spectral asymptotics for the third order operator with periodic coefficients abstract we consider the self adjoint third order operator with 1 periodic coefficients on the real line the spectrum of the operator is absolutely continuous and covers the real line we determine the high energy asymptotics of the periodic antiperiodic eigenvalues and of the branch points of the lyapunov function furthermore in the case of small coefficients we show that either whole spectrum has multiplicity one or the spectrum has multiplicity one except for a small spectral nonempty interval with multiplicity three in the last case the asymptotics of this small interval is determined

i v fuzzy relations and sanchez s approach for medical diagnosis abstract this paper introduces the concept of i v fuzzy relations i v fuzzy tolerance relations composition of i v fuzzy relations etc several useful propositions are proved finally sanchez s approach for medical diagnosis is considered and discussed using the idea of i v fuzzy relations

hilbert space frames containing a riesz basis and banach spaces which have no subspace isomorphic toc0 abstract we prove that a hilbert space frame fi i icontains a riesz basis if every subfamily fi i j j i is a frame for its closed span secondly we give a new characterization of banach spaces which do not have any subspace isomorphic toc0 this result immediately leads to an improvement of a recent theorem of holub concerning frames consisting of a riesz basis plus finitely many elements

a note on the infinitary action of triangular norms and conorms in this note the action of triangular norms and conorms on subsets of the unit interval with arbitrary cardinality is defined and the properties of these generalized operations are also considered

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

frames and pseudo inverses abstract we point out some connections between the existing theories for frames and pseudo inverses in particular using the pseudo inverse of an unbounded operator we show how to make frame like decompositions with respect to some sequences which do not satisfy the upper frame condition as a special case this approach immediately gives nontrivial results for usual frames

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

a meshless method for solving an inverse spacewise dependent heat source problem in this paper an effective meshless and integration free numerical scheme for solving an inverse spacewise dependent heat source problem is proposed due to the use of the fundamental solution as basis functions the method leads to a global approximation scheme in both spatial and time domains the standard tikhonov regularization technique with the generalized cross validation criterion for choosing the regularization parameter is adopted for solving the resulting ill conditioned system of linear algebraic equations the effectiveness of the algorithm is illustrated by several numerical examples

on an unconditional basis of generalized eigenvectors of the nonself adjoint gribov operator in bargmann space abstract in this article we prove that the system of generalized eigenvectors of the gribov operator is an unconditional basis in bargmann space we also give a generalized diagonalization in the abel sense of the semigroups respectively associated to this operator and to its square root finally some open problems are pointed out

equations of fuzzy relations defined on fuzzy subsects abstract in this paper some results of the theory of fuzzy relation equations are generalized when we consider fuzzy relations defined on fuzzy sets instead of crisp sets if the extension of classical definitions for composition of relations 12 13 is not straightforward we provide suitables counterexamples illustrating the necessity of change in definitions we find the greatest or the least solutions of fuzzy relation equations with different types of compositions like the sup t inf t inf or sup compositions

fuzzy topology on fuzzy sets and tolerance topology in this paper fuzzy topology has been defined on a fuzzy set the notion of quasi coincidence is extended in order to fit this new situation and to generalize the concept of q neighbourhood introduced originally by ming and ming 1980 the generalized q neighbourhood system has been utilized to introduce tolerance topology on a fuzzy set with a fuzzy tolerance relation

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

on an unconditional basis of generalized eigenvectors of an analytic operator and application to a problem of radiation of a vibrating structure in a light fluid abstract in this paper we prove that the system of generalized eigenvectors of the perturbed operator t e t 0 e t 1 e 2 t 2 e k t k forms an unconditional basis with parentheses in a separable hilbert space x where e c t 0 is a closed densely defined linear operator on x with domain d t 0 having compact resolvent while t 1 t 2 are linear operators on x with the same domain d d t 0 satisfying a specific growing inequality an application to a problem of radiation of a vibrating structure in a light fluid is presented

some specific types of fuzzy relation equations in this paper we study some specific types of fuzzy equations more specifically we focus on analyzing equations involving two fuzzy subsets of the same referential and a fuzzy relation defined over fuzzy subsets

on fuzzy equivalence i fuzzy reflexive symmetric and transitive relations on fuzzy subsets are studied various types of reflexivities and corresponding equivalences are considered the possible fuzzy partitioning of a fuzzy subset is investigated

dual reciprocity hybrid boundary node method for free vibration analysis abstract as a truly meshless method of boundary type the hybrid boundary node method hbnm has the advantages of both boundary element method bem and meshless method the main problem is that it is only suitable for the homogeneous problems now the dual reciprocity method drm is introduced into hbnm to deal with the integral for the inhomogeneous terms of the governing equations and the rigid body motion approach is employed to solve the hyper singular integrations a new meshless method named dual reciprocity hybrid boundary node method drhbnm is proposed and applied to solve free vibration problems in this method the solution composes into two parts i e the general solution and the particular solution the general solution is solved by hbnm and the particular one is obtained by drm drhbnm is a true boundary type meshless method it does not require the boundary element mesh either for the purpose of interpolation of the variables or for the integration of energy the points in the domain are only used to interpolate particular solution by the radial basis function finally the boundary variables are interpolated by the independent smooth boundary segments the q r algorithm and householder algorithm are applied to solve the eigenvalues and eigenvectors of the transformed matrix numerical examples for free vibration problems show that a good convergence with mesh refinement is achievable and the computational results for the natural circular frequencies and free vibration modes are very accurate furthermore the computation parameters have little influence on the results and can be chosen in a wide range it is shown that the present method is effective and can be widely applied in practical engineering

on a riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non selfadjoint problem deduced from a perturbation method for sound radiation in the present paper we prove that the family of exponentials associated to the eigenvalues of the perturbed operator t t0 t1 2t2 ktk forms a riesz basis in l2 0 t t 0 where c t0 is a closed densely defined linear operator on a separable hilbert space h with domain d t0 having isolated eigenvalues with multiplicity one while t1 t2 are linear operators on h having the same domain d d t0 and satisfying a specific growing inequality after that we generalize this result using a h lipschitz function as application we consider a non selfadjoint problem deduced from a perturbation method for sound radiation

angle criteria for frame sequences and frames containing a riesz basis we obtain a condition implying that the union of two frame sequences is also a frame sequence christensen found a condition for this in terms of orthogonal projections we phrase our condition by use of the angle between closed subspaces also a lower bound formula is obtained we then apply the results to find conditions for a frame containing a riesz basis to be a riesz frame

diversity analysis based on ordered patterns abstract diversity index based on entropy such as emlen index e i is suggested as a highly effective algorithm to detect complexity in nonlinear systems in this paper a method considering the amplitude information called weighted emlen index w e i is proposed to extract the amplitude information and track the signal changes and then we expand e i w e i methods to multiple time scales thus multiscale emlen index m s e i and multiscale weighted emlen index m s w e i will be used to discuss the complexity of traffic time series under different scales results show that there are differences between the complexity of weekend traffic time series and workday time series which gives a better classification of traffic systems for making prediction

a characterization of the schechter essential spectrum on banach spaces and applications abstract in a recent article by the author c r acad sci paris ser i 331 2000 525 530 boll un mat ital 2002 to appear the schechter spectrum of closed densely defined linear operators has been characterized on spaces which possess the dunford pettis property or which are isomorphic to one of the spaces l p p 1 the purpose of the present work is to extend this analysis to the case of banach spaces further we apply the obtained results to investigate the schechter essential spectrum of one dimensional transport equations with different boundary conditions

adaptive spatial decomposition in fast multipole method this work presents a new adaptive node cluster algorithm for fast multipole method in the algorithm we use rectangular boxes instead of cubes subdivide a box based on its shape and tighten the child boxes at each subdivision step more importantly we determine the number of expansion terms in multipole to local translations according to the distance between the two interaction boxes our method is tested using benchmark examples for three dimensional potential problems the results obtained show that the new algorithm can solve a problem with 100 thousands nodes in about 20 min and runs nearly three times faster than the standard algorithm the proposed algorithm is especially suitable for treating slender and shell like structures

reduction of fuzzy strict order relations abstract fuzzy strict order relations and the notion of their reduction are defined a necessary and sufficient condition is obtained for the transitive closure of the reduction to coincide with the strict order itself some possible graph theoretic significances of these results are discussed in the conclusion

adjointness of fuzzy systems this paper deals with two adjoint fuzzy systems based on and compositions which correspond to the normal use of and in l fuzzy logic respectively the resolution of composite fuzzy relational inequations for these adjoint fuzzy systems can be skillfully treated by the gentzen type sequent calculus as well as by the lattice theoretical way owing to the adjointness of and compositions

t eigen fuzzy sets abstract this paper concerns the study of the solutions of sup t equations such that atr a where t is a triangular norm and r is a fuzzy relation by generalizing a result from sanchez 12 we determine the greatest t eigen fuzzy set of a fuzzy relation a t eigen fuzzy set of r being a fuzzy set a which is a solution of atr a we also study some algebraic properties for the class of the t eigen sets of a fuzzy relation and for the set of fuzzy relations leaving invariant a given fuzzy set finally properties related with the transitive closure are established

numerical analysis of the non uniform sampling problem we give an overview of recent developments in the problem of reconstructing a band limited signal from nonuniform sampling from a numerical analysis view point it is shown that the appropriate design of the finite dimensional model plays a key role in the numerical solution of the nonuniform sampling problem in the one approach often proposed in the literature the finite dimensional model leads to an ill posed problem even in very simple situations the other approach that we consider leads to a well posed problem that preserves important structural properties of the original infinite dimensional problem and gives rise to efficient numerical algorithms furthermore a fast multilevel algorithm is presented that can reconstruct signals of unknown bandwidth from noisy nonuniformly spaced samples we also discuss the design of efficient regularization methods for ill conditioned reconstruction problems numerical examples from spectroscopy and exploration geophysics demonstrate the performance of the proposed methods

weighted projections and riesz frames abstract let h be a separable hilbert space and e k k 1 a fixed orthonormal basis of h motivated by many papers on scaled projections angles of subspaces and oblique projections we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis this is used to refine previous work on scaled projections and to obtain a new characterization of riesz frames

an approach to group choice with fuzzy preference relations abstract this paper presents an approach to group choice with fuzzy preference relations the experts judgements are presented as fuzzy preorder relations as group choice we assume the nearest relation to these relations in the sense of the hamming distance in this paper an algorithm for finding a preorder relation as an expression of group choice is given and a way is pointed out to find the best alternative on the basis of this group choice furthermore the connection between the impossibility theorem of arrow and this group choice is considered

on an riesz basis of generalized eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid abstract in this paper we prove that the system of generalized eigenvectors of the operator i ek 1d4 dx4 forms a riesz basis of l2 l l where k is the integral operator with kernel the hankel function of the first kind and order 0 this operator was introduced in j sound vibration 177 1994 259 275 we give positive answers to the hypotheses posed in that article

on extended fuzzy relational model with proximity relations in this paper shenoi and melton s model of fuzzy relational database is considered proximity relation being an important tool of the model is characterized theoretically an optimal distribution in 0 1 and consequently the domain partition are defined and studied with examples on fuzzy queries

fuzzy relational structures the state of art fuzzy relational structures built with the aid of fuzzy sets and fuzzy relations constitute a fundamental class of constructs arising in fuzzy set theory they give rise to fuzzy relation equations in this paper we will develop the concepts of single and multilevel relational structures different logic operations will be discussed in detail aspects of the knowledge representation will be studied and illustrated with several schemes of applications

fuzzy antisymmetry and order abstract fuzzy antisymmetry and various types of ordering are defined and theorems relating to them proved a few constants associated with a fuzzy relation are introduced and some of their properties investigated

frames containing a riesz basis and approximation of the frame coefficients using finite dimensional methods abstract we consider frames which contain a riesz basis among those we find riesz frames i e frames with the property that every subfamily is a frame for its closed linear span with a common lower bound we point out the connection to the projection method which can be used to approximate the frame coefficients for a riesz frame using finitely many elements of the frame under different conditions we show that the projection method even approximates the frame coefficient in l 2 sense

regranulation a granular algorithm enabling communication between granular worlds abstract in this paper we describe a granular algorithm for translating information between two granular worlds represented as fuzzy rulebases these granular worlds are defined on the same universe of discourse but employ different granulations of this universe in order to translate information from one granular world to the other we must regranulate the information so that it matches the information granularity of the target world this is accomplished through the use of a first order interpolation algorithm implemented using linguistic arithmetic a set of elementary granular computing operations we first demonstrate this algorithm by studying the common fuzzy pd rulebase at several different granularities and conclude that the 3 3 granulation may be too coarse for this objective we then examine the question of what the natural granularity of a system might be this is studied through a 10 fold cross validation experiment involving three different granulations of the same underlying mapping for the problem under consideration we find that a 7 7 granulation appears to be the minimum necessary precision

q similitudes and q fuzzy partitions abstract the concept of q reflexive q transitive relation q similitude and q fuzzy partition of a fuzzy set are introduced and it is proved that there exists a one to one correspondence between q similitudes and q fuzzy partitions some results on compositions of q reflexive relations and q similitudes are also obtained

a two stage logarithmic goal programming method for generating weights from interval comparison matrices a two stage logarithmic goal programming tlgp method is proposed to generate weights from interval comparison matrices which can be either consistent or inconsistent the first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency the weights are assumed to be multiplicative rather than additive in the case of hierarchical structures a nonlinear programming method is used to aggregate local interval weights into global interval weights a simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process the proposed tlgp is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a level sets and the extension principle six numerical examples including a group decision analysis problem with a group of comparison matrices a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods comparisons with other existing procedures are made whenever possible

decomposition of riesz frames and wavelets into a finite union of linearly independent sets we characterize riesz frames and prove that every riesz frame is the union of a finite number of riesz sequences furthermore it is shown that for piecewise continuous wavelets with compact support the associated regular wavelet systems can be decomposed into a finite number of linearly independent sets finally for finite sets an equivalent condition for decomposition into a given number of linearly independent sets is presented

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

continuous and discrete wavelet transforms this paper is an expository survey of results on integral representations and discrete sum expansions of functions in l 2 bf r in terms of coherent states two types of coherent states are considered weyl heisenberg coherent states which arise from translations and modulations of a single function and affine coherent states called wavelets which arise as translations and dilations of a single function in each case it is shown how to represent any function in l 2 bf r as a sum or integral of these states most of the paper is a survey of literature most notably the work of i daubechies a grossmann and j morlet a few results of the authors are included

eigenvalues of the far field operator for the helmholtz equation in an absorbing medium it is shown that there exist an infinite number of eigenvalues of the far field operator corresponding to the scattering of a time harmonic plane wave by either an imperfectly conducting obstacle or an absorbing inhomogeneous medium regions in the complex plane are found where these eigenvalues must lie and in the case of obstacle scattering numerical examples are given showing how precise these regions are

regularized moving least square method and regularized improved interpolating moving least square method with nonsingular moment matrices abstract the moving least square mls method has been popular applied in surface construction and meshless methods however the moment matrix in mls method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult to overcome this problem a regularized moving least square method with nonsingular moment matrix is proposed the shape functions obtained from the regularized mls method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized mls based meshless method to overcome this problem a regularized improved interpolating moving least square iimls method based on the iimls method is also proposed compared with the regularized mls method the regularized iimls not only has nonsingular moment matrices but also obtains shape functions with delta function property shape functions of the proposed methods are compared in 1d and 2d cases and the methods have been applied in curve fitting surface fitting and meshless method in numerical examples

algorithms for the computation of t transitive closures we present two weight driven algorithms for the computation of the t transitive closure of a symmetric binary fuzzy relation on a finite universe x with cardinality n or equivalently of a symmetric n spl times n matrix with elements in 0 1 with t a triangular norm the first algorithm is proven to be valid for any triangular norm t whereas the second algorithm is shown to be valid when t is either the minimum operator or an archimedean triangular norm furthermore we investigate how these algorithms can be appropriately adapted to generate the t transitive closure of nonsymmetric binary fuzzy relations or matrices as well

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

analytical methods for recovering coefficients in differential equations from spectral data in this paper analytical methods for recovering coefficients from spectral data are discussed properties of these methods are given and mathematical models for which these methods might apply are presented

the use of fuzzy variables in pert abstract in this paper we present a method called fpert for estimating a project completion time in the situation when activity duration times in the project network model are given in the form of fuzzy variables fuzzy sets on time space theoretical foundations of the method as well as results of calculations derived from a simple example are included

studies in fuzzy relations over fuzzy subsets in this paper a generalisation of fuzzy relations is introduced fuzzy relations are defined on fuzzy subsets properties like ordered reflexivity symmetry transitity transitive closures of such generalised relations and operations on them are discussed

some results on the addition of fuzzy intervals abstract a simple new method of computing t sum of fuzzy intervals having the same results as the sum of fuzzy intervals based on the weakest t norm t w is introduced this work extends that of mesiar fuzzy sets and systems 91 1997 231 237 and markova fuzzy sets and systems 91 1997 253 258

novel meshless method for solving the potential problems with arbitrary domain in this article a non singular and boundary type meshless method in two dimensions is developed to solve the potential problems the solution is represented by a distribution of the kernel functions of double layer potentials by using the desingularization technique to regularize the singularity and hypersingularity of the kernel functions the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined the main difficulty of the coincidence of the source and collocation points then disappears by employing the two point function the off diagonal coefficients of influence matrices are easily obtained the numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of exact solution conventional mfs and bem for the dirichlet neumann and mix type boundary conditions bcs of interior and exterior problems with simple and complicated boundaries good agreements with exact solutions are observed

meshless analysis of potential problems in three dimensions with the hybrid boundary node method combining a modified functional with the moving least squares mls approximation the hybrid boundary node method hybrid bnm is a truly meshless boundary only method the method may have advantages from the meshless local boundary integral equation mlbie method and also the boundary node method bnm in fact the hybrid bnn requires only the discrete nodes located on the surface of the domain the hybrid bnm has been applied to solve 2d potential problems in this paper the hybrid bnm is extended to solve potential problems in three dimensions formulations of the hybrid bnm for 3d potential problems and the mls approximation on a generic surface are developed a general computer code of the hybrid bnm is implemented in c the main drawback of the boundary layer effect in the hybrid bnm in the 2d case is circumvented by an adaptive face integration scheme the parameters that influence the performance of this method are studied through three different geometries and known analytical fields numerical results for the solution of the 3d laplace s equation show that high convergence rates with mesh refinement and high accuracy are achievable copyright 2004 john wiley sons ltd

nullspaces and frames in this paper we give new characterizations of riesz and conditional riesz frames in terms of the properties of the nullspace of their synthesis operators on the other hand we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms

uniqueness for near constant data in fourth order inverse eigenvalue problems abstract let l p u d4u dx4 d dx p1 du dx p2u u 0 u 0 u 1 u 1 0 where p l2 0 1 l2 0 1 we show that for near constant coefficients if p is even about 1 2 and l p and l p have the same eigenvalues then knowledge of the first coefficient uniquely determines the second up to average value further we show that knowledge of the second coefficient uniquely determines the first we derive precise eigenfunction asymptotics using resolvent perturbation theory and prove the result using a simple perturbation of basis argument

on the riesz basis of a family of analytic operators in the sense of kato and application to the problem of radiation of a vibrating structure in a light fluid abstract in this paper we prove that the system formed by some of generalized eigenvectors of the operator t 0 e t 1 e 2 t 2 which are analytic on e forms a riesz basis of the separable hilbert space h where e c and t 0 t 1 t 2 some linear transformations on h which have the same domain d h after that we give an application for a problem concerning the radiation of a vibrating structure in a light fluid

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

the hybrid boundary node method accelerated by fast multipole expansion technique for 3d potential problems this paper presents a fast formulation of the hybrid boundary node method hybrid bnm for solving problems governed by laplace s equation in 3d the preconditioned gmres is employed for solving the resulting system of equations at each iteration step of the gmres the matrix vector multiplication is accelerated by the fast multipole method green s kernel function is expanded in terms of spherical harmonic series an oct tree data structure is used to hierarchically subdivide the computational domain into well separated cells and to invoke the multipole expansion approximation formulations for the local and multipole expansions and also conversion of multipole to local expansion are given and a binary tree data structure is applied to accelerate the moving least square approximation on surfaces all the formulations are implemented in a computer code written in c numerical examples demonstrate the accuracy and efficiency of the proposed approach copyright 2005 john wiley sons ltd