the entropy of fuzzy vectors several types of entropy of fuzzy variables or fuzzy sets have been given in the literature in order to measure the degree of uncertainty in order to measure the degree of uncertainty of fuzzy vectors a new definition of entropy of fuzzy vectors is proposed some properties are then investigated and the relations between the entropy of fuzzy variables and fuzzy vectors are discussed

eigenproblem formulation solution and interpretation for non proportionally damped continuous beams abstract a rationalized approach is described for formulating the eigenproblems associated with continuous beams where damping non proportionalities are introduced through the use lumped dampers partial damping layers or arbitrary complex impedances an efficient algorithm is then presented for determining an exact solution to the resulting complex eigenvalue equations and for computing the coefficients associated with the complex eigenfunctions a normalization procedure is developed which embodies all pertinent modal information yet presents the complex modes in a manner which approximates the instantaneous displacement patterns associated with the natural frequencies this scheme also allows an analyst to assess qualitatively and quantitatively the extent of non proportionality in the damping distribution and determine which parts of the system it most affects the formulation and normalization techniques are illustrated with two example cases

on quantification of different facets of uncertainty abstract with a brief introduction to three major types of uncertainties randomness nonspecificity and fuzziness we discuss various attempts to quantify them we also discuss several attempts to quantify total uncertainty in a system we then talk about some new facets of uncertainty like higher order fuzzy entropy hybrid entropy and conflict in a body of evidence in conclusion we indicate some other aspects of uncertainty that need to be modeled and quantified

transversal waves in beams via the network simulation method abstract in this paper the network simulation method nsm is proposed as a tool for solving the transverse motion of thin beams resulting from a bending action the reliability and robustness of the proposed technique is demonstrated with two examples in which a pinned pinned beam and a clamped mass load beam are respectively submitted to different flexural forces the nsm is a numerical technique for the solution of linear and non linear problems which are defined by a mathematical model assuming that the electrical variables of voltage and current are equivalent respectively to the displacement and the spatial variation of the displacement a network model for each volume element is designed such that electrical equations are formally equivalent to the spatial discretised equations of the mechanical model the whole network model including the devices associated with the boundary conditions is solved by the numerical computer code pspice the numerical results have been compared with those obtained by the mode superposition method the agreement between them is impressive the temporal behaviour of each quantity involved in the problem is obtained without transform complications since the whole study has been conducted in the time domain with the possibility of obtaining the corresponding spectral content at the end of calculation the main contribution of the present paper therefore is to employ the nsm numerical method in order to arrive at solutions in the time domain of dynamic mechanical problems one must also emphasize that nsm has not previously been used by other authors to solve physical problems like the ones presented here

graph ambiguity in this paper we propose a rigorous way to define the concept of ambiguity in the domain of graphs in past studies the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept to strengthen the theoretical results we discuss the application of the graph ambiguity concept to the graph classification setting conceiving a new kind of inexact graph matching procedure the results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs

a probabilistic definition of a nonconvex fuzzy cardinality the existing methods to assess the cardinality of a fuzzy set with finite support are intended to preserve the properties of classical cardinality in particular the main objective of researchers in this area has been to ensure the convexity of fuzzy cardinalities in order to preserve some properties based on the addition of cardinalities such as the additivity property we have found that in order to solve many real world problems such as the induction of fuzzy rules in data mining convex cardinalities are not always appropriate in this paper we propose a possibilistic and a probabilistic cardinality of a fuzzy set with finite support these cardinalities are not convex in general but they are most suitable for solving problems and contrary to the generalizing opinion they are found to be more intuitive for humans their suitability relies mainly on the fact that they assume dependency among objects with respect to the property to be in a fuzzy set the cardinality measures are generalized to relative ones among pairs of fuzzy sets we also introduce a definition of the entropy of a fuzzy set by using one of our probabilistic measures finally a fuzzy ranking of the cardinality of fuzzy sets is proposed and a definition of graded equipotency is introduced

an overview of wavelet based multiresolution analyses in this paper an overview of wavelet based multiresolution analyses is presented first the continuous wavelet transform in its simplest form is discussed then the definition of a multiresolution analysis is given and how wavelets fit into it is shown the authors take a closer look at orthogonal biorthogonal and semiorthogonal wavelets the fast wavelet transform wavelets on an interval multidimensional wavelets and wavelet packets are discussed several examples of wavelet families are introduced and compared finally the essentials of two major applications are outlined data compression and compression of linear operators

the wavelet transform in aeromagnetic processing the discrete wavelet transform dwt provides an effective and efficient alternative to traditional fourier and spatial convolution processing techniques in the enhancement of aeromagnetic data standard operators such as horizontal and vertical derivatives integrals of any order and the hilbert transform can be diagonalized in the wavelet domain leading to an efficient algorithm the dwt preserves the spatial localization of the components of the signal allowing for intelligent discrimination between noise and signal in a given frequency range this for example allows for more accurate calculation of higher order derivatives from noisy signals than is possible with conventional techniques additional accuracy can be gained by using a cycle spinning algorithm to minimize local artifacts from the dwt denoising procedure

bending vibration of axially loaded timoshenko beams with locally distributed kelvin voigt damping abstract utilizing the timoshenko beam theory and applying hamilton s principle the bending vibration equations of an axially loaded beam with locally distributed internal damping of the kelvin voigt type are established the partial differential equations of motion are then discretized into linear second order ordinary differential equations based on a finite element method a quadratic eigenvalue problem of a damped system is formed to determine the eigenfrequencies of the damped beams the effects of the internal damping sizes and locations of damped segment axial load and restraint types on the damping and oscillating parts of the damped natural frequency are investigated it is believed that the present study is valuable for better understanding the influence of various parameters of the damped beam on its vibration characteristics

on locking free shear deformable beam finite elements abstract this is an elementary exposition of beam finite element models an overview of existing and new displacement finite element models of the euler bernoulli and shear deformation beam theories is presented a locking free finite element model using the form of the exact solution of the timoshenko beam theory is developed the element contains the euler bernoulli beam element as a special case and yields exact nodal values for the generalized displacements for constant material and geometric properties of beams the procedure is extended to develop a locking free finite element model of the simplified third order theory of beams the element contains the euler bernoulli and the locking free timoshenko beam finite elements as special cases the element stiffness matrix of the unified beam bending element is 4 4 and yet has the superconvergence character the advantage of this element is that it can be used to obtain exact nodal displacements and forces from the equilibrium equations of the element in a frame structural analysis using one finite element per a structural member this cannot be achieved with the traditional equal interpolation reduced integration element because the element exhibits shear locking for thin members unless two or more elements per a structural member are used

entropy of credibility distributions for fuzzy variables this paper deals with the degree of uncertainty associated with fuzzy variables based on the notion of credibility measure a definition of entropy is formulated from an information theoretical view and its properties are investigated finally some comments are given on the construction of alternative definitions of entropy and axiomatic characterization

convergence properties and derivative extraction of the superconvergent timoshenko beam finite element abstract the superconvergent timoshenko beam element of reddy comput methods appl mech engrg 149 1997 113 132 is derived here using an assumed strain approach a method of reference field formulation is proposed from which pointwise higher order derivatives moments and shears can be derived for this element and theoretical proofs of the existence of such points are presented it is shown that the order of convergence may be at least two orders higher than the fe derivative field in the cases where uniform discretization is adopted finally a smoothed derivative field is derived by using a least square polynomial fit over these points several simple numerical examples are presented to demonstrate the ability of the method to extract exact derivative fields from the fe results

non local finite element analysis of damped beams non local viscoelastic beam models are used to analyse the dynamics of beams with different boundary conditions using the finite element method unlike local damping models the internal force of the non local model is obtained as weighted average of state variables over a spatial domain via convolution integrals with spatial kernel functions that depend on a distance measure in the finite element analysis the interpolating shape functions of the element displacement field are identical to those of standard two node beam elements however for non local damping nodes remote from the element do have an effect on the energy expressions and hence on the damping matrix the expressions of these direct and cross damping matrices may be obtained explicitly for some common spatial kernel functions and euler bernoulli beam theory alternatively numerical integration may be applied to obtain solutions examples are given where the eigenvalues are compared to the exact solution for a pinned pinned beam to demonstrate the convergence of the finite element method the results for beams with other boundary conditions are used to demonstrate the versatility of the finite element technique 2007 elsevier ltd all rights reserved

measuring fuzzy uncertainty first this paper reviews several well known measures of fuzziness for discrete fuzzy sets then new multiplicative and additive classes are defined we show that each class satisfies five well known axioms for fuzziness measures and demonstrate that several existing measures are relatives of these classes the multiplicative class is based on nonnegative monotone increasing concave functions the additive class requires only nonnegative concave functions some relationships between several existing and the new measures are established and some new properties are derived the relative merits and drawbacks of different measures for applications are discussed a weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced finally we comment on the construction of measures that may assess all of the uncertainties associated with a physical system

frequency time decomposition of seismic data using wavelet based methods spectral analysis is an important signal processing tool for seismic data the transformation of a seismogram into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods however for seismograms whose frequency content vary with time a simple 1 d fourier frequency transformation is not sufficient improved spectral decomposition in frequency time ft space is provided by the sliding window short time fourier transform although this method suffers from the time frequency resolution limitation recently developed transforms based on the new mathematical field of wavelet analysis bypass this resolution limitation and offer superior spectral decomposition the continuous wavelet transform with its scale translation plane is conceptually best understood when contrasted to a short time fourier transform the discrete wavelet transform and matching pursuit algorithm are alternative wavelet transforms that map a seismogram into ft space decomposition into ft space of synthetic and calibrated explosive source seismic data suggest that the matching pursuit algorithm provides excellent spectral localization and reflections direct and surface waves and artifact energy are clearly identifiable wavelet based transformations offer new opportunities for improved processing algorithms and spectral interpretation methods

a note on the vibrations of restrained beams and rods with point masses abstract this paper is concerned with the approximate determination of the fundamental frequency and first mode shape of a beam or rod to which springs and point masses are attached after formulating the general eigenvalue problem which forms the basis of the analysis the theory is applied to three examples and it is shown that the results are quite satisfactory

improved eigenvalues for combined dynamical systems using a modified finite element discretization scheme new approaches are presented to discretize an arbitrarily supported linear structure carrying various lumped attachments specifically the exact eigendata i e the exact natural frequencies and mode shapes of the linear structure without the lumped attachments are first used to modify its finite element mass and stiffness matrix so that the eigensolutions of the discretized system coincide with the exact modes of vibration this is achieved by identifying a set of minimum changes in the finite element system matrices and enforcing certain constraint conditions once the updated matrices for the linear structure are found the finite element assembling technique is then used to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices numerical experiments show that for the same number of elements the proposed scheme returns higher natural frequencies that are substantially more accurate than those given by the finite element model alternatively the proposed discretization scheme allows one to efficiently and accurately determine the higher natural frequencies of a combined system without increasing the number of elements in the finite element model

a note on the use of a fuzzy approach in adaptive partitioning algorithms for global optimization in global optimization adaptive partitioning algorithms apa operate on the basis of partitioning the feasible region into subregions sampling and evaluating each subregion and selecting one or more subregions for repartitioning the purpose of the repartitioning process is to locate a narrow neighborhood around the global optimum in this correspondence we propose to use a fuzzy approach in the assessment of subregions using random samples taken from these subregions we discuss different types of uncertainties involved in apa and we conclude that the use of a fuzzy approach in the assessment of subregions is in concurrence with apa s convergence property we provide numerical results for the fuzzy approach on 13 test functions from the literature

frequency response of a combined structure using a modified finite element method a modified finite element method is proposed to analyze the frequency response of an arbitrarily supported linear structure carrying various lumped attachments this is accomplished by updating the finite element mass and stiffness matrices of the linear structure without any lumped attachments using its exact natural frequencies and mode shapes so that the eigensolutions of the updated linear structure coincide with the exact eigendata once the updated matrices for the linear structure are found the finite element assembling technique is then exploited to include the lumped attachments by adding their parameters to the appropriate elements in the modified mass and stiffness matrices after assembling the global mass and stiffness matrices the frequency response of the combined system can be easily obtained numerical experiments show that using only a few finite elements the proposed scheme returns natural frequencies and frequency responses that are nearly identical to those obtained by using a finite element model with a very fine mesh the new method is easy to apply and efficient to use and it can be extended to determine the frequency response of any combined linear structure over any specified range of excitation frequencies

a galerkin method for distributed systems with non local damping in this paper a non local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of euler bernoulli beams and kirchoff plates unlike ordinary local damping models the damping force in a non local model is obtained as a weighted average of the velocity field over the spatial domain determined by a kernel function based on distance measures the resulting equation of motion for the beam or plate structures is an integro partial differential equation rather than the partial differential equation obtained for a local damping model approximate solutions for the complex eigenvalues and modes with non local damping are obtained using the galerkin method numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions for non local and non viscous damping models and different kernel functions

higher order fuzzy entropy and hybrid entropy of a set new entropy measures such as higher order fuzzy entropy and hybrid entropy of a set have been introduced various properties along with their proofs have been included applicability of these new measures to various problems has been highlighted

an exact generalised function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping abstract this paper concerns the frequency response analysis of beams and plane frames with an arbitrary number of kelvin voigt viscoelastic dampers typical external and internal dampers are considered as grounded translational tuned mass rotational and axial dampers for bending and axial vibrations respectively using the theory of generalised functions within a 1d formulation of equations of motion exact closed form expressions are derived for beam dynamic green s functions and frequency response functions under arbitrary polynomial load for any number of dampers for a plane frame exact global frequency response matrix and load vector are built with size depending only on the number of beam to column nodes for any number of dampers and point polynomial loads along the frame members from the nodal displacement solution the exact frequency response in all frame members is also obtained in closed analytical form numerical applications show many of the advantages of the proposed method

maximum entropy membership functions for discrete fuzzy variables due to the deficiency of information the membership function of a fuzzy variable cannot be obtained explicitly it is a challenging work to find an appropriate membership function when certain partial information about a fuzzy variable is given such as expected value or moments this paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints a genetic algorithm is designed to solve the general maximum entropy model for discrete fuzzy variables which is illustrated by some numerical experiments

some properties of the exponential entropy abstract a new definition of probabilistic entropy based on the exponential behavior of gain function has recently been introduced by the authors 1 1 it has also been extended to define various image entropy measures 2 2 and hybrid and higher order entropy of fuzzy sets 3 3 the present work investigates some additional properties in the light of both probability theory and fuzzy set theory of this new entropy definition to ensure its greater range of applications

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

an exact modal analysis approach to vibration analysis of structures with mass spring subsystems and rotational joints abstract a novel exact modal analysis approach is presented for vibration analysis of plane continuous structures which are coupled with discrete mass spring subsystems and include elastic rotational joints modelling local flexibility using the theory of generalised functions to handle the discontinuities of the response variables every continuous member with any number of mass spring subsystems and joints is treated as a two node element for which a 6 6 exact dynamic stiffness matrix is obtained in closed form as a result the global dynamic stiffness matrix is built by a standard finite element assembling procedure with size depending only on the number of nonzero nodal degrees of freedom of member to member nodes upon deriving pertinent orthogonality conditions for the modes the system response under arbitrary loads is obtained by modal impulse and modal frequency response functions under the assumption of proportional damping the solutions are exact and can be used as benchmark for classical finite element solutions the approach is formulated for various mass spring subsystems acting in transverse and axial directions relative to every member

exact frequency and mode shape formulae for studying vibration and stability of timoshenko beam system two sets of exact natural frequency and mode shape formulae for an axially loaded timoshenko uniform single span beam carrying elastically supported end masses are derived the end masses are restrained against rotation and translation with linear springs the two equations of motion of references 1 2 are used in the problem formulation comparisons between the derived frequency equations for a typical example of a clamped free beam are made the difference between natural frequencies is significant for beams subjected to high loads and for high modes of vibration most of the well known published exact expressions for determining the natural frequencies and the mode shapes can be obtained from the present equations as special cases the influence of beam rotary inertia and end mass es geometrical parameters on the natural frequency and critical buckling load coefficients has been studied when an axial compressive load is acting at the centre of gravity of the end mass es the same critical buckling load coefficients are found for free free pinned free and pinned pinned beams and similarly for clamped sliding and sliding sliding beams in addition if the slope due to bending is allowed at one end of the beam the same critical buckling loads are found for clamped free sliding free and sliding pinned beam configurations the present work includes graphs and numerical tables describing the variation of the natural frequencies and the critical buckling load coefficients from the design point of view

a novel approach to determine the frequency equations of combined dynamical systems abstract a novel approach is presented which can be used to reduce the generalized eigenvalue problem associated with the free vibration of a linear elastic structure carrying lumped elements atsdistinct locations usingncomponent modes in the assumed modes method the free vibration of such a combined dynamical system is governed by the solution of a generalized eigenvalue problem of ordern n whose stiffness and mass matrices consist of diagonal matrices modified by a total ofsrank one matrices wherescorresponds to the number of attachment points this generalized eigenvalue problem can be manipulated such that the natural frequencies governing free vibration can be calculated instead by solving a much smaller characteristic determinant of orders s interestingly enough this smaller and simpler characteristic determinant can also be obtained by using the lagrange multipliers formalism in conjunction with lagrange s equations

wave propagation and sampling theory part ii sampling theory and complex waves morlet et al 1982 this issue showed the advantages of using complex values for both waves and characteristics of the media we simulated the theoretical tools we present here using the goupillaud kunetz algorithm now we present sampling methods for complex signals or traces corresponding to received waves and sampling methods for complex characterization of multilayered or heterogeneous media regarding the complex signals we present a twodimecsional 2 d method of sampling in the time frequency domain using a special or extended gabor expansion on a set of basic wavelets adapted to phase preservation such a 2 d expansion permits us to handle in a proper manner instantaneous frequency spectra we show the differences between wavelet resolution and sampling grid resolution we also show the importance of phase preservation in high resolution seismic regarding the media we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution analytical studies of wave propagation in periodic structures are well known in solid state physics and lead to the so called bloch waves the introduction of complex waves leads to replacing the classical wave equation by a schriidinger equation finally we show that complex wave equations gabor expansion and bloch waves are three different ways of introducing the tools of quantum mechanics in highresolution seismic gabor 1946 kittel 1976 morlet 1975 and conversely the goupillaud kunetz algorithm and an extended gabor expansion may be of some use in solid state physics

wave propagation and sampling theory part i complex signal and scattering in multilayered media from experimental studies in digital processing of seismic reflection data geophysicists know that a seismic signal does vary in amplitude shape frequency and phase versus propagation time to enhance the resolution of the seismic reflection method we must investigate these variations in more detail we present quantitative results of theoretical studies on propagation of plane waves for normal incidence through perfectly elastic multilayered media as wavelet shapes we use zero phase cosine wavelets modulated by a gaussian envelope and the corresponding complex wavelets a finite set of such wavelets for an appropriate sampling of the frequency domain may be taken as the basic wavelets for a gabor expansion of any signal or trace in a two dimensional 2 d domain time and frequency we can then compute the wave propagation using complex functions and thereby obtain quantitative results including energy and phase of the propagating signals these results appear as complex 2 d functions of time and frequency i e as instantaneous frequency spectra choosing a constant sampling rate on the logarithmic scale in the frequency domain leads to an appropriate sampling method for phase preservation of the complex signals or traces for this purpose we developed a gabor expansion involving basic wavelets with a constant time duration mean period ratio for layered media as found in sedimentary basins

eigensensitivity based optimal distribution of a viscoelastic damping layer for a flexible beam abstract in this paper optimal distribution of a viscoelastic damping layer is sought for suppression of the transient vibration of a flexible beam for the damping design eigenvalues in the range of interest are taken as design criteria rather than the responses at a specific frequency two eigensensitivity based optimizing procedures are proposed which are analogous to the pole placement technique and optimal control theory for dynamic system design for the eigenanalysis of the structure with frequency dependent material golla hughes mctavish ghm model is used in expressing the viscoelastic material property and an approximate eigensolution is employed to avoid the intensity of iterative computation in the optimization process which is caused by additional degrees of freedom due to ghm modelling optimized partial coverage configurations are illustrated and compared to the full coverage configuration demonstrating the improved vibration characteristic of the optimally layered structure

symmetric state space method for a class of nonviscously damped systems multiple degree of freedom linear nonviscously damped systems are considered it is assumed that the nonviscousdampingforcesdependonthepasthistoryofvelocitiesviaconvolutionintegralsoverexponentiallydecaying kernel functions the traditional state space approach well known for viscously damped systems is extended to such nonviscously damped systems using a set of internal variables suitable numerical examples are provided to illustrate the proposed approach i introduction v iscousdampingisthemostcommonmodelforthemodeling of vibration damping in linear systems this model e rst introduced by rayleigh 1 assumes that the instantaneous generalized velocities are the only relevant variables that determine damping viscous damping models are used widely for their simplicity and mathematical convenience even though the behavior of real structural materials is at best poorly mimicked by simple viscous models forthisreason itiswellrecognizedthat ingeneral aphysically realistic model of damping will not be viscous damping models in whichthedissipativeforcesdependonanyquantityotherthantheinstantaneous generalized velocities are nonviscous damping models mathematically any causal model that makes the energy dissipation functional nonnegative is a possible candidate for a nonviscous damping model clearly a wide range of choice is possible either based on the physics of the problem or by selecting a model a priori and e tting its parameters from experiments here we will use a particular type of damping model that is not viscous and throughout the paper the terminology nonviscous damping will refer to this specie c model only possiblythemostgeneralwaytomodeldampingwithinthelinear range is to use nonviscous damping models that depend on the past history of motion via convolution integrals over kernel functions 2 the equations of motion of an n degree of freedom linear system with such damping can be expressed by

finite element analysis of vibrating linear systems with fractional derivative viscoelastic models abstract fractional derivative rheological models are known to be very effective in describing the viscoelastic behaviour of materials especially of polymers and when applied to dynamic problems the resulting equations of motion after a fractional state space expansion can still be studied in terms of modal analysis but the growth in matrix dimensions carried by this expansion is in general so fast to make the calculations exceedingly cumbersome this paper presents a method for reducing the computational effort due to finite element fe analysis of vibrating linear systems with a fractional derivative viscoelastic model namely the fractional kelvin voigt the proposed method may be applied also to problems involving other fractional derivative linear models and it takes under control the computational effort by reducing the main eigenproblem of large dimension to the solution of two standard related eigenproblems of lower size numerical examples are provided in order to validate both the accuracy and the efficiency of the proposed methodology

a new analytical technique for vibration analysis of non proportionally damped beams abstract vibrating linear mechanical systems in particular continuous systems are often modelled considering proportional damping distributions only although in many real situations this simplified approach does not describe the dynamics of the system with sufficient accuracy in this paper an analytical method is given to take into account the effects of a more general viscous damping model referred to as non proportional damping on a class of vibrating continuous systems a state form expansion applied in conjunction with a transfer matrix technique is adopted to extract the eigenvalues and to express the eigenfunctions in analytical form i e complex modes corresponding to non synchronous motions numerical examples are included in order to show the efficiency of the proposed method non proportional damping distributions of different type such as internal and external lumped or distributed viscous damping are tested on non homogeneous euler bernoulli beams in bending vibration with different boundary conditions finally a discussion on root locus diagrams behaviour and on modal damping ratio significance for non proportionally damped systems is presented

a general approach to formulating the frequency equation for a beam carrying miscellaneous attachments beams carrying various lumped attachments have been studied extensively over the years in this paper a simple approach is proposed that can be used to readily determine the eigenvalues of an arbitrarily supported single span or multi span beam carrying any combination of lumped mass rotary inertia grounded translational or torsional spring grounded translational or torsional viscous damper an undamped or damped oscillator with or without a rigid body degree of freedom rather than solving a generalized eigenvalue problem to obtain the eigenvalues of the system a frequency equation is formulated instead whose solution can be easily solved either numerically or graphically the proposed scheme is easy to code and can be easily modified to accommodate beams with arbitrary supports and carrying any number of miscellaneous lumped attachments

some new information measures for fuzzy sets abstract after reviewing some existing measures for fuzzy sets we introduce a new informative measure for discrimination between two fuzzy sets this discriminating measure reduces to the nonprobabilistic entropy of deluca and termini 7 under a special condition the divergence measure between two sets has been defined along with a large set of properties it has also been used to define an ambiguity fuzziness measure renyi s 17 probabilistic entropy of order has been extended to define nonprobabilistic entropy of a fuzzy set various properties of this definition have also been proved applications of these measures to clustering image processing vision etc are highlighted

estimating depth and model type using the continuous wavelet transform of magnetic data the continuous wavelet transform has been proposed recently for the interpretation of potential field anomalies using poisson wavelets which are equivalent to an upward continuation of the analytic signal this technique allows one to estimate the depth of burial of homogeneous field sources and to determine the nature of the source in the form of a structural index moreau et al 1999 accomplish this by successively testing the least squares misfit on a log log plot of the wavelet transform amplitude versus the sum of the depth and the dilation upward continuation height we extend this methodology by analyzing the ratio of the poisson wavelet coefficients of the first and second orders for simple pole sources this ratio at one dilation is enough to estimate the depth and index uniquely but for extended sources of finite size we must analyze the variation of the estimates with dilations the technique gives good results on synthetic and field examples

on the use of fuzzy constraints in semisupervised clustering this paper introduces fuzzy hss a semisupervised hierarchical clustering approach that uses fuzzy instance level constraints these constraints are external information on the shape of fuzzy must link and fuzzy cannot link restrictions they allow uncertainty when indicating whether two instances of a dataset belong to the same group fuzzy must link constraints give a degree of belief of two instances belonging to the same group analogously fuzzy cannot link constraints indicate the degree of belief of two instances not belonging to the same group these constraints have been introduced in a hierarchical clustering process allowing us to obtain the optimal number of groups in a dendrogram when the number of clusters is not known the optimal amount of constraints needed in the process is determined by means of fuzzy entropy an extensive experimental study is provided by comparing this fuzzy semisupervised approach with classic unsupervised methods as well as a crisp semisupervised alternative

analysis of non homogeneous timoshenko beams with generalized damping distributions abstract this paper presents a study on the effects of generalized damping distributions on non homogeneous timoshenko beams on the basis of some fundamentals of modal analysis for damped continuous systems applied to the particular case of the timoshenko beam model the eigenproblem is solved by applying a method combining a state space representation with a transfer matrix technique yielding closed form expressions for the eigenfunctions after validation by means of numerical examples using the finite element method response functions in both the time and the frequency domain are discussed and compared according to different damping distributions

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed