on the variance of fuzzy random variables abstract this paper deals with an expectation and a real valued variance of fuzzy random variables the expectation and the variance of a fuzzy random variable is characterized by frechet s principle in a metric space we study properties of the variance of a fuzzy random variable and compare it with the common variance of real valued random variables using the expectation and the variance of fuzzy random variables we consider a linear regression problem and limit theorems

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

component models for fuzzy data the fuzzy perspective in statistical analysis is first illustrated with reference to the informational paradigm allowing us to deal with different types of uncertainties related to the various informational ingredients data model assumptions the fuzzy empirical data are then introduced referring to j lr fuzzy variables as observed on i observation units each observation is characterized by its center and its left and right spreads lr1 fuzzy number or by its left and right centers and its left and right spreads lr2 fuzzy number two types of component models for lr1 and lr2 fuzzy data are proposed the estimation of the parameters of these models is based on a least squares approach exploiting an appropriately introduced distance measure for fuzzy data a simulation study is carried out in order to assess the efficacy of the suggested models as compared with traditional principal component analysis on the centers and with existing methods for fuzzy and interval valued data an application to real fuzzy data is finally performed

an implicit immersed boundary method for three dimensional fluid membrane interactions we present an implicit immersed boundary method for the incompressible navier stokes equations capable of handling three dimensional membrane fluid flow interactions the goal of our approach is to greatly improve the time step by using the jacobian free newton krylov method jfnk to advance the location of the elastic membrane implicitly the most attractive feature of this jacobian free approach is newton like nonlinear convergence without the cost of forming and storing the true jacobian the generalized minimal residual method gmres which is a widely used krylov subspace iterative method is used to update the search direction required for each newton iteration each gmres iteration only requires the action of the jacobian in the form of matrix vector products and therefore avoids the need of forming and storing the jacobian matrix explicitly once the location of the boundary is obtained the elastic forces acting at the discrete nodes of the membrane are computed using a finite element model we then use the immersed boundary method to calculate the hydrodynamic effects and fluid structure interaction effects such as membrane deformation the present scheme has been validated by several examples including an oscillatory membrane initially placed in a still fluid capsule membranes in shear flows and large deformation of red blood cells subjected to stretching force

conditional density estimation using probabilistic fuzzy systems we consider conditional density approximation by fuzzy systems fuzzy systems are typically used to approximate deterministic functions in which the stochastic uncertainty is ignored we propose probabilistic fuzzy systems pfss in which the probabilistic nature of uncertainty is taken into account these systems take also fuzzy uncertainty into account by their fuzzy partitioning of input and output spaces we discuss an additive reasoning scheme for pfss that leads to the estimation of conditional probability densities and prove how such fuzzy systems compute the expected value of this conditional density function we show that some of the most commonly used fuzzy systems can compute the same expected output value and we derive how their parameters should be selected in order to achieve this goal the additional information and process understanding provided by the different interpretations of the pfs models are illustrated using a real world example

the fuzzy hyperbolic inequality index associated with fuzzy random variables the aim of this paper is focussed on the quantification of the extent of the inequality associated with fuzzy valued random variables in general populations for this purpose the fuzzy hyperbolic inequality index associated with general fuzzy random variables is presented and a detailed discussion of some of the most valuable properties of this index extending those for classical inequality indices is given two examples illustrating the computation of the fuzzy inequality index are also considered some comments and suggestions are finally included

the approximation method for two stage fuzzy random programming with recourse in this paper a new class of fuzzy random optimization problem called two stage fuzzy random programming or fuzzy random programming with recourse frpr problem is first presented then its deterministic equivalent programming problem is characterized because the frpr problems include fuzzy random variable parameters with an infinite support they are inherently infinite dimensional optimization problems that can rarely be solved directly therefore an approximation approach to the fuzzy random variables with infinite supports by finitely supported ones is proposed which results in finite dimensional frpr problems after that this paper is devoted to establishing the conditions under which the objective value optimal objective value and minimizers of such finite dimensional frpr problem can be shown to converge to the objective value respectively optimal objective value and minimizers of the original infinite dimensional frpr problem

on the formalization of fuzzy random variables abstract in this paper we develop a discussion on the mathematical formalization of the concept of fuzzy random variable this discussion is mainly focused on finding an adequate notion of measurability to be coherent with the notions on the space these random elements take values

simulation of fuzzy random variables this work deals with the simulation of fuzzy random variables which can be used to model various realistic situations where uncertainty is not only present in form of randomness but also in form of imprecision described by means of fuzzy sets utilizing the common arithmetics in the space of all fuzzy sets only induces a conical structure as a consequence it is difficult to directly apply the usual simulation techniques for functional data in order to overcome this difficulty two different approaches based on the concept of support functions are presented the first one makes use of techniques for simulating hilbert space valued random elements and afterwards projects on the cone of all fuzzy sets it is shown by empirical results that the practicability of this approach is limited the second approach imitates the representation of every element of a separable hilbert space in terms of an orthonormal basis directly on the space of fuzzy sets in this way a new approximation of fuzzy sets useful to approximate and simulate fuzzy random variables is developed this second approach is adequate to model various realistic situations

scalable parallel methods for monolithic coupling in fluid structure interaction with application to blood flow modeling we introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries the incompressible navier stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls our method features an unstructured dynamic mesh capable of modeling complicated geometries an arbitrary lagrangian eulerian framework that allows for large displacements of the moving fluid domain monolithic coupling between the fluid and structure equations and fully implicit time discretization simulations based on blood vessel geometries derived from patient specific clinical data are performed on large supercomputers using scalable newton krylov algorithms preconditioned with an overlapping restricted additive schwarz method that preconditions the entire fluid structure system together the algorithm is shown to be robust and scalable for a variety of physical parameters scaling to hundreds of processors and millions of unknowns

the fuzzy decision problem an approach to the problem of testing statistical hypotheses with fuzzy information abstract this paper is devoted to the problems of testing statistical hypotheses about an experiment when the available information from its sampling is vague when the information supplied by the experimental sampling is exact the problems of testing statistical hypotheses about the experiment can be regarded as a particular statistical decision problem in addition decision procedures may be used in problems of testing hypotheses in a similar manner the problem of testing statistical hypotheses about an experiment when the available sample information is vague is approached in this paper as a particular fuzzy decision problem as defined by tanaka okuda and asai this approach assumes that the previous information about the experiment can be expressed by means of certain conditional probabilistic information whereas the present information about it can be expressed by means of fuzzy information the preceding framework allows us to extend the notion of risk function and some nonfuzzy decision procedures to the fuzzy case and particularize them to the problem of testing finally several illustrative examples are presented

simulation of random fuzzy variables an empirical approach to statistical probabilistic studies with fuzzy experimental data in this paper we simulate different types of random fuzzy variables to get some conclusions concerning fuzzy valued random variables this simulation was carried out to illustrate certain limit results formalizing the convergence of the arithmetic mean of sampled fuzzy data to the population mean or an expected value of the random fuzzy variable like the well known strong law of large numbers and the law of iterated logarithm since the theoretical results have recently been proved this simulation analysis represents a complementary study in which we can determine sample sizes providing us with suitable approximations finally future directions regarding statistical inference with fuzzy data and other applications are commented

reconstruction of kauffman networks applying trees abstract according to kauffman s theory s kauffman the origins of order self organization and selection in evolution oxford university press new york 1993 enzymes in living organisms form a dynamic network which governs their activity for each enzyme the network contains a collection of enzymes affecting the enzyme and a boolean function prescribing next activity of the enzyme as a function of the present activity of the affecting enzymes kauffman s original pure random structure of the connections was criticized by barabasi and albert a l barabasi r albert emergence of scaling in random networks science 286 1999 509 512 their model was unified with kauffman s network by aldana and cluzel m aldana p cluzel a natural class of robust networks proc natl acad sci usa 100 2003 8710 8714 kauffman postulated that the dynamic character of the network determines the fitness of the organism if the network is either convergent or chaotic the chance of survival is lessened if however the network is stable and critical the organism will proliferate kauffman originally proposed a special type of boolean functions to promote stability which he called the property canalyzing this property was extended by shmulevich et al i shmulevich h lahdesmaki e r dougherty j astola w zhang the role of certain post classes in boolean network models of genetic networks proc natl acad sci usa 100 2003 10734 10739 using post classes following their ideas we propose decision tree functions for enzymatic interactions the model is fitted to microarray data of cogburn et al l a cogburn w wang w carre l rejt t e porter s e aggrey j simon system wide chicken dna microarrays gene expression profiling and discovery of functional genes poult sci assoc 82 2003 939 951 l a cogburn x wang w carre l rejt s e aggrey m j duclos j simon t e porter functional genomics in chickens development of integrated systems microarrays for transcriptional profiling and discovery of regulatory pathways comp funct genom 5 2004 253 261 in microarray measurements the activity of clones is measured the problem here is the reconstruction of the structure of enzymatic interactions of the living organism using microarray data the task resembles summing up the whole story of a film from unordered and perhaps incomplete collections of its pieces two basic ingredients will be used in tackling the problem in our earlier works l rejt g tusnady evolution of random boolean nk models in tierra environment in i berkes e csaki m csorg eds limit theorems in probability an statistics budapest vol ii 2002 pp 499 526 we used an evolutionary strategy called tierra which was proposed by ray t s ray evolution complexity entropy and artificial reality physica d 75 1994 239 263 for investigating complex systems here we apply this method together with the tree structure of clones found in our earlier statistical analysis of microarray measurements l rejt g tusnady clustering methods in microarrays period math hungar 50 2005 199 221

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

an efficient configuration for probabilistic fuzzy logic system a novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process the probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set besides the faster inference operation it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound the computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method its effectiveness can be further demonstrated on the application to modeling of an industrial curing process the robust modeling performance discloses its potential in process modeling under complex environment

sparse partition universal graphs for graphs of bounded degree abstract in 1983 chvatal trotter and the two senior authors proved that for any there exists a constant b such that for any n any 2 colouring of the edges of the complete graph k n with n b n vertices yields a monochromatic copy of any graph h that has n vertices and maximum degree we prove that the complete graph may be replaced by a sparser graph g that has n vertices and o n 2 1 log 1 n edges with n b n for some constant b that depends only on consequently the so called size ramsey number of any h with n vertices and maximum degree is o n 2 1 log 1 n our approach is based on random graphs in fact we show that the classical erd s renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability namely that any 2 colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree the main tool in our proof is the regularity method adapted to a suitable sparse setting the novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed

curvilinear immersed boundary method for simulating fluid structure interaction with complex 3d rigid bodies the sharp interface curvib approach of ge and sotiropoulos l ge f sotiropoulos a numerical method for solving the 3d unsteady incompressible navier stokes equations in curvilinear domains with complex immersed boundaries journal of computational physics 225 2007 1782 1809 is extended to simulate fluid structure interaction fsi problems involving complex 3d rigid bodies undergoing large structural displacements the fsi solver adopts the partitioned fsi solution approach and both loose and strong coupling strategies are implemented the interfaces between immersed bodies and the fluid are discretized with a lagrangian grid and tracked with an explicit front tracking approach an efficient ray tracing algorithm is developed to quickly identify the relationship between the background grid and the moving bodies numerical experiments are carried out for two fsi problems vortex induced vibration of elastically mounted cylinders and flow through a bileaflet mechanical heart valve at physiologic conditions for both cases the computed results are in excellent agreement with benchmark simulations and experimental measurements the numerical experiments suggest that both the properties of the structure mass geometry and the local flow conditions can play an important role in determining the stability of the fsi algorithm under certain conditions the fsi algorithm is unconditionally unstable even when strong coupling fsi is employed for such cases however combining the strong coupling iteration with under relaxation in conjunction with the aitken s acceleration technique is shown to effectively resolve the stability problems a theoretical analysis is presented to explain the findings of the numerical experiments it is shown that the ratio of the added mass to the mass of the structure as well as the sign of the local time rate of change of the force or moment imparted on the structure by the fluid determine the stability and convergence of the fsi algorithm the stabilizing role of under relaxation is also clarified and the upper bound of the under relaxation coefficient required for stability is derived

polynomial extensions of van der waerden s and szemeredi s theorems an extension of the classical van der waerden and szemeredi the orems is proved for commuting operators whose exponents are polynomials as a consequence for example one obtains the following result let s zl be a set of positive upper banach density let p1 n pk n be polynomials with rational coefficients taking integer values on the integers and satisfying pi 0 0 i 1 k then for any v1 vk zl there exist an integer n and a vector u zl such that u pi n vi s for each i k department of mathematics ohio state university columbus ohio 43210 e mail address vitaly math ohio state edu department of mathematics technion haifa 23000 israel e mail address sashal techunix technion ac il current address department of mathematics stanford university stanford california 94305 e mail address leibman math stanford edu license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

an algorithmic regularity lemma for hypergraphs in this paper we will consider the problem of designing an efficient algorithm that finds an epsilon regular partition of an l uniform hypergraph

new bounds for szemeredi s theorem i progressions of length 4 in finite field geometries let k 3 be an integer and let g be a finite abelian group with g n w here n k 1 1 we write rk g for the largest cardinality a of a set a g which does not contain k distinct elements in arithmetic progression the famous theorem of szemeredi essentially asserts that rk z nz ok n it is known in fact that the estimate rk g ok n h olds for allg t here have been many papers concerning the issue of finding quantitative bounds for rk g a result of bourgain states thatr3 g n loglogn logn 1 2 for all g in this paper we obtain a similar bound for r4 g in the particular case g f n w heref is a fixed finite field with char f 3 for example f f5 we prove that r4 g f n logn c for some absolute constant c 0 in future papers we will treat the general abelian groups g eventually obtaining a comparable result for an arbitrary g

forecasting methods using fuzzy concepts in this paper fuzzy concepts are applied in forecasting product price and sales in the semiconductor industry which is often conceived as a highly dynamic environment first two fuzzy forecasting methods including fuzzy interpolation fi and fuzzy linear regression flr are developed and discussed forecasts generated by these methods are fuzzy valued next the subjective beliefs about whether the industry is booming or slumping and the speed at which this change in prosperity takes place during a given period are also considered two subjective functions are defined and used to adjust fuzzy forecasts practically fuzzy forecasts are incorporated with fuzzy programming like fuzzy linear programming flp or fuzzy nonlinear programming fnp for mid term or long term planning advantages over traditional methods are shown in our examples

on strong laws of large numbers for random upper semicontinuous functions a short proof of the strong law of large numbers for random upper semicontinuous functions fuzzy random variables with compact support is given this approach allows us to deduce many results on convergence of fuzzy random variables from the relevant results on random sets that appear as their level sets

overview on the development of fuzzy random variables this paper presents a backward analysis on the interpretation modelling and impact of the concept of fuzzy random variable after some preliminaries the situations modelled by means of fuzzy random variables as well as the main approaches to model them are explained we also summarize briefly some of the probabilistic studies concerning this concept as well as some statistical applications

the convergent results about approximating fuzzy random minimum risk problems abstract based on mean chance theory this paper presents a new class of two stage fuzzy random minimum risk problem frmrp in order to solve the two stage frmrp we use a sequence of finitely supported primitive fuzzy random variables to approximate a continuous fuzzy random variable which result in a finite dimensional two stage frmrp we also discuss the convergence of the approximation method including the convergence of the objective value optimal value and optimal solutions to illustrate the modeling idea of this paper we apply the proposed two stage frmrp to the capacitated location allocation problem with fuzzy random demands finally we integrate the approximation method neural network nn and particle swarm optimization pso to design a hybrid pso algorithm to solve the two stage capacitated location allocation problem and provide a numerical example with five facilities and ten customers to demonstrate the effectiveness of the algorithm

a convergence study of a new partitioned fluid structure interaction algorithm based on fictitious mass and damping we develop analyze and validate a new method for simulating fluid structure interactions fsis which is based on fictitious mass and fictitious damping in the structure equation we employ a partitioned method for the fluid and structure motions in conjunction with sub iteration and aitken relaxation in particular the use of such fictitious parameters requires sub iterations in order to reduce the induced error in addition to the local temporal truncation error to this end proper levels of tolerance for terminating the sub iteration procedure have been obtained in order to recover the formal order of temporal accuracy for the coupled fsi problem these fictitious terms have a significant effect leading to better convergence rate and hence substantially smaller number of sub iterations through analysis we identify the proper range of these parameters which we then verify by corresponding numerical tests we implement the method in the context of spectral element discretization which is more sensitive than low order methods to numerical instabilities arising in the explicit fsi coupling however the method we present here is simple and general and hence applicable to fsi based on any other discretization we demonstrate the effectiveness of the method in applications involving 2d vortex induced vibrations viv and in 3d flexible arteries with structural density close to blood density we also present 3d results for a patient specific aneurysmal flow under pulsatile flow conditions examining in particular the sensitivity of the results on different values of the fictitious parameters

the fuzzy decision problem an approach to the point estimation problem with fuzzy information abstract this paper is devoted to the extension of the bayesian method for the point estimation when the available information is vague in the nonfuzzy case the parametric estimation can be approached as a particularization in the statistical decision problem this motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem defined by tanaka okuda and asia in this way concepts in the fuzzy decision problem are first expressed in the estimation terminology then on the basis of these concepts we shall introduce some notions and state some interesting results finally several illustrative examples will be exposed

a numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains we present a new numerical methodology for simulating fluid structure interaction fsi problems involving thin flexible bodies in an incompressible fluid the fsi algorithm uses the dirichlet neumann partitioning technique the curvilinear immersed boundary method curvib is coupled with a rotation free finite element fe model for thin shells enabling the efficient simulation of fsi problems with arbitrarily large deformation turbulent flow problems are handled using large eddy simulation with the dynamic smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries the curvib and fe solvers are coupled together on the flexible solid fluid interfaces where the structural nodal positions displacements velocities and loads are calculated and exchanged between the two solvers loose and strong coupling fsi schemes are employed enhanced by the aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems the coupled curvib fe fsi method is validated by applying it to simulate two fsi problems involving thin flexible structures 1 vortex induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low reynolds number and 2 the more challenging high reynolds number problem involving the oscillation of an inverted elastic flag for both cases the computed results are in excellent agreement with previous numerical simulations and or experiential measurements grid convergence tests studies are carried out for both the cantilever and inverted flag problems which show that the curvib fe fsi method provides their convergence finally the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the fsi of a tri leaflet prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions

a generalized strong law of large numbers strong laws of large numbers have been stated in the literature for measurable functions taking on values on different spaces in this paper a strong law of large numbers which generalizes some previous ones like those for real valued random variables and compact random sets is established this law is an example of a strong law of large numbers for borel measurable nonseparably valued elements of a metric space

quasi random set systems there are many properties of mathematical objects that satisfy what is sometimes called a 0 1 law in the following sense under some natural probability measure on the set of objects the measure of the subset of objects having the given property is either 0 or 1 in the latter case we can say that almost all the objects have the property familiar examples of this phenomenon are the following almost all real numbers are transcendental or normal to every base almost all integers are composite almost all continuous real functions are nondifferentiable etc it is often the case that the objects under consideration can be partitioned into a countable number of finite classes cn with the probability assigned to an object in cn being just 1 icn i in this case we say that a property pn satisfies a 0 1 law if the fraction of the number of objects in cn that satisfy pn either tends to 0 or tends to 1 as n x 0o for example almost all graphs on n vertices have maximum cliques and maximum independent sets of size at most 2 log n almost all boolean functions with n variables have circuit complexity 1 o 1 2n and almost all binary codes of length n with at most 2nr codewords with r less than the binary symmetric channel capacity c have arbitrarily small error probability a special case of shannon s coding theorem see s48 one of the first general results of this type was the theorem of fagin f76 and glebskii et al gklt69 which asserts that every property of graphs that can be expressed in first order logic satisfies a 0 1 law see ss88 for recent striking developments in this topic one obvious method for finding explicit objects having some property pn shared by almost all objects in cn is simply to select one at random with overwhelming probability tending to 1 as n x oc the selected object will have property pn unfortunately it may be and often is extremely difficult to prove that any particular object does indeed satisfy pn it is our purpose in this paper to describe a method that can to a certain extent circumvent this difficulty we will show that for a variety of families it is possible to identify a natural hierarchy of equivalence classes of properties all of which are shared by almost all objects in the family any object satisfying

two sample hypothesis tests of means of a fuzzy random variable abstract in this paper we will consider some two sample hypothesis tests for means concerning a fuzzy random variable in two populations for this purpose we will make use of a generalized metric for fuzzy numbers and we will develop an exact study for the case of normal fuzzy random variables and an asymptotic study for the case of simple general fuzzy random variables

a hybrid cartesian immersed boundary method for simulating flows with 3d geometrically complex moving bodies a numerical method is developed for solving the 3d unsteady incompressible navier stokes equations in cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics the governing equations are discretized on a hybrid staggered non staggered grid layout using second order accurate finite difference formulas the discrete equations are integrated in time via a second order accurate dual time stepping artificial compressibility iteration scheme unstructured triangular meshes are employed to discretize complex immersed boundaries the nodes of the surface mesh constitute a set of lagrangian control points used to track the motion of the flexible body at every instant in time the influence of the body on the flow is accounted for by applying boundary conditions at cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity which show that the method is second order accurate the method is validated by applying it to calculate flow in a cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing the ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish like body and flow past an anatomically realistic planktonic copepod performing an escape like maneuver euver

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

the shortest path problem on a fuzzy time dependent network in this study we introduce a fuzzy time dependent network ftdn and analyze its shortest path problem the ftdn is a network in which travel times are represented as fuzzy sets and are also time dependent under these circumstances the shortest path problem on the ftdn is far more complex in comparison with the shortest path problem on the existing networks to highlight the complexity we show that on the ftdn standard shortest path algorithms e g the well known dijkstra algorithm are not able to come up with solutions subsequently we construct a suitable method which is suitable to deal with the shortest problem a fuzzy programming model is presented for finding the shortest path on the ftdn the proposed model is handled through the techniques which combine mechanisms of fuzzy simulation and genetic optimization in this particular setting fuzzy simulation is exploited to estimate the value of uncertain functions which do not exist in the general networks the proposed model is evaluated with the use of numerical experimentation a comparative analysis demonstrates that the proposed model leads to the shortest path while standard algorithms are not capable of finding the path when dealing with the shortest path problem on the ftdn

approximating integrably bounded fuzzy random variables in terms of the generalized hausdorff metric abstract consider the class of the mappings from a euclidean space to the unit interval 0 1 that is the class of the fuzzy sets of this space which are upper semicontinuous the closure of their supports is compact and the inverse images of the singleton are nonempty sets when the metric d which generalizes the hausdorff metric is defined on the preceding class the resulting metric space is complete but nonseparable consequently for this nonseparability given a probability space and an integrably bounded fuzzy random variable associated with it one cannot ensure the existence of a sequence of simple fuzzy random variables d converging almost surely to the former one however we are going to show in this paper that for any given integrably bounded fuzzy random variable we can guarantee the existence of a sequence of integrably fuzzy random variables whose level functions are simple random compact sets and which d converges at every point to the former variable on the basis of this result we will obtain in this paper a constructive definition of integrably bounded fuzzy random variables and an operational way to compute their fuzzy expected values

the hypergraph regularity method and its applications szemeredi s regularity lemma asserts that every graph can be decomposed into relatively few random like subgraphs this random like behavior enables one to find and enumerate subgraphs of a given isomorphism type yielding the so called counting lemma for graphs the combined application of these two lemmas is known as the regularity method for graphs and has proved useful in graph theory combinatorial geometry combinatorial number theory and theoretical computer science here we report on recent advances in the regularity method for k uniform hypergraphs for arbitrary k 2 this method purely combinatorial in nature gives alternative proofs of density theorems originally due to e szemeredi h furstenberg and y katznelson further results in extremal combinatorics also have been obtained with this approach the two main components of the regularity method for k uniform hypergraphs the regularity lemma and the counting lemma have been obtained recently rodl and skokan based on earlier work of frankl and rodl generalized szemeredi s regularity lemma to k uniform hypergraphs and nagle rodl and schacht succeeded in proving a counting lemma accompanying the rodl skokan hypergraph regularity lemma the counting lemma is proved by reducing the counting problem to a simpler one previously investigated by kohayakawa rodl and skokan similar results were obtained independently by w t gowers following a different approach

a monolithic approach to fluid structure interaction using space time finite elements abstract the paper presents a simultaneous solution procedure for fluid structure interaction problems the structural motion is described by geometrically nonlinear elastodynamics the fluid is modeled by the incompressible navier stokes equations the space time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure in order to enforce momentum conservation and geometric continuity at the interface a weighted residual formulation of coupling conditions is introduced the discretized model equations for fluid structure and coupling conditions are formulated in a single equation system the nonlinear system and the fluid mesh movement are solved in a single iteration loop two dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology

a projection semi implicit scheme for the coupling of an elastic structure with an incompressible fluid we address the numerical simulation of fluid structure systems involving an incompressible viscous fluid this issue is particularly difficult to face when the fluid added mass acting on the structure is strong as it happens in hemodynamics for example indeed several works have shown that in such situations implicit coupling seems to be necessary in order to avoid numerical instabilities although significant improvements have been achieved during the last years solving implicit coupling often exhibits a prohibitive computational cost in this work we introduce a semi implicit coupling scheme which remains stable for a reasonable range of the discretization parameters the first idea consists in treating implicitly the added mass effect whereas the other contributions geometrical non linearities viscous and convective effects are treated explicitly the second idea relies on the fact that this kind of explicit implicit splitting can be naturally performed using a chorin temam projection scheme in the fluid we prove conditional stability of the scheme for a fully discrete formulation several numerical experiments point out the efficiency of the present scheme compared to several implicit approaches

on the use of zadeh s probabilistic definition for testing statistical hypotheses from fuzzy information abstract a statistical hypothesis is an assertion about the distribution of an experiment we consider the study of the problem of testing a statistical hypothesis that is the problem of concluding whether or not the hypothesis is correct on the basis of data from the experiment when its outcomes do not provide exact but rather fuzzy information for establishing optimality criteria of testing we will use the definition of probability of a fuzzy event given by zadeh in order to extend both neyman pearson and bayes theories to the fuzzy framework then we will analyze several properties for the new criteria particularly the goodness of optimal procedures in both the fuzzy and the nonfuzzy situation will be compared for each criterion finally we will apply the extended criteria for testing simple hypotheses this application leads us to prefer bayesian procedures to neyman pearson procedures in the fuzzy context

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

an efficient parallel immersed boundary algorithm using a pseudo compressible fluid solver we propose an efficient algorithm for the immersed boundary method on distributed memory architectures that has the computational complexity of a completely explicit method and also has excellent parallel scaling the algorithm utilizes the pseudo compressibility method recently proposed by guermond and minev that uses a directional splitting strategy to discretize the incompressible navier stokes equations thereby reducing the linear systems to a series of one dimensional tridiagonal systems we perform numerical simulations of several fluid structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm we also compare the proposed algorithm with other second order projection based fluid solvers lastly the execution time and scaling properties of the proposed algorithm are investigated and compared to alternate approaches

bootstrap techniques and fuzzy random variables synergy in hypothesis testing with fuzzy data in previous studies we have stated that the well known bootstrap techniques are a valuable tool in testing statistical hypotheses about the means of fuzzy random variables when these variables are supposed to take on a finite number of different values and these values being fuzzy subsets of the one dimensional euclidean space in this paper we show that the one sample method of testing about the mean of a fuzzy random variable can be extended to general ones more precisely to those whose range is not necessarily finite and whose values are fuzzy subsets of finite dimensional euclidean space this extension is immediately developed by combining some tools in the literature namely bootstrap techniques on banach spaces a metric between fuzzy sets based on the support function and an embedding of the space of fuzzy random variables into a banach space which is based on the support function

limit theorems for fuzzy random variables a strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables whose values are fuzzy sets with compact levels the proofs are based on embedding theorems as well as on probability techniques in banach space