wavelet like bases for the fast solutions of second kind integral equations a class of vector space bases is introduced for the sparse representation of discretizations of integral operators an operator with a smooth nonoscillatory kernel possessing a finite number of singularities in each row or column is represented in these bases as a sparse matrix to high precision a method is presented that employs these bases for the numerical solution of second kind integral equations in time bounded by o n log 2 n where n is the number of points in the discretization numerical results are given which demonstrate the effectiveness of the approach and several generalizations and applications of the method are discussed

szpilrajn s theorem on fuzzy orderings fuzzy relation matrices are considered and the well known szpilrajn theorem on orderings is generalized to fuzzy orderings zadeh has already shown a generalized theorem but another generalization is given in matrix form some interesting operations on fuzzy matrices are introduced and their properties are mentioned briefly the theorem is represented in terms of the matrix operations the operations have many properties and are useful in the various applications of fuzzy matrices or fuzzy relations

lie bialgebroids and poisson groupoids lie bialgebras arise as infinitesimal invariants of poisson lie groups a lie bialgebra is a lie algebra g with a lie algebra structure on the dual g which is compatible with the lie algebra g in a certain sense for a poisson group g the multiplicative poisson structure induces a lie algebra structure on the lie algebra dual g which makes g g into a lie bialgebra in fact there is a one one correspondence between poisson lie groups and lie bialgebras if the lie groups are assumed to be simply connected 7 16 19 the importance of poisson lie groups themselves arises in part from their role as classical limits of quantum groups 8 and in part because they provide a class of poisson structures for which the realization problem is tractable 15 poisson groupoids were introduced by weinstein 24 as a generalization of both poisson lie groups and the symplectic groupoids which arise in the integration of arbitrary poisson manifolds 4 11 he noted that the lie algebroid dual a g of a poisson groupoid g itself has a lie algebroid structure but did not develop the infinitesimal structure further in this paper we introduce and study a natural infinitesimal invariant for poisson groupoids the lie bialgebroids of the title our ultimate purpose is to develop a lie theory for poisson groupoids parallel to that for poisson groups in this paper we are primarily concerned with the first half of this process that is with the construction of the lie bialgebroid of a poisson groupoid after the preliminary 2 in which we describe the generalization to arbitrary lie algebroids of the exterior calculus and schouten calculus in 3 we define a lie bialgebroid to be a lie algebroid a whose dual a is also equipped with a lie algebroid structure such that the coboundary operator d a a associated to a satisfies a cocycle equation with respect to a the lie algebra of sections of a this is clearly a straightforward extension of the concept of a lie bialgebra 16 but cannot be formalized in lie algebroid cohomological terms since there is no satisfactory adjoint representation for a general lie algebroid most of 3 is devoted to proving that this definition is self dual if a a is a lie bialgebroid then a a is also in 4 we briefly consider the special case of lie bialgebroids satisfying a triangularity condition which include some important examples such as the usual triangular lie bialgebras and lie bialgebroids associated to poisson manifolds the techniques used in 2 4 are similar to those known for lie bialgebras it would be possible by suitably generalizing the proof for poisson groups to prove

dirac nijenhuis structures in this paper we study the concept of dirac nijenhuis structures we consider them to be a pair where d is a dirac structure defined with respect to a lie bialgebroid a a and is a nijenhuis operator which defines a deformation of the lie algebroid structure of d in a compatible way the transformation can be considered to deform also the double of the lie bialgebroid which leads to the concept of dirac nijenhuis structures of type i or to not affect it leading to dirac nijenhuis structures of type ii we prove that the concept contains poisson nijenhuis structures as a particular case and provides another example for the case of kahler manifolds

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

fixed points of functions with max weighted quasi arithmetic mean operator abstract let 0 1 and f be a continuous strictly monotone real valued function the weighted quasi arithmetic mean of two numbers a b is defined by a b f 1 f a 1 f b let a a i j be an n n real matrix and x x 1 x 2 x n t r n we construct a function a 1 a 2 a n a r n r n by j a x max 1 l n x l a l j for all j 1 2 n in this paper we show that a has a unique fixed point x a moreover it can be shown that for each x r n the sequence x a k generated by the following iterative scheme x a 0 x and x a k a x a k 1 for all k 1 converges to the unique fixed point x a besides some properties of the fixed point are derived as an application our results imply that the max weighted quasi arithmetic mean powers of any matrix are always convergent the continuity of the function m n n r r n defined by a x a is proposed as well

adaptive multiscale moment method ammm for analysis of scattering from perfectly conducting plates adaptive multiscale moment method ammm is presented for the analysis of scattering from a thin perfectly conducting plate this algorithm employs the conventional moment method and a special matrix transformation which is derived from the tensor products of the two one dimensional 1 d multiscale triangular basis functions that are used for expansion and testing functions in the conventional moment method the special feature of these new basis functions introduced through this transformation is that they are orthogonal at the same scale except at the initial scale and not between scales from one scale to another scale the initial estimate for the solution can be predicted using this multiscale technique hence the compression is applied directly to the solution and the size of the linear equations to be solved is reduced thereby improving the efficiency of the conventional moment method the basic difference between this methodology and the other techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly using an iterative solution methodology the extrapolated results at the higher scale thus provide a good initial guess for the iterative method typically when the number of unknowns exceeds a few thousand unknowns the matrix solution time exceeds generally the matrix fill time hence the goal of this method is directed in solving electrically larger problems where the matrix solution time is of concern two numerical results are presented which demonstrate that the ammm is a useful method to analyze scattering from perfectly conducting plates

an efficient numerical method for studying interfacial motion in two dimensional creeping flows we present new methods for computing the motion of two dimensional closed interfaces in a slow viscous flow the interfacial velocity is found through the solution to an integral equation whose analytic formulation is based on complex variable theory for the biharmonic equation the numerical methods for solving the integral equations are spectrally accurate and employ a fast multipole based iterative solution procedure which requires only o n operations where n is the number of nodes in the discretization of the interface the interface is described spectrally and we use evolution equations that preserve equal spacing in arclength of the marker points a small scale decomposition is performed to extract the dominant term in the evolution of the interface and we show that this dominant term leads to a cfl type stability constraint when in an equal arclength frame this term is linear and we show that implicit time integration schemes that are explicit in fourier space can be formulated we verify this analysis through several numerical examples

transitivity of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called a path algebra transitivity of generalized fuzzy matrices is defined and some properties of transitivity are shown especially properties of the composition of transitive fuzzy matrices representing transitive fuzzy relations are examined by introducing a third operation on the semiring with two operations the transitivity is closely related to metrics distances ultrametrics and so on

reduction of poisson manifolds and jacobi manifolds via dirac theory we give two kinds of reduction relating poisson manifolds and jacobi manifolds by classifying reducible dirac and jacobi dirac structures into two classes respectively the proof needs only some direct calculation without using the existence of momentum mappings or the introducing of admissible functions etc meanwhile we present some examples and applications

the transitive closure convergence of powers and adjoint of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called an incline and their transitive closure powers determinant and adjoint matrices are studied an expression for the transitive closure of a matrix a as a sum of its powers and some su2cient conditions for powers of a matrix to converge are given if the incline is commutative a su2cient condition for nilpotency of a matrix is obtained namely the determinants of the principal submatrices of the matrix are all equal to zero element in addition it is proved that a n 1 is equal to the adjoint matrix of a if the matrix a satis5es a in

on the power sequence of a fuzzy matrix with convex combination of max product and max min operations in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper we consider the powers of a fuzzy matrix with convex combination of max product and max min operations we show that the powers of a fuzzy matrix a with such operations are asymptotical p period if and only if the powers of an associated boolean matrix a are p periodic moreover necessary and sufficient conditions for such a fuzzy matrix to be nilpotent are proposed

transitivity of fuzzy matrices under generalized connectedness abstract generalizing the ordinary connectedness of binary relations we show some properties of transitive fuzzy matrices under generalized connectedness that is introducing a special type if subtraction operation we obtain several conditions for a given fuzzy matrix to become transitive under connectedness obtained results are generalizations of propositions on boolean matrices representing tournaments which are asymmetric and weakly connected relations or asymmetric and complete digraphs they are considered to be useful for discussions of fuzzy preferences fuzzy digraphs and so on the generalized propositions hold for boolean matrices as well and as a special case we can have properties of ordinary tournaments

regular article a fast adaptive multipole algorithm in three dimensions we present an adaptive fast multipole method for the laplace equation in three dimensions it uses both new compression techniques and diagonal forms for translation operators to achieve high accuracy at a reasonable cost

an efficient solution for cauchy likesystems of linear equations using the displacement approach and transformation of vectors the complexity ofsolving strongly nonsingular cauchy like systems of linear equations email protected email protected will be improved off a factor of log n from the known algorithms of the recursive triangular factorization where f is a field and email protected f n x 1 is a vector and c f n x n is a strongly nonsingular cauchy like matrix the efficient algorithms were presented by morf bitmead and anderson to solve strongly nonsingular toeplitz like equations of linear systems by using the recursive triangular factorization in 1980 recently this approach of the recursive triangular factorization was extended to solve cauchy like systems with the complexity of o n log 3n operations by pan et al this is the best known complexity bound by using the direct approach of recursive triangular factorization in cauchy like cases however these algorithms are still slower than the well known algorithms with the asymptotic bound of o n log 2n operations which have been proposed by the means of reducing cauchy like matrices into toeplitz like matrices in our present paper the algorithms of the recursive triangular factorization are modified so that the complexity bound of the direct recursive approach can be decreased to o n log 2n operations this matches the asymptotic bound without transforming to toeplitz like matrices our improvement of the direct recursive approach is by a factor of log n due to changing the original vectors expressed in the given cauchy like matrix into the special vectors where the entries are unit roots the applications of structured matrices include nevanlinna pick tangential interpolation problems

short note moore s law and the saffman taylor instability ten years ago hou lowengrub and shelley 4 published a state of the art boundary integral simulation of a classical viscous fingering problem the saffman taylor instability 12 in terms of complexity and level of detail those computations 4 are still among the most ramified and accurately computed interfacial instability patterns that have appeared in the literature since 1994 the computational power of a standard workstation has increased a hundredfold as predicted by moore s law 7 the purpose of this note is to consider moore s law and its consequences in computational science and in particular its impact on studying the saffman taylor instability we illustrate moore s law and fast algorithms in action by presenting the worlds largest viscous fingering simulation to date viscous fingering is one of the fundamental interfacial instabilities in fluid dynamics perturbations to an expanding circular air bubble displacing a viscous fluid in a thin gap flow device become unstable resulting in intricate densely branched interfacial patterns the viscous fingering problem is governed by the three dimensional incompressible navier stokes equations with moving free boundaries at the fluid air interface without simplification this problem is computationally intractable and will remain so for the foreseeable future the simulations in this note build upon decades of advances in mathematical modeling and numerical methods i the fluid dynamics in a thin gap is reduced from the threedimensional navier stokes equations by asymptotic analysis to a darcy s law 12

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

robust exponential convergence of hp fem in balanced norms for singularly perturbed reaction diffusion problems corner domains abstract the h p version of the finite element method is applied to singularly perturbed reaction diffusion type equations on polygonal domains the solution exhibits boundary layers as well as corner layers on a class of meshes that are suitably refined near the boundary and the corners robust exponential convergence in the polynomial degree is shown in both a balanced norm and the maximum norm

on pseudo transitive approximations of fuzzy relations abstract in the present paper we consider a generalization of the well known notion of transitive fuzzy relations this may be useful for preference relations or similarity relations describing butterfly like configurations where the widely used transitive closure is rather different from the original relation moreover the proposed concept enables us to determine relations which are transitive only for a part of the elements under consideration some examples demonstrate the usefulness of our approach

convergence of max arithmetic mean powers of a fuzzy matrix fuzzy matrices provide convenient representations for fuzzy relations on finite universes in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper the max arithmetic mean composition is considered for the fuzzy relations we show that the max arithmetic mean powers of a fuzzy matrix always are convergent

analysis of arbitrarily shaped dielectric radomes using adaptive integral method based on volume integral equation the adaptive integral method aim is employed to solve the volume integral equation vie for analyzing the radiation of the antenna with an arbitrarily shaped radome small dipoles are used as exciting sources modeling the radomes by tetrahedron cells the induced volume current is determined by the aim based on vie the application of aim significantly reduces cpu time and computer memory requirement hence the method presented in the paper can be applied to simulate electrically large sized radomes finally the radiation patterns of small dipole arrays in the presence of spherical and conical radomes are calculated

on nilpotency of generalized fuzzy matrices in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some properties and characterizations for nilpotent generalized fuzzy matrices are established reduction of generalized fuzzy matrices is defined and some properties of reduction of nilpotent generalized fuzzy matrices are obtained partial results obtained in this paper generalize the corresponding ones on fuzzy matrices on lattice matrices and on incline matrices

on the fast matrix multiplication in the boundary element method by panel clustering the boundary element method bem leads to a system of linear equations with a full matrix while fem yields sparse matrices this fact seems to require much computational work for the definition of the matrix for the solution of the system and in particular for the matrix vector multiplication which always occurs as an elementary in this paper a method for the approximate matrix vector multiplication is described which requires much less arithmetical work in addition the storage requirements are strongly reduced

a fast high order solver for problems of scattering by heterogeneous bodies a new high order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented here a scatterer is described by a continuously or discontinuously varying refractive index n x within a two dimensional 2d bounded region solutions of the associated helmholtz equation under given incident fields are then obtained by high order inversion of the lippmann schwinger integral equation the algorithm runs in o nlog n operations where n is the number of discretization points a wide variety of numerical examples provided include applications to highly singular geometries high contrast configurations as well as acoustically electrically large problems for which supercomputing resources have been used recently our method provides highly accurate solutions for such problems on small desktop computers in cpu times of the order of seconds

twisted jacobi manifolds twisted dirac jacobi structures and quasi jacobi bialgebroids we study twisted jacobi manifolds a concept that we had introduced in a previous note twisted jacobi manifolds can be characterized using twisted dirac jacobi which are sub bundles of courant jacobi algebroids we show that each twisted jacobi manifold has an associated lie algebroid with a 1 cocycle we introduce the notion of quasi jacobi bialgebroid and prove that each twisted jacobi manifold has a quasi jacobi bialgebroid canonically associated moreover the double of a quasi jacobi bialgebroid is a courant jacobi algebroid several examples of twisted jacobi manifolds and twisted dirac jacobi structures are presented

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

jacobi structures revisited jacobi algebroids i e graded lie brackets on the grassmann algebra associated with a vector bundle which satisfy a property similar to that of the jacobi brackets are introduced they turn out to be equivalent to generalized lie algebroids in the sense of iglesias and marrero jacobi bialgebroids are defined in the same manner a lifting procedure of elements of this grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding lie brackets is developed this gives the possibility of associating canonically a lie algebroid with any local lie algebra in the sense of kirillov

on identification in fuzzy systems and its applications in control problems abstract the problem of identification in fuzzy systems described by the use of fuzzy equation is considered the identification method and its performance index is also presented the formal procedure of the identification algorithm is illustrated by means of a numerical example the possibility of using the proposed algorithm for the solution of a control problem is given as well

jacobi nijenhuis algebroids and their modular classes jacobi nijenhuis algebroids are defined as a natural generalization of poisson nijenhuis algebroids in the case where there exists a nijenhuis operator on a jacobi algebroid which is compatible with it we study modular classes of jacobi and jacobi nijenhuis algebroids

deformation of lie derivative and μ symmetries we introduce in the spirit of witten s gauging of exterior differential a deformed lie derivative that allows a geometrical interpretation of and symmetries in complete analogy with standard symmetries the case of variational symmetries both for odes and for pdes is also considered in this approach leading to and conservation laws

on transitivity of generalized fuzzy matrices abstract in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some elementary properties and characterizations for transitive generalized fuzzy matrices are established and transitivity of powers of a generalized fuzzy matrix is discussed also the transitive closure of a generalized fuzzy matrix is considered and some properties of the transitive closures are obtained partial results obtained in this paper generalize the corresponding ones on nilpotent matrices and on matrices with periods

a fast algorithm for the multiplication of generalized hilbert matrices with vectors on presente un algorithme rapide de complexite logarithmique pour la multiplication des matrices de hilbert generalisees par des vecteurs

a fast multi level boundary element method for the helmholtz equation abstract most recently we have developed a novel multi level boundary element method mlbem for the solution of the steady heat diffusion equation involving asymptotically decaying non oscillatory log singular and strongly singular kernels this hierarchical approach generalizes the pioneering work of brandt and lubrecht on multi level multi integration mlmi and c cycle multi grid to the broader class of mixed boundary value problems the result is a fast accurate and efficient boundary element method the present paper extends this new computational methodology to the solution of the helmholtz equation involving oscillatory log singular and strongly singular kernels for two dimensional problems we consider a direct boundary element formulation and due to the nature of the fundamental solutions split the corresponding boundary integral equation into real and imaginary parts then we introduce double noded corners to facilitate a patch by patch application of the mlmi algorithm for fast matrix vector and matrix transpose vector multiplications within bi conjugate gradient methods the performance of the proposed fast mlbem is investigated using a numerical example that possesses an exact solution for wave numbers 20 and below we demonstrate that the fast mlbem algorithm for the helmholtz equation is robust accurate and exceptionally efficient

lie algebroid foliations and script e1 m dirac structures we prove some general results about the relation between the 1 cocycles of an arbitrary lie algebroid a over m and the leaves of the lie algebroid foliation on m associated with a using these results we show that a 1 m dirac structure l induces on every leaf f of its characteristic foliation a 1 f dirac structure lf which comes from a precontact structure or from a locally conformal presymplectic structure on f in addition we prove that a dirac structure on m can be obtained from l and we discuss the relation between the leaves of the characteristic foliations of l and

the schrodinger operator as a generalized laplacian the schrodinger operators on the newtonian spacetime are defined in a way which make them independent of the class of inertial observers in this picture the schrodinger operators act not on functions on the spacetime but on sections of a certain one dimensional complex vector bundle the schrodinger line bundle this line bundle has trivializations indexed by inertial observers and is associated with an u 1 principal bundle with an analogous list of trivializations the schrodinger principal bundle if an inertial frame is fixed the schrodinger bundle can be identified with the trivial bundle over spacetime but as there is no canonical trivialization inertial frame these sections interpreted as wavefunctions cannot be viewed as actual functions on the spacetime in this approach the change of an observer results not only in the change of actual coordinates in the spacetime but also in a change of the phase of wavefunctions for the schrodinger principal bundle a natural differential calculus for wave forms is developed that leads to a natural generalization of the concept of the laplace beltrami operator associated with a pseudo riemannian metric the free schrodinger operator turns out to be the laplace beltrami operator associated with a naturally distinguished invariant pseudo riemannian metric on the schrodinger principal bundle the presented framework does not involve any ad hoc or axiomatically introduced geometrical structures it is based on the traditional understanding of the schrodinger operator in a given reference frame which is supported by producing right physics predictions and it is proven to be strictly related to the frame independent formulation of analytical newtonian mechanics and hamilton jacobi equations that makes a bridge between the classical and quantum theory

manin triples for lie bialgebroids in his study of dirac structures a notion which includes both poisson structures and closed 2 forms t courant introduced a bracket on the direct sum of vector fields and 1 forms this bracket does not satisfy the jacobi identity except on certain subspaces in this paper we systematize the properties of this bracket in the definition of a courant algebroid this structure on a vector bundle e rightarrow m consists of an antisymmetric bracket on the sections of e whose jacobi anomaly has an explicit expression in terms of a bundle map e rightarrow tm and a field of symmetric bilinear forms on e when m is a point the definition reduces to that of a lie algebra carrying an invariant nondegenerate symmetric bilinear form for any lie bialgebroid a a over m a notion defined by mackenzie and xu there is a natural courant algebroid structure on a oplus a which is the drinfel d double of a lie bialgebra when m is a point conversely if a and a are complementary isotropic subbundles of a courant algebroid e closed under the bracket such a bundle with dimension half that of e is called a dirac structure there is a natural lie bialgebroid structure on a a whose double is isomorphic to e the theory of manin triples is thereby extended from lie algebras to lie algebroids our work gives a new approach to bihamiltonian structures and a new way of combining two poisson structures to obtain a third one we also take some tentative steps toward generalizing drinfel d s theory of poisson homogeneous spaces from groups to groupoids

on the max contraction powers of a fuzzy matrix abstract in the literature the powers of a fuzzy matrix with max arithmetic mean convex combination of max min and max arithmetic mean convex combination of max product and max min compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper we consider the max contraction powers of a fuzzy matrix which is an extension of the max arithmetic mean convex combination of max min and max arithmetic mean convex combination of max product and max arithmetic mean operation we show that the powers of such a fuzzy matrix are always convergent and the limit matrix has the feature that all elements of each column are identical

on the geometric quantization of jacobi manifolds the geometric quantization of jacobi manifolds is discussed a natural cohomology termed lichnerowicz jacobi on a jacobi manifold is introduced and using it the existence of prequantization bundles is characterized to do this a notion of contravariant derivatives is used in such a way that the procedure developed by vaisman for poisson manifolds is naturally extended a notion of polarization is discussed and the quantization problem is studied the existence of prequantization representations is also considered

the fast solution of poisson s and the biharmonic equations on irregular regions we present fast methods for solving laplace s and the biharmonic equations on irregular regions with smooth boundaries the methods used for solving both equations make use of fast poisson solvers on a rectangular region in which the irregular region is embedded they also both use an integral equation formulation of the problem where the integral equations are fredholm integral equations of the second kind the main idea is to use the integral equation formulation to define a discontinuous extension of the solution to the rest of the rectangular region fast solvers are then used to compute the extended solution aside from solving the equations we have also been able to compute derivatives of the solutions with little loss of accuracy when the data was sufficiently smooth

computing a t transitive lower approximation or opening of a proximity relation since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation assuming that such a violation is mainly due to decision maker estimation errors in some way the more number of elicitations the more probable inconsistency is this is mostly the case within a fuzzy framework even when the number of alternatives or object to be classified is relatively small in this paper we propose a fast method to compute a t indistinguishability from a reflexive and symmetric fuzzy relation being t any left continuous t norm the computed approximation we propose will take o n 3 time complexity where n is the number of elements under consideration and is expected to produce a t transitive opening to the authors knowledge there are no other proposed algorithm that computes t transitive lower approximations or openings while preserving the reflexivity and symmetry properties

stokes flow around cylinders in a bounded two dimensional domain using multipole accelerated boundary element methods the multipole technique has recently received attention in the field of boundary element analysis as a means of reducing the order of data storage and calculation time requirements from o n2 iterative solvers or o n3 gaussian elimination to o n log n or o n where n is the number of nodes in the discretized system such a reduction in the growth of the calculation time and data storage is crucial in applications where n is large such as when modelling the macroscopic behaviour of suspensions of particles in such cases a minimum of 1000 particles is needed to obtain statistically meaningful results leading to systems with n of the order of 10 000 for the smallest problems when only boundary velocities are known the indirect boundary element formulation for stokes flow results in fredholm equations of the second kind which generally produce a well posed set of equations when discretized a necessary requirement for iterative solution methods the direct boundary element formulation on the other hand results in fredholm equations of the first kind which upon discretization produce ill conditioned systems of equations the model system here is a two dimensional wide gap couette viscometer where particles are suspended in the fluid between the cylinders this is a typical system that is efficiently modelled using boundary element method simulations the multipolar technique is applied to both direct and indirect formulations it is found that the indirect approach is sufficiently well conditioned to allow the use of fast multipole methods the direct approach results in severe ill conditioning to a point where application of the multipole method leads to non convergence of the solution iteration copyright 1999 john wiley sons ltd

convergence of powers for a fuzzy matrix with convex combination of max min and max arithmetic mean operations fuzzy matrices have been proposed to represent fuzzy relations on finite universes since thomason s paper in 1977 showing that powers of a max min fuzzy matrix either converge or oscillate with a finite period conditions for limiting behavior of powers of a fuzzy matrix have been studied it turns out that the limiting behavior depends on the algebraic operations employed which usually in the literature includes max min max product max archimedean t norm max t norm max arithmetic mean operations respectively in this paper we consider the powers of a fuzzy matrix with convex combination of max min and max arithmetic mean operations we show that the powers of such a fuzzy matrix are always convergent

fast adaptive summation of point forces in the two dimensional poisson equation direct summation of the velocity field introduced by point vortices tends to be time consuming since the velocity of each vortex is found as a sum over all other vortices the resulting number of numerical operations is proportional to the square of the number of vortices here a relatively simple procedure is outlined which significantly reduces the number of operations by replacing selected partial sums by asymptotic series the resulting number of operations appears to vary roughly in proportion to the number of unknowns corresponding to a fast solver

efficient numerical methods for multiple surfactant coated bubbles in a two dimensional stokes flow we present efficient and highly accurate numerical methods to compute the deformation of surfactant coated two dimensional bubbles in a slow viscous flow surfactant acts to locally alter the surface tension and thereby change the nature of the interface motion in this paper we restrict our attention to the case of a dilute insoluble surfactant the convection diffusion equation for the surfactant concentration on the interface is coupled with the stokes equations in the fluid domain through a boundary condition based on the laplace young condition the stokes equations are first recast as an integral equation and then solved using a fast multipole accelerated iterative procedure the computational cost per time step is only o n log n operations with n being the number of discretization points on the interface the bubble interfaces are described by a spectral mesh and is advected according to the fluid velocity in such a manner so as to preserve equal arc length spacing of marker points this equal arc length framework has the dual advantage of dynamically maintaining the spatial mesh and allowing efficient implicit treatment of the stiffest terms in the dynamics several phenomenologically different examples are presented

dirac structures for generalized lie bialgebroids we study dirac structures for generalized courant algebroids which are doubles of generalized lie bialgebroids the cases investigated include graphs of bivector fields and characteristic pairs of some sub bundles

multiply rooted multiscale models for large scale estimation divide and conquer or multiscale techniques have become popular for solving large statistical estimation problems the methods rely on defining a state which conditionally decorrelates the large problem into multiple subproblems each more straightforward than the original however this step cannot be carried out for asymptotically large problems since the dimension of the state grows without bound leading to problems of computational complexity and numerical stability in this paper we propose a new approach to hierarchical estimation in which the conditional decorrelation of arbitrarily large regions is avoided and the problem is instead addressed piece by piece the approach possesses promising attributes it is not a local method the estimate at every point is based on all measurements it is numerically stable for problems of arbitrary size and the approach retains the benefits of the multiscale framework on which it is based a broad class of statistical models a stochastic realization theory an algorithm to calculate statistical likelihoods and the ability to fuse local and nonlocal measurements

poisson jacobi reduction of homogeneous tensors the notion of homogeneous tensors is discussed we show that there is a one to one correspondence between multivector fields on a manifold m homogeneous with respect to a vector field on m and first order polydifferential operators on a closed submanifold n of codimension 1 such that is transversal to n this correspondence relates the schouten nijenhuis bracket of multivector fields on m to the schouten jacobi bracket of first order polydifferential operators on n and generalizes the poissonization of jacobi manifolds actually it can be viewed as a super poissonization this procedure of passing from a homogeneous multivector field to a first order polydifferential operator can also be understood as a sort of reduction in the standard case a half of a poisson reduction a dual version of the above correspondence yields in particular the correspondence between homogeneous symplectic structures on m and contact structures on n

a fast bie iteration method for an arbitrary body in a flow of incompressible inviscid fluid the paper is concerned with the new iteration algorithm to solve boundary integral equations arising in boundary value problems of mathematical physics the stability of the algorithm is demonstrated on the problem of a flow around bodies placed in the incompressible inviscid fluid with a discrete numerical treatment we approximate the exact matrix by a certain toeplitz one and then apply a fast algorithm for this matrix on each iteration step we illustrate the convergence of this iteration scheme by a number of numerical examples both for hard and soft boundary conditions it appears that the method is highly efficient for hard boundaries being much less efficient for soft boundaries

adaptive multiscale moment method ammm for analysis of scattering from three dimensional perfectly conducting structures the adaptive multiscale moment method ammm is presented for the analysis of scattering from three dimensional 3d perfectly conducting bodies this algorithm employs the conventional moment method mm using the subsectional triangular patch basis functions and a special matrix transformation which is derived from solving the fredholm equation of the first kind by the multiscale technique this methodology is more suitable for problems where the matrix solution time is much greater than the matrix fill time the widely used triangular patch vector basis functions developed by rao et al 1982 are used for expansion and testing functions in the conventional mm the objective here is to compress the unknowns in existing mm codes which solves for the currents crossing the edges of the triangular patch basis functions by use of a matrix transformation the currents source terms and impedance matrix can be arranged in the form of different scales from one scale to another scale the initial guess for the solution can be predicted according to the properties of the multiscale technique ammm can reduce automatically the size of the linear equations so as to improve the efficiency of the conventional mm the basic difference between this methodology and the other wavelet based techniques that have been presented so far is that we apply the compression not to the impedance matrix but to the solution itself directly in an iterative fashion even though it is an unknown two numerical results are presented which demonstrate that the ammm is a useful method for analysis of electromagnetic scattering from arbitrary shaped 3d perfectly conducting bodies

on a new relation between jacobi and homogeneous poisson manifolds we establish a new very close relationship which links jacobi structures and homogeneous poisson structures defined on the same manifold and study the characteristic foliations of the related structures several examples of this construction are also given

on the geometry of lambda symmetries and pde reduction we give a geometrical characterization of prolongations of vector fields and hence of symmetries of odes this allows an extension to the case of pdes and systems of pdes in this context the central object is a horizontal 1 form and we speak of prolongations of vector fields and symmetries of pdes we show that these are as good as standard symmetries in providing symmetry reduction of pdes and systems and explicit invariant solutions

combining kronecker product approximation with discrete wavelet transforms to solve dense function related linear systems a new solution technique is proposed for linear systems with large dense matrices of a certain class including those that come from typical integral equations of potential theory this technique combines kronecker product approximation and wavelet sparsification for the kronecker product factors the user is only required to supply a procedure for computation of each entry of the given matrix the main sources of efficiency are the incomplete cross approximation procedure adapted from the mosaic skeleton method of the second author and data sparse preconditioners the incomplete lu decomposition with dynamic choice of the fill in structure with a prescribed threshold and the inverse kronecker product preconditioner constructed for the sum of kronecker products of sparsified finger like matrices computed by the discrete wavelet transform in some model but quite representative examples the new technique allowed us to solve dense systems with more than 1 million unknowns in a few minutes on a personal computer with 1 gbyte operative memory

on generalized fuzzy matrices with periods in this paper generalized fuzzy matrices are considered as matrices over a special type of semiring which is called path algebra some properties and characterizations for generalized fuzzy matrices with periods are established and an expression for the transitive closure of a generalized fuzzy matrix with a period as a sum of its powers is shown reduction of generalized fuzzy matrices is defined and some properties for reduction of generalized fuzzy matrices with periods are obtained also the structure of all standard eigenvectors for a generalized fuzzy matrix with a period is determined

a multipole expansion technique in solving boundary integral equations abstract the boundary integral equation method reduces the spatial dimension of an elliptic problem by converting the original n dimensional partial differential equation to an n 1 dimensional boundary integral equation defined on the boundary of the domain of the original problem at the same time the discretisation of the problem is also remarkably simplified the price of these advantages however is that the structure as well as the algebraic properties of the resulting boundary element matrices are somewhat unpleasant since they are neither sparse nor self adjoint in general even if the original problem is self adjoint consequently the computational cost of the boundary integral equation method seems to be unnecessarily high to make the method more economic from a computational point of view we present a numerical technique based on the multipole expansion method which reduces the computational cost of the appearing matrix vector multiplications i e the evaluations of the discretized boundary integrals by a remarkable amount the method is applicable also to the reconstruction problem when the inner solution is to be reconstructed from the boundary solutions

on the max nilpotent t norm powers of a fuzzy matrix fuzzy matrices have been proposed to represent fuzzy relations in finite universes various studies have evaluated the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions indicating that the limiting behavior of the powers of a fuzzy matrix depends on its composition in this paper max nilpotent composition is considered for the fuzzy relations we demonstrate that the max nilpotent powers of a fuzzy matrix either converge or oscillate in a finite period moreover the max nilpotent t norm powers of a fuzzy matrix a are p periodic if and only if the powers of an associated boolean matrix a c are p periodic finally necessary and sufficient conditions are proposed for nilpotent fuzzy matrices that exhibit max nilpotent composition

subinverses of fuzzy matrices abstract a matrix operation is examined for fuzzy matrices and interesting properties of fuzzy matrices are obtained using the operation particularly some properties concerning subinverses and regularity of fuzzy matrices are given and the largest subinverse is shown by the properties the properties are closely related to inverses of fuzzy matrices and fuzzy equations moreover fuzzy preorders are examined using the matrix operation and basic properties are obtained the results are considered to be useful for the theory of fuzzy matrices

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

the graded jacobi algebras and co homology jacobi algebroids i e jacobi versions of lie algebroids are studied in the context of graded jacobi brackets on graded commutative algebras this unifies various concepts of graded lie structures in geometry and physics a method of describing such structures by classical lie algebroids via certain gauging in the spirit of e witten s gauging of the exterior derivative is developed one constructs a corresponding cartan differential calculus graded commutative one in a natural manner this in turn gives canonical generating operators for triangular jacobi algebroids one gets in particular the lichnerowicz jacobi homology operators associated with classical jacobi structures courant jacobi brackets are obtained in a similar way and used to define an abstract notion of a courant jacobi algebroid and dirac jacobi structure