random matrix eigenvalue problems in structural dynamics natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems considering that the system parameters are known only probabilistically we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems current methods to deal with such problems are dominated by mean centred perturbation based methods here two new approaches are proposed the first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is best in some sense the second approach is based on an asymptotic approximation of multidimensional integrals a closed form expression is derived for a general rth order moment of the eigenvalues two approaches are presented to obtain the probability density functions of the eigenvalues the first is based on the maximum entropy method and the second is based on a chi square distribution both approaches result in simple closed form expressions which can be easily calculated the proposed methods are applied to two problems and the analytical results are compared with monte carlo simulations it is expected that the small randomness assumption usually employed in mean centred perturbation based methods can be relaxed considerably using these methods

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

adaptive sparse polynomial chaos expansion based on least angle regression polynomial chaos pc expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable so called polynomial chaos basis the number of terms to be computed grows dramatically with the size of the input random vector which makes the computational cost of classical solution schemes may it be intrusive i e of galerkin type or non intrusive unaffordable when the deterministic finite element model is expensive to evaluate to address such problems the paper describes a non intrusive method that builds a sparse pc expansion first an original strategy for truncating the pc expansions based on hyperbolic index sets is proposed then an adaptive algorithm based on least angle regression lar is devised for automatically detecting the significant coefficients of the pc expansion beside the sparsity of the basis the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon the accuracy of the pc metamodel is checked using an estimate inspired by statistical learning theory namely the corrected leave one out error as a consequence a rather small number of pc terms are eventually retained sparse representation which may be obtained at a reduced computational cost compared to the classical full pc approximation the convergence of the algorithm is shown on an analytical function then the method is illustrated on three stochastic finite element problems the first model features 10 input random variables whereas the two others involve an input random field which is discretized into 38 and 30 500 random variables respectively

fuzzy evaluation of cogeneration alternatives in a petrochemical industry this paper derives fuzzy net present value npv and pay back year pby models as decision indexes for cogeneration alternatives decision making the mellin transform is employed to establish the means and variances of the fuzzy indexes in order to rank various cogeneration alternatives it is noted that the mean and variance values depend only on the vertexes of the fuzzy index and are independent of their height the current paper verifies the performance of the proposed models by simulating two numerical examples and by considering a cogeneration program in a petrochemical industry it is shown that the results of the proposed fuzzy economic models are consistent with those of the conventional crisp models and that the developed concepts are straightforward and easily implemented compared to the fuzzy ranking methods proposed in previous studies furthermore the developed methods serve as readily implemented sensitivity analysis tools for use in the arena of uncertain decision making

computing the error linear complexity spectrum of a binary sequence of period 2 sup n binary sequences with high linear complexity are of interest in cryptography the linear complexity should remain high even when a small number of changes are made to the sequence the error linear complexity spectrum of a sequence reveals how the linear complexity of the sequence varies as an increasing number of the bits of the sequence are changed we present an algorithm which computes the error linear complexity for binary sequences of period spl lscr 2 sup n using o spl lscr log spl lscr sup 2 bit operations the algorithm generalizes both the games chan 1983 and stamp martin 1993 algorithms which compute the linear complexity and the k error linear complexity of a binary sequence of period spl lscr 2 sup n respectively we also discuss an application of an extension of our algorithm to decoding a class of linear subcodes of reed muller codes

analysis and efficient implementations of a class of composited de bruijn sequences a binary de bruijn sequence is a sequence of period 2 n 2 n in which every binary n n tuple occurs exactly once in each period a de bruijn sequence has good randomness properties such as long period ideal tuple distribution and high linear complexity and can be generated by a nonlinear feedback shift register nlfsr finding an efficient nlfsr that can generate a de bruijn sequence with a long period is a significant challenge composited construction is a technique for constructing a de bruijn sequence of period 2 n k 2 n k by an nlfsr from a de bruijn sequence of period 2 n 2 n through a composition operation repeatedly applying k k times the goal of this article is to further investigate the composited construction of de bruijn sequences with efficient hardware implementations and determine randomness properties such as linear complexity our contributions in this article are as follows first we present a generalized construction of composited de bruijn sequences that is constructed by adding a combination of conjugate pairs of different lengths in the feedback function of the composited construction which results in generating a class of de bruijn sequences of size 2 k 2 k whereas the original composited construction can generate only two sequences second we investigate the linear complexity and the correlation property of the new class of de bruijn sequences we prove theoretically that the linear complexity of this class of de bruijn sequences is optimal or close to optimal interestingly we also prove that the linear complexities of all the sequences of this class are equal which strengthens etzion s conjecture jcta 1985 ieee it 1999 about the number of de bruijn sequences with equal linear complexity this is the first known construction of de bruijn sequences of an arbitrarily long period whose linear complexities are determined theoretically finally we implement our construction in hardware to demonstrate its practicality we synthesize our implementations for a 65 nm asic and a xilinx spartan fpga and present hardware areas and performances of de bruijn sequences of periods in the range of 2 160 2 160 to 2 1056 2 1056 for instance a class of de bruijn sequences of period 2 160 2 160 resp 2 288 2 288 can be implemented with an area of 3 43 resp 6 71 kges in 65 nm asic and 83 resp 229 slices in spartan6 fpga

feedback reconstruction and implementations of pseudorandom number generators from composited de bruijn sequences a binary de bruijn sequence of order n is a sequence of zeros and ones of period 2 n that contains every binary n tuple exactly once in a period of the sequence a composited construction of a de bruijn sequence is a construction of a nonlinear feedback shift register nlfsr that generates a de bruijn sequence where the composited feedback function of the nlfsr is the sum of a feedback function with k th order composition and a sum of k 1 product of sum terms the goals of this article are to perform a profound analysis of composited de bruijn sequences for use in cryptography and find an efficient implementation of the composited feedback function we first determine the lower bound of the linear complexity of a composited de bruijn sequence and then conduct a profound analysis on the composited construction by introducing the notion of the higher order d morphic preimages of a binary sequence our analysis aims at the reconstruction of a composited de bruijn sequence from a segment known as k th order d morphic order n de bruijn preimages n k dmdps of length 2 n k and k th order d morphic order n m sequence preimages n k dmmps of length 2n k for a nonlinearly and linearly generated composited de bruijn sequence respectively we also provide the success probability of finding an n k dmmp dmdp from a composited de bruijn sequence for the reconstruction furthermore we develop a new iterative technique with its parallel extension for computing the feedback function and the new technique is faster than other known techniques for producing de bruijn sequences of long period in addition we present three instances of composited de bruijn sequences of period 2 64 together with their software implementations and performances

behavior of derivatives of eigenvalues and eigenvectors in curve veering and mode localization and their relation to close eigenvalues the problem to measure the phenomena of eigenvalue curve veering and mode localization is addressed in this paper the second derivative of an eigenvalue and the first derivative of an eigenvector are taken as the measures numerically showing curve veering and mode localization based on the measurement close eigenvalues as a key factor for the occurrence of the phenomena are defined two eigenvalues are considered to be close if their difference is small enough to cause the occurrence of the phenomena the curve veering and mode localization can be noted by comparison of the derivatives with a critical value and hence the associated eigenvalues are close weakly coupled springs are given as an example

the fuzzy mathematics of finance this paper develops fuzzy analogues of the elementary compound interest problems in the mathematics of finance we find the fuzzy present value and fuzzy future value of fuzzy cash amounts using fuzzy interest rates over n periods where n may be crisp or fuzzy this paper also develops a method of comparing fuzzy net cash flows in order to rank fuzzy investment alternatives from best to worst

constructions for perfect maps and pseudorandom arrays a construction of perfect maps i e periodic r v binary arrays in which each n m binary matrix appears exactly once is given a similar construction leads to arrays in which only the zero n m matrix does not appear and to a construction in which only a few n m binary matrices do not appear a generalization to the nonbinary case is given the constructions involve an interesting problem in shift register theory the solution is given for almost all the case of this problem

efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition a new procedure for characterizing the solution of the eigenvalue problem in the presence of uncertainty is presented the eigenvalues and eigenvectors are described through their projections on the polynomial chaos basis an efficient method for estimating the coefficients with respect to this basis is proposed the method uses a galerkin based approach by orthogonalizing the residual in the eigenvalue eigenvector equation to the subspace spanned by the basis functions used for approximation in this way the stochastic problem is framed as a system of deterministic non linear algebraic equations this system of equations is solved using a newton raphson algorithm although the proposed approach is not based on statistical sampling the efficiency of the proposed method can be significantly enhanced by initializing the non linear iterative process with a small statistical sample synthesized through a monte carlo sampling scheme the proposed method offers a number of advantages over existing methods based on statistical sampling first it provides an approximation to the complete probabilistic description of the eigensolution second it reduces the computational overhead associated with solving the statistical eigenvalue problem finally it circumvents the dependence of the statistical solution on the quality of the underlying random number generator copyright 2007 john wiley sons ltd

frequency coalescence and mode localization phenomena a geometric theory physical systems the natural frequencies of which depend parametrically on certain quantities may exhibit the phenomenon of frequency coalescence when two or more natural frequencies become equal or the phenomenon of avoided crossings when two or more frequencies approach rapidly and then avoid crossing each other in the process the natural modes undergo significant variations it is shown that both phenomena can be described in a unified manner from the singularities of the mapping from the complex parameter plane into the complex frequency plane in particular the formation of a saddle point in the frequency plane and a branch point in the parameter space is the basis for explaining the properties associated with these phenomena the question of sensitivity of the system response near such singularities is subsequently examined it is shown that the development of a branch point singularity in the complex parameter plane can cause large or even infinite sensitivity of the system about this point depending on the distance of the branch point from the real axis in the parameter space it is further shown that mode localization is also associated with the appearance of a branch point near the real axis of the complex parameter plane which causes the large sensitivity that characterizes the phenomenon the theory is applied to examples of conservative and dissipative systems undergoing free vibrations

the properties of a class of linear fsrs and their applications to the construction of nonlinear fsrs in this paper the cycle structure and adjacency graphs of a class of linear feedback shift registers lfsrs are determined by recursively applying the d morphism to the maximum length lfsrs and representing the cycles by generating functions a new family of maximum length nonlinear feedback shift registers nfsrs are proposed based on the properties of these lfsrs the number of nfsrs in the proposed family is also considered

a survey of full length nonlinear shift register cycle algorithms shift registers have been used to generate sequences of 0 s and 1 s for over thirty years a wide variety of applications has been made of these sequences principally communications have made use of the sequences generated one particular class of shift register sequences for which applications exist is the full length nonlinear shift register sequences these sequences are periodic and of length 2 n and all 2 n different binary n tuples appear exactly one time in a periodic portion of the sequence in this paper we discuss various algorithms which have been suggested for generating these sequences

beyond the limitations of perturbation methods for real random eigenvalue problems using exceptional points and analytic continuation a numerical method is proposed to approximate the solution of parametric eigenvalue problem when the variability of the parameters exceed the radius of convergence of low order perturbation methods the radius of convergence of eigenvalue perturbation methods based on taylor series is known to decrease when eigenvalues are getting closer to each other this phenomenon knwon as veering in structural dynamics is a direct consequence of the existence of branch point singularity in the complex plane of the varying parameters where some eigenvalues are defective when this degeneracy referred to as exceptional point ep is close to the real axis the veering becomes stronger the main idea of the proposed approach is to combined a pair of eigenvalues to remove this singularity to do so two analytic auxiliary functions are introduced and are computed through high order derivatives of the eigenvalue pair with respect to the parameter this yields a new robust eigenvalue reconstruction scheme which is compared to taylor and puiseux series in all cases theoretical bounds are established and all approximations are compared numerically on a three degrees of freedom toy model this system illustrate the ability of the method to handle the vibrations of a structure with a randomly varying parameter computationally efficient the proposed algorithm could also be relevant for actual numerical models of large size arising from other applications involving parametric eigenvalue problems e g waveguides rotating machinery or instability problems such as squeal or flutter

construction of de bruijn sequences of minimal complexity it is well known that the linear complexity of a de bruijn sequence s of length 2 n is bounded below by 2 n 1 n for n geq 3 it is shown that this lower bound is attainable for all n

constructing de bruijn sequences by concatenating smaller universal cycles abstract we present sufficient conditions for when an ordering of universal cycles 1 2 m for disjoint sets s 1 s 2 s m can be concatenated together to obtain a universal cycle for s s 1 s 2 s m when s is the set of all k ary strings of length n the result of such a successful construction is a de bruijn sequence our conditions are applied to generalize two previously known de bruijn sequence constructions and then they are applied to develop three new de bruijn sequence constructions

linear complexity of de bruijn sequences old and new results the linear complexity of a de bruijn sequence is the degree of the shortest linear recursion which generates the sequence it is well known that the complexity of a binary de bruijn sequence of length 2 sup n is bounded below by 2 sup n 1 n and above by 2 sup n 1 for n spl ges 3 we briefly survey the known knowledge in this area some new results are also presented in particular it is shown that for each interval of length 2 sup log n 1 in the above range there exist binary de bruijn sequences of length 2 sup n with linear complexity in the interval

parallel solution methods for stochastic finite element analysis using monte carlo simulation in the present paper innovative solution strategies for parallel computer implementation have been developed in connection with the monte carlo simulation mcs and the weighted integral method to produce efficient numerical handling of stochastic finite element analysis for 2d plane stress strain problems furthermore mcs in conjunction with the local average method is also used to extend the stochastic finite element analysis to 3d solid structures although mcs approaches have the major advantage that accurate solutions can be obtained for any type of problem whose deterministic solution is known either numerically or analytically their applicability is hindered by the high computational effort that is required the implementation of innovative parallel solution techniques in this study resulted in cost effective treatment of these highly computationally demanding problems one and two level domain decomposition methods have been implemented numerical results revealed that the proposed approaches permit an efficient treatment of stochastic finite element analysis for real scale 2d plane stress strain and 3d solid structures

an approximate solution scheme for the algebraic random eigenvalue problem a reduced basis formulation is presented for the efficient solution of large scale algebraic random eigenvalue problems this formulation aims to improve the accuracy of the first order perturbation method and also allow the efficient computation of higher order statistical moments of the eigenparameters in the present method the two terms of the first order perturbation approximation for the eigenvector are used as basis vectors for ritz analysis of the governing random eigenvalue problem this leads to a sequence of reduced order random eigenvalue problems to be solved for each eigenmode of interest since only two basis vectors are used to represent each eigenvector explicit expressions for the random eigenvalues and eigenvectors can readily be derived this enables the statistics of the random eigenparameters and the forced response to be efficiently computed numerical studies are presented for free and forced vibration analysis of a linear stochastic structural system it is demonstrated that the reduced basis method gives better results as compared to the first order perturbation method

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

a context dependent method for ordering fuzzy numbers using probabilites in this work we suggest an approach to comparing fuzzy numbers motivated by a probabilistic view of the underlying uncertainty an important aspect of the method suggested is its context dependency the numbers being compared affect the process we discuss the effect of decision attitude and show that this approach is particularly useful for aiding decision makers having a temperate decision attitude optimism in the face of adversity and conservatism in the face plenty

a fast algorithm for determining the complexity of a binary sequence with period 2 n corresp the complexity of a periodic sequence s is defined to be the least number of stages in a linear feedback shift register that generates s

mode localization and eigenvalue loci veering phenomena in disordered structures an investigation of the effects of disorder on the modes of vibration of nearly periodic structures is presented it is shown that in structures with close eigenvalues small structural irregularities result in both strong localization of the mode shapes and abrupt veering away or mutual repulsion of the loci of the eigenvalues when these are plotted against a parameter representing the disorder in the system perturbation methods for the eigenvalue problem are applied to predict the occurrence of strong localization and eigenvalue loci veering which are shown to be two manifestations of the same phenomenon also perturbation methods that handle the dramatic effects of small disorder are developed to analyze eigenvalue loci veering and strong localization two representative disordered nearly periodic structures are studied a mistuned assembly of coupled oscillators and a multi span beam with irregular spacing of the supports

eigensolutions of perturbed nearly defective matrices abstract perturbation methods for approximating eigenvalues and eigenvectors of perturbed nearly defective mistuned systems have been discussed it is shown that the mistuning causes taylor expansions to be not uniformly valid even in small intervals of the perturbation parameter subsequently rendering them useless for practical purposes the problem is overcome by starting the perturbation expansion from an exactly defective tuned system close to the mistuned one asymptotic expansions are then obtained in terms of fractional powers of two parameters the modification and the mistuning parameter however as the tuned system is unknown an inverse problem has to be solved in order to determine it an algorithm valid for the particular but frequent case of several couples of nearly coincident eigenvalues has been detailed for this problem an outline of a more general case is also given illustrative examples are presented

modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties this paper presents two efficient modal approaches as an alternative to direct formulations for the time harmonic dynamic analysis of structures with random material and shape parameters in both approaches the structural eigenproblem is solved and complemented by a sensitivity analysis to the random parameters the modal perturbation stochastic finite element method sfem then condenses the response sensitivities to assess the response variability the mixed perturbation monte carlo sfem assesses the response statistics by sampling the structural eigenmodes according to the perturbation estimation of their probability distribution functions pdfs geometric uncertainties are handled through an appropriate shape parameterisation and a shape design sensitivity analysis two numerical applications examine both approaches in terms of accuracy variability level and computational requirements the applications involve a plate bending problem with random young modulus or edge length and a plate with a random flatness default particular observations related to the influence of the parameter pdfs in simulation based methods are also provided

perfect maps given positive integers r s u and spl upsi an r s u spl upsi perfect map pm is defined to be a periodic r spl times s binary array in which every u spl times spl upsi binary array appears exactly once as a periodic subarray perfect maps are the natural extension of the de bruijn sequences to two dimensions in the paper the existence question for perfect maps is settled by giving constructions for perfect maps for all parameter sets subject to certain simple necessary conditions extensive use is made of previously known constructions by finding new conditions which guarantee their repeated application these conditions are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of perfect maps

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

interaction of eigenvalues in multi parameter problems the paper presents a new general theory of interaction of eigenvalues of matrix operators depending on parameters both complex and real eigenvalues are considered strong and weak interactions are distinguished and their geometric interpretation on the complex plane is given mechanical examples are presented and discussed in detail