the solutions are arbitrarily close to each other the mismatch in the impact time instants demands a careful choice of the distance function to allow for an intuitively correct comparison of the discontinuous solutions resulting from the impacts we propose a distance function induced by the quotient metric which is based on an equivalence relation using the impact map the distance function obtained in this way is continuous in time when evaluated along jumping solutions the property of maximal monotonicity which is fulfilled by most commonly used impact laws is used to significantly reduce the complexity of the distance function based on the simplified distance function a lyapunov function is constructed to investigate the synchronization problem for two identical one dimensional mechanical systems sufficient conditions for the uncoupled individual systems are provided under which local synchronization is guaranteed furthermore we present an interaction law which ensures global synchronization also in the presence of grazing trajectories and accumulation points zeno behavior the results are illustrated using numerical examples of a 1 dof mechanical impact oscillator which serves as stepping stone in the direction of more general systems

implementation of diffuse reflection boundary conditions in a thermal lattice boltzmann model with flux limiters we discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice boltzmann model their accuracy is investigated in the case of couette flow by considering the slip regime the best results are recovered with versions 2 and 3 which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain version 2 is found to be more economical since it involves no interpolation procedure this version was thereafter used to investigate the temperature profile in couette flow for various values of prandtl number as well as the capability of the thermal lb model to capture the knudsen minimum in poiseuille flow

signatures definitions operators and applications to fuzzy modelling this paper presents a new framework for the symbolic representation of data which is referred to as signatures the definitions of signatures and of signature trees are first given original operators on signatures are next presented i e contraction extension pruning addition multiplication and grafting attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed an example is included to accompany the theoretical results

energy conserving lattice boltzmann thermal model in two dimensions a discrete velocity model is presented for lattice boltzmann thermal fluid dynamics this model is implemented and tested in two dimensions with a finite difference scheme comparison with analytical solutions shows an excellent agreement even for wide temperature differences an alternative approximate approach is then presented for traditional lattice transport schemes

lattice valued f transforms and similarity relations abstract the relationships between lattice valued f transforms and similarity relations are investigated several similarity relations are naturally associated with f transforms three types of such similarity relations related to lattice valued f transforms are investigated namely similarity relationships that are related to spaces with fuzzy partitions as ground structures of the f transform relationships between extensional hulls with respect to similarity relations and f transforms and relationships between similarities of pairs of functions on the one hand and similarities of the f transforms of these functions on the other some examples of possible applications are also presented

tracking control for hybrid systems with state triggered jumps this paper addresses the tracking problem in which the controller should stabilize time varying reference trajectories of hybrid systems despite the fact that discrete events or jumps in hybrid systems can often not be controlled directly as e g is the case in impacting mechanical systems the controller should still stabilize the desired trajectory a major complication in the analysis of this hybrid tracking problem is that in general the jump times of the plant do not coincide with those of the reference trajectory consequently the conventional euclidean tracking error does not converge to zero even if trajectories converge to the reference trajectory in between jumps and the jump times converge to those of the reference trajectory hence standard control approaches can not be applied we propose a novel definition of the tracking error that overcomes this problem and formulate lyapunov based conditions for the global asymptotic stability of the hybrid reference trajectory using these conditions we design hysteresis based controllers that solve the hybrid tracking problem for two exemplary systems including the well known bouncing ball problem

deformations for linear periodic discrete time systems the adjoint normal form following the technique proposed by arnold for matrices time invariant autonomous systems and extended by tannenbaum to time invariant linear control systems with inputs and outputs a normal form for linear periodic discrete time systems depending on physical parameters is proposed the considered actions are deformations i e linear periodic transformations depending on the parameters being identity at the nominal values of them

a color image reduction based on fuzzy transforms we present a new method for color image reduction based on the concept of fuzzy transform any image in a single band can be considered as a fuzzy matrix which is subdivided into submatrices called blocks each block is compressed with various compression rates by means of a fuzzy transform in two variables we compare our method with recent three algorithms due to g beliakov h bustince and d paternain based on the minimizing penalty functions defined over a discrete lattice the quality of the reduced image is measured by the mean square error mse and penalty function pen obtained by comparing both magnified and original images we also point out a threshold of the compression rate beyond which the mse follows a linear trend and the corresponding loss of information is still acceptable

extensive analysis of the lattice boltzmann method on shifted stencils standard lattice boltzmann methods lbms are based on a symmetric discretization of the phase space which amounts to study the evolution of particle distribution functions pdfs in a reference frame at rest this choice induces a number of limitations when the simulated flow speed gets closer to the sound speed such as velocity dependent transport coefficients the latter issue is usually referred to as a galilean invariance defect to restore the galilean invariance of lbms it was proposed to study the evolution of pdfs in a comoving reference frame by relying on asymmetric shifted lattices n frapolli s s chikatamarla and i v karlin phys rev lett 117 010604 2016 from the numerical viewpoint this corresponds to overcoming the rather restrictive courant friedrichs lewy conditions on standard lbms and modeling compressible flows while keeping memory consumption and processing costs to a minimum therefore using the standard first neighbor stencils in the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions edfs and collision models thanks to them it is possible to 1 better understand the effect of this solution on both physics and stability 2 assess its viability as a way to extend the validity range of lbms and 3 quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path the results clearly show that in theory the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity furthermore just like the zero mach flow for the standard stencils it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties in addition a detailed analysis of the obtained results shows that the properties of different collision models and edfs remain unchanged under the shift of stencil in other words by introducing a velocity shift in the stencil the optimal operating point in terms of physics and numerics will also be shifted by the same vector regardless of the edf or collision model considered eventually while limited to the d2q9 stencil with the nine possible first neighbor shifts the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner

computation of gas solid flows by finite difference boltzmann equation abstract in this paper we will discuss in detail how to use a finite difference lattice boltzmann equation model in which an external force term is involved to simulate two way coupling gas solid flows the numerical results are found to be in good agreement with analytical data and some other numerical results

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

follow the bouncing ball global results on tracking and state estimation with impacts in this paper we formulate tracking and state estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set due to the discontinuous trajectories arising from the impacts we use hybrid systems stability analysis tools to establish the results using a novel concept of mirrored images of the target mass we prove that 1 a tracking control algorithm and 2 an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards including rectangles moreover we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking the results are illustrated via simulations

boundary conditions for the upwind finite difference lattice boltzmann model evidence of slip velocity in micro channel flow we conduct a systematic study of the effect of various boundary conditions bounce back and three versions of diffuse reflection for the two dimensional first order upwind finite difference lattice boltzmann model simulation of couette flow in a micro channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the knudsen number e l l where l is the mean free path and l is the channel width for walls moving in opposite directions with speeds u w the slip velocity satisfies u s l i p 2 eu w a l l 1 2 e in the case of poiseuille flow in a micro channel the slip velocity is found to depend on the lattice spacing ds and knudsen number e to both first and second order the best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes

lattice boltzmann models based on half range gauss hermite quadratures we discuss general features of thermal lattice boltzmann models based on half range gauss quadratures specialising to the half range gauss hermite and gauss laguerre cases the main focus of the paper is on the construction of high order half range hermite lattice boltzmann hhlb models the performance of the hhlb models is compared with that of laguerre lattice boltzmann llb and full range hermite lattice boltzmann hlb models by conducting convergence tests with respect to the quadrature order on stationary profiles of the particle number density macroscopic velocity temperature and heat fluxes in the two dimensional couette flow the bhatnagar gross krook bgk collision term is used throughout the paper to reduce the computational costs of the numerical simulations we use mixed lattice boltzmann models constructed using different quadrature methods on each cartesian axis for kn 0 01 the hlb models require the least number of velocities to satisfy our convergence test when kn 0 05 the hlb models are outperformed in terms of number of velocities employed by both the llb and the hhlb models moreover we find that the hhlb models require less quadrature points than the llb models at all tested values of kn which we attribute to the maxwellian form of the weight function for the half range hermite polynomials

construction of image reduction operators using averaging aggregation functions in this work we present an image reduction algorithm based on averaging aggregation functions we axiomatically define the concepts of image reduction operator and local reduction operator we study the construction of the latter by means of averaging functions and we propose an image reduction algorithm image reduction operator we analyze the properties of several averaging functions and their effect on the image reduction algorithm finally we present experimental results where we apply our algorithm in two different applications analyzing the best operators for each concrete application

comments on control of a planar underactuated biped on a complete walking cycle the authors point out several approximations and flaws in the above article by chemori and loria see ibid vol 49 no 5 p 838 843 2004

finite difference lattice boltzmann methods for binary fluids we investigate two fluid bhatnagar gross krook bgk kinetic methods for binary fluids the developed theory works for asymmetric as well as symmetric systems for symmetric systems it recovers sirovich s theory and is summarized in models a and b for asymmetric systems it contributes models c d and e which are especially useful when the total masses and or local temperatures of the two components are greatly different the kinetic models are discretized based on an octagonal discrete velocity model the discrete velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations the combination of a discrete velocity kinetic model and an appropriate finite difference scheme composes a finite difference lattice boltzmann method the validity of the formulated methods is verified by investigating i uniform relaxation processes ii isothermal couette flow and iii diffusion behavior

fuzzy transforms for compression and decompression of color videos we use fuzzy transforms for coding decoding color frames of videos and we compare the results with the same frames reconstructed with the standard jpeg method we classify all the frames in intra frames and predictive frames by adopting a similarity measure based on the lukasiewicz t norm and a pre processing phase which determines the best similarity threshold value the compression is made on particular frames called d frames obtained from a suitable difference defined on the values of the pixels of an intra frame and a predictive frame under high compression rates we see that the peak signal to noise ratio of the frames obtained with the fuzzy transforms is averagely close to the psnr obtained with the jpeg method we use the videos at url sampl eng ohiostate edu sampl database htm

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

two dimensional thermal model of the finite difference lattice boltzmann method with high spatial isotropy the existing lattice boltzmann method multispeed thermal models show a limited accuracy this paper proposes a two dimensional multispeed thermal model for the finite difference lattice boltzmann method fdlbm to recover correct fluid equations up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy in the fdlbm particle velocities can be selected independently from the lattice configuration therefore particle velocities of octagonal directions which have up to seventh rank isotropic tensors are adopted the proposed model was verified by two simulations the model showed excellent numerical stability in addition to strict accuracy

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

trajectory tracking for a particle in elliptical billiards an infinitely rigid unitary mass particle is considered moving on a planar region delimited by a rigid elliptical barrier elliptical billiards under the action of proper control forces a class of periodic trajectories involving an infinite sequence of non smooth impacts between the mass and the barrier at fixed times is found by using an lmis based procedure the jumps in the velocities at the impact times render difficult if not impossible to obtain the classical stability and attractivity properties for the dynamic system describing the tracking error behaviour hence the tracking control problem is properly stated using notions similar to the quasi stability concept in v lakshmikantham d d bainov and p s simeonov theory of impulsive differential equations 6 world scientific 1989 a controller whose state is subject to discontinuities based on the internal model principle is shown to solve the proposed tracking problem giving rise to control forces that are piecewise continuous fun

f transform with parametric generalized fuzzy partitions the fuzzy transform f transform has some interesting properties that allow its use in curve fitting and smoothing we suggest the following a a generalization of fuzzy partitions for the f transform to control and improve the smoothing effect and b a parametrization of the fuzzy numbers constituting the basic functions related to the fuzzy partitions an optimization criterion is then suggested to obtain the f transform with best approximation properties by estimating the basic functions from a family of parametric fuzzy numbers the generalized fuzzy partitions are characterized by the number of subintervals the bandwidth of the partition forming the core of each basic function and we suggest two procedures for bandwidth selection one based on taut string variation and a second based on generalized cross validation some illustrative examples are included

lyapunov based sufficient conditions for exponential stability in hybrid systems lyapunov based sufficient conditions for exponential stability in hybrid systems are presented the focus is on converting non strict lyapunov conditions having certain observability properties into strict lyapunov conditions for exponential stability both local and global results are considered the utility of the results is illustrated through an example

general approximation of fuzzy numbers by f transform in this paper we will prove that in most of the cases the extended inverse fuzzy transform preserves the quasi concavity of a fuzzy number and hence it can be used to generate fuzzy numbers by approximating the restriction of the membership function to its support in the case of continuous fuzzy numbers with cores containing more than one element the rate of uniform convergence is of linear type and the same holds when we approximate the important characteristics of a fuzzy number such as the value or the ambiguity moreover we have the preservation of the support and the convergence of the core which in addition can be determined precisely in the case of continuous fuzzy numbers with one element core it is in general necessary to normalize the approximation but the support is preserved again and the core can be determined exactly in this case too moreover the approximations have again linear rate of uniform convergence

development of autofocusing algorithm based on fuzzy transforms in this paper we propose a new passive auto focusing algorithm to acquire images with enhanced quality through a digital camera the focus measure operations play a key role in a passive auto focusing method the proposed focus measure operation is based on a localized version of image variance method the localization of the image variance focus measure operation can be implemented with the use of fuzzy partition and fuzzy transform in order to validate our approach experimental comparative studies are conducted on test images with the use of different focus measure operators the selected operators have been chosen from an extensive review of the state of the art approaches a comparative analysis demonstrates that the proposed algorithm is superior to the conventional methods

trajectory tracking control of multiconstraint complementarity lagrangian systems in this study one considers the tracking control problem of a class of nonsmooth fully actuated lagrangian systems subject to frictionless unilateral constraints the task under consideration contains both free motion and constraint motion phases a switching controller that guarantees an approximate tracking is designed particular attention is paid to transition impacting and detachment between different phases of motion the exogenous signals that assure the stabilization on take off from some constraints are explicitly defined this paper extends previous works on the topic as it considers more than one constraint for n degree of freedom systems numerical examples illustrate the main results

fuzzy transforms of monotone functions with application to image compression this paper is focused on the special properties of functions monotonicity lipschitz continuity that are invariant with fuzzy transform on the basis of the monotonicity invariance we propose an efficient algorithm for improved image compression and reconstruction based on fuzzy transform

distance function design and lyapunov techniques for the stability of hybrid trajectories the comparison between time varying hybrid trajectories is crucial for tracking observer design and synchronisation problems for hybrid systems with state triggered jumps in this paper a generic distance function is designed that can be used for this purpose the so called peaking phenomenon which occurs when using the euclidean distance to compare two hybrid trajectories is circumvented by taking the hybrid nature of the system explicitly into account based on the proposed distance function we define the stability of a trajectory and present sufficient lyapunov type conditions for hybrid system with state triggered jumps a constructive lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane the stability conditions can then be verified using linear matrix conditions finally for this class of systems we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example

modeling and control of impact in mechanical systems theory and experimental results considers the equations of motion of mechanical systems subject to inequality constraints which can be obtained by looking for the stationary value of the action integral two different methods are used to take into account the inequality constraints in the computation of the stationary value of the action integral the valentine variables method and the penalty functions method the equations of motion resulting from the application of the valentine variables method which introduces the concept of nonsmooth impacts constitute the exact model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system are very stiff the equations of motion resulting from the application of the penalty functions method which introduces the concept of smooth impacts constitute an approximate model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system show some flexibility various feedback control laws from the natural outputs and from their time derivatives are studied with reference to both models of impact the closed loop systems resulting from the application of the same control law to both models show pretty much the same global asymptotic stability properties the proposed control laws are only concerned with regulation problems in the presence of possible contacts and impacts among parts of the mechanical system or with the external environment the effectiveness of the proposed control structure has been tested experimentally with reference to a single link robot arm showing a valuable behavior

two dimensional lattice boltzmann model for compressible flows with high mach number abstract in this paper we present an improved lattice boltzmann model for compressible navier stokes system with high mach number the model is composed of three components i the discrete velocity model by m watari and m tsutahara phys rev e 67 2003 036306 ii a modified lax wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included iii artificial viscosity the improved model is convenient to compromise the high accuracy and stability the included dispersion term can effectively reduce the numerical oscillation at discontinuity the added artificial viscosity helps the scheme to satisfy the von neumann stability condition shock tubes and shock reflections are used to validate the new scheme in our numerical tests the mach numbers are successfully increased up to 20 or higher the flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems

asymptotic tracking of periodic trajectories for a simple mechanical system subject to nonsmooth impacts an infinitely rigid mass is considered which moves on a plane under the action of proper control forces within a closed region delimited by an infinitely massive and rigid circular barrier a suitably amended tracking problem for a class of periodic trajectories involving an infinite number of nonsmooth impacts between the mass and the barrier is formally stated and solved

fuzzy transforms theory and applications the technique of direct and inverse fuzzy f transforms of three different types is introduced and approximating properties of the inverse f transforms are described all three types of the direct f transform are transformations from a function space to a finite dimensional vector space the first ordinary f transform is constructed on the basis of the ordinary algebra of reals while the other two types of the f transform are constructed on the basis of residuated lattice the core idea of the technique of f transforms is a fuzzy partition of a universe into fuzzy subsets factors clusters granules etc we claim that for a sufficient representation of a function defined on this universe we may consider its average values over fuzzy subsets from the partition thus a function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values a number of theorems establishing best approximation properties of the inverse f transforms are proved in fact three types of the inverse f transform are the best approximations in average from below and from above respectively as one of many possible applications we present a method of image compression and reconstruction on the basis of the f transform

finite difference lattice boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations abstract the current finite difference lattice boltzmann method fdlbm gives a fixed specific heat ratio because internal energy is limited to the translational freedom of the space yan et al and kataoka et al clarified the conditions for deriving models with arbitrary specific heat ratio and proposed euler models however these model applications to numerical simulations showed the weakness in the numerical stability in this paper a two dimensional fdlbm navier stokes model and a three dimensional fdlbm euler model which allow arbitrary values to be set for the specific heat ratio were proposed these models stably performed numerical simulations from subsonic to supersonic ranges

a novel coupled lattice boltzmann model for low mach number combustion simulation abstract a novel coupled lattice boltzmann model is developed for two and three dimensional low mach number combustion simulations in which the fluid density can bear sharp changes different to the hybrid lattice boltzmann scheme o filippova d hanel a novel lattice bgk approach for low mach number combustion j comput phys 158 2000 139 this scheme is strictly pure lattice boltzmann style i e we solve the flow temperature and concentration fields using the lattice boltzmann method only different to the non coupled lattice boltzmann scheme k yamamoto x he g d doolen simulation of combustion field with lattice boltzmann method j stat phys 107 2002 367 the fluid density in this model is coupled directly with the temperature in this model the time step and the fluid particle speed can be adjusted dynamically depending on the particle characteristic temperature and the algorithm is still a simple process of hopping from one grid point to the next the same as the standard lattice boltzmann method therefore the outstanding advantages of the standard lattice boltzmann method are retained in this model besides better numerical stability excellent agreement between the present results and other numerical or experimental data shows that this scheme is an efficient numerical method for practical combustion simulations

three dimensional finite difference lattice boltzmann model and its application to inviscid compressible flows with shock waves abstract in this paper a three dimensional 3d finite difference lattice boltzmann model for simulating compressible flows with shock waves is developed in the framework of the double distribution function approach in the model a density distribution function is adopted to model the flow field while a total energy distribution function is adopted to model the temperature field the discrete equilibrium density and total energy distribution functions are derived from the hermite expansions of the continuous equilibrium distribution functions the discrete velocity set is obtained by choosing the abscissae of a suitable gauss hermite quadrature with sufficient accuracy in order to capture the shock waves in compressible flows and improve the numerical accuracy and stability an implicit explicit finite difference numerical technique based on the total variation diminishing flux limitation is introduced to solve the discrete kinetic equations the model is tested by numerical simulations of some typical compressible flows with shock waves ranging from 1d to 3d the numerical results are found to be in good agreement with the analytical solutions and or other numerical results reported in the literature

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem