moment conditions and support theorems for radon transforms on affine grassmann manifolds abstract let g p n and g q n be the affine grassmann manifolds of p and q planes in r n respectively and let r p q be the radon transform from smooth functions on g p n to smooth functions on g q n arising from the inclusion incidence relation when p q and dim g p n dim g p n we present a range characterization theorem for r p q via moment conditions we then use this range result to prove a support theorem for r p q this complements a previous range characterization theorem for r p q via differential equations when dim g p n dim g p n we also present a support theorem in this latter case

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

asymptotic formulas for the dual radon transform and applications caracterisation de la transformation de radon duale d une fonction indefiniment differentiable formules asymptotiques et applications

a study of wavelets for the solution of electromagnetic integral equations the use of wavelet basis functions for the efficient solution of electromagnetic integral equations is studied it has previously been demonstrated that the use of wavelets for expansion and testing functions produces a sparse moment method matrix here this effect is examined and analyzed in terms of the radiation receiving characteristics of the wavelet basis functions the limitations of wavelets as an efficient solution technique are discussed and a comparison is made to other fast algorithms

an axiomatic approach to the definition of the entropy of a discrete choquet capacity to extend the classical shannon entropy to nonadditive measures marichal recently introduced the concept of generalized entropy for discrete choquet capacities we provide a first axiomatization of this new concept on the basis of three axioms the symmetry property a boundary condition for which the entropy reduces to the shannon entropy and a generalized version of the well known recursivity property we also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy like measure lastly we provide an interpretation of it in the framework of aggregation by the discrete choquet integral

inversion of the radon transform on the laguerre hypergroup by using generalized wavelets abstract we consider the radon transform r 0 on the laguerre hypergroup k 0 r we characterize a space of infinitely differentiable and rapidly decreasing functions together with their derivatives such that r is a bijection from this space onto itself we establish an inversion formula and a plancherel theorem for the operator r finally by using the continuous wavelet transform on the laguerre hypergroup k we deduce another expression for the inverse r 1 of the operator r

piecewise complementary lidstone interpolation and error inequalities the purpose of this paper is to develop piecewise complementary lidstone interpolation in one and two variables and establish explicit error bounds for the derivatives in l and l 2 norms

invariant differential operators on grassmann manifolds for a lie group g and a closed subgroup h c g let d g h denote the algebra of differential operators d on the manifold g h which are invariant under the action of g in this note we determine this algebra in the case when g is the group m n of rigid motions of the euclidean space r and h is the subgroup of m n leaving a certain p dimensional plane in r invariant here 0 6 p 6 ii 1 and is the space

theory of regular m band wavelet bases orthonormal m band wavelet bases have been constructed and applied by several authors this paper makes three main contributions first it generalizes the minimal length k regular 2 band wavelets of daubechies 1988 to the m band case by deriving explicit formulas for k regular m band scaling filters several equivalent characterizations of k regularity are given and their significance explained second two approaches to the construction of the m 1 wavelet filters and associated wavelet bases are described one relies on a state space characterization with a novel technique to obtain the unitary wavelet filters the other uses a factorization approach third this paper gives a set of necessary and sufficient condition on the m band scaling filter for it to generate an orthonormal wavelet basis the conditions are very similar to those obtained by cohen 1990 and lawton 1990 for 2 band wavelets

domain semantics of possibility computations the purpose of this paper is to introduce a kind of computational model called possibility computation to deal with non determinism both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified in this approach the denotational semantics will be set up by assigning to programs possibility state transformers i e scott continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states this possibility powerdomain of a dcpo will consist of all possibility valuations ordered pointwise of this dcpo the logical semantics will be given by fuzzy predicate transformers introduced by the first author and jung following dijkstra s predicate transformers two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations the categorical monad of the possibility powerdomain will be investigated

efficient estimation of linear functionals in emission tomography in emission tomography the spatial distribution of a radioactive tracer is estimated from a finite sample of externally detected photons we present an algorithm independent theory of statistical accuracy attainable in emission tomography that makes minimal assumptions about the underlying image let f denote the tracer density as a function of position i e f is the image being linebreak estimated we consider the problem of estimating the linear functional phi f equiv hbox normalfont footnotesize int phi x f x dx where phi is a smooth function from n independent observations identically distributed according to the radon transform of f assuming only that f is bounded above and below away from 0 we construct statistically efficient estimators for phi f by definition the variance of the efficient estimator is a best possible lower bound depending on phi and f on the variance of unbiased estimators of phi f our results show that in general the efficient est

a functional from geometry with applications to discrepancy estimates and the radon transform estimates of discrepancy or irregularities of distribution are obtained for measures without atoms two estimators are used the half space or separation discrepancy ds and a geometric functional 1a a representation formula for the generalized energy integral pa is developed norm inequalities for the radon transform are obtained as an application of the continuous discrepancy results integral geometric notions play a prominent role

harmonic analysis on grassmannian bundles the harmonic analysis of the grassmannian bundle of k dimensional affine subspaces of rn as a homogeneous space of the euclidean motion group is given explicitly this is used to obtain the diagonalization of various generalizations of the radon transform between such bundles in abstract form the same technique gives the plancherel formula for any unitary representation of a semidirect product g x v v a normal abelian subgroup induced from an irreducible unitary representation of a subgroup of the form h x w introduction let gn k denote the grassmannian manifold of linear k dimensional subspaces of rn and let pn k denote the grassmannian bundle of affine kdimensional subspaces also called k planes so pn k is a bundle over gn k with fibre dimension m where m k n in group theoretic terms gn k g h where g so n and h s o k x 0 m or we could just as well take g 0 n and h o k x 0 m let p denote the standard representation of g on v rn and form the semidirect product g x v the euclidean motion group with group law gi xi o g x gig xi p gl x the eucidean motion group acts naturally on the bundle pn k if we let wr0 denote the subspace spanned by the first k basis elements el ek then the isotropy subgroup of wro is h x w where w is the subspace 7r0 thus pn k g v h x w in this paper we obtain the explicit harmonic analysis on pn k the decomposition of l2 pn k with respect to the invariant measure into a direct integral of irreducible representations of g x v this is accomplished in two stages in the first abstract stage 2 we let g be any compact lie group and p any real representation of g on v and for functions f g x invariant under the right action of a subgroup h x w we obtain the fourier decomposition formula f g x j e fa 6 g x dv a a6g here a is an index set for the orbits in w under the action of h if we choose a point za in each orbit and let gc and ha denote the isotropy subgroup of za in g and h respectively then a x denotes the set of irreducible representations of gca that occur in l2 gca ha the measure dv a is determined by dz da dv a where dz is lebesgue measure on w and da is the invariant measure on the orbit received by the editors march 7 1985 1980 mathematics subject classification primary 43a85 secondary 22d30 44a15

k intolerant capacities and choquet integrals we define an aggregation function to be at most k intolerant if it is bounded from above by its kth lowest input value applying this definition to the discrete choquet integral and its underlying capacity we introduce the concept of k intolerant capacities which when varying k from 1 to n cover all the possible capacities on n objects just as the concepts of k additive capacities and p symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities k intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation we also introduce axiomatically indices to appraise the extent to which a given capacity is k intolerant and we apply them on a particular recruiting problem

fuzzy measure and probability distributions distorted probabilities this work studies fuzzy measures and their application to data modeling we focus on the particular case when fuzzy measures are distorted probabilities we analyze their properties and introduce a new family of measures m dimensional distorted probabilities the work finishes with the application of two dimensional distorted probabilities to a modeling problem results of the application of such fuzzy measure to data modeling using choquet integral are discussed

radon inversion on grassmannians via garding gindikin fractional integrals we study the radon transform rf of functions on stiefel and grassmann manifolds we establish a connection between rf and garding gindikin frac tional integrals associated to the cone of positive definite matrices by using this connection we obtain abel type representations and explicit inversion for mulae for rf and the corresponding dual radon transform we work with the space of continuous functions and also with l p spaces

dual radon transforms on affine grassmann manifolds fix 0 p n we will show that the range of this transform is given by smooth functions on g p n annihilated by a system of pfaffian type differential operators we also study aspects of the exceptional case p q n

fuzzy measure of fuzzy events defined by fuzzy integrals abstract we define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by murofushi called fuzzy t conorm integral encompassing previous definitions zadeh defined the probability measure of a fuzzy event and later the possibility measure of fuzzy event using a duality property of fuzzy t conorm integral we propose a general definition of fuzzy measure of fuzzy events which is compatible with previous definitions of zadeh and possesses all properties of a fuzzy measure in particular the duality property using our definition we examine the case of decomposable measures and belief functions a comparison with previous works is provided

on the relationship between the crescent method and suowa operators different families of functions have been proposed in the literature with the purpose of simultaneously generalizing weighted means and ordered weighted averaging owa operators see for instance weighted owa and semiuninorm based owa suowa operators recently jin et al have introduced in the literature a new procedure called the crescent method to melt additive capacities with those of owa operators the main aim of this article is to establish a relationship between the crescent method and suowa operators from this relationship we give closed form expressions for some well known indices such as the shapley values the veto and favor indices and the k conjunctiveness and k disjunctiveness indices

new inversion formulas for radon transforms on affine grassmannians abstract we obtain new inversion formulas for the radon transform and the corresponding dual transform acting on affine grassmann manifolds of planes in r n the consideration is performed in full generality on continuous functions and functions belonging to l p spaces

integral geometry on grassmann manifolds and calculus of invariant differential operators abstract in this paper we mainly deal with two problems in integral geometry the range characterizations and construction of inversion formulas for radon transforms on higher rank grassmann manifolds the results will be described explicitly in terms of invariant differential operators we will also study the harmonic analysis on grassmann manifolds using the method of integral geometry in particular we will give eigenvalue formulas and radial part formulas for invariant differential operators

random generation of k interactive capacities abstract the theory of capacities provides powerful formal methodology to account for criteria dependencies in multiple criteria decision problems the discrete choquet and sugeno integrals aggregate criteria valuations accounting for criteria synergies and redundancies we address an important problem of randomly generating capacities of special classes for simulation studies and for capacity learning through evolutionary algorithms we discuss two efficient methods suitable for k interactive capacities the results are supported by the extensive numerical evidence and provide a useful tool for large scale simulations

minimum variance capacity identification abstract in the framework of multi criteria decision making whose aggregation process is based on the choquet integral we present a maximum entropy like method enabling to determine if it exists the least specific capacity compatible with the initial preferences of the decision maker the proposed approach consists in solving a strictly convex quadratic program whose objective function is equivalently either the opposite of a generalized entropy measure or the variance of the capacity the application of the proposed approach is illustrated on two examples

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

tolerant or intolerant character of interacting criteria in aggregation by the choquet integral abstract in many multi criteria decision making problems the decision criteria present some interaction whose nature may vary from one situation to another for example some criteria may be statistically correlated thus making them somewhat redundant or opposed some others may be somewhat substitutive or complementary depending on the behavior of the decision maker some others may be decisive in the sense that the global score of any alternative obtained by aggregation is bounded by the partial score along one of them in this paper we analyze this latter form of interaction when a criterion bounds the global score from above it is called a blocker or a veto due to its rather intolerant character when it bounds the global score from below it is then called a pusher or a favor we thus investigate the tolerance of criteria or equivalently the tolerance of the weighted aggregation operator here the choquet integral that is used to aggregate criteria more specifically we propose axiomatically indices to appraise the extent to which each criterion behaves like a veto or a favor in the aggregation by the choquet integral previous to this we also propose global tolerance degrees measuring the extent to which the choquet integral is conjunctive or disjunctive

a study of least squares and maximum likelihood for image reconstruction in positron emission tomography positron emission tomography pet is a radiologic tool offering a unique capability for measuring tissue metabolism in vivo a number of biological and physical factors limit the resolution of pet so often the statistical aspects of image reconstruction have an appreciable effect on the quality of information obtained from a study to a first approximation reconstruction involves the solution of a linear inverse problem with a line integral radon type transform standard filtered back projection reconstruction is based on the method of least squares although computationally efficient the method does not enforce positivity constraints leading to undesirable negative artifacts in the results maximum likelihood based approaches to reconstruction do not suffer from this problem but their computational complexity has limited the ability to determine quantitatively the improvements in image quality in this paper asymptotic approximations and numerical simulations are used to examine the least squares and maximum likelihood methods in some detail the studies are carried out for idealized representations of conventional and time of flight tomographs the asymptotic analysis indicates that for a range of sobolev norms the rates of estimation of least squares and maximum likelihood reconstructions are of the same order this is borne out by numerical studies however in these studies maximum likelihood is found to be more efficient than least squares on a conventional distance angle tomograph the root mean square error is on the order of 10 20 smaller for maximum likelihood reconstructions the corresponding reduction in the root mean square error on a time of flight tomograph is in the 5 range similar results are found using more complex region of interest based measures of reconstruction accuracy in addition it is found that much of the effect of maximum likelihood can apparently be realized by postprocessing least squares solutions in an ad hoc manner to reduce negativity artifacts since the postprocessing scheme is computationally fast this suggests that in pet it may be possible to realize the benefits of maximum likelihood without the substantial computational overhead of the em algorithm

suowa operators an analysis of their conjunctive disjunctive character abstract choquet integrals mainly weighted means and owa operators are a well known family of functions widely used in several scientific fields because of this it is very important to know the behavior of these functions in order to choose the best suited operators in practical applications in this sense the analysis of the conjunctive disjunctive character is very interesting given that allow understand the behavior of functions in relation to order statistics in this paper we focus on some classes of suowa operators which are choquet integrals that simultaneously generalize weighted means and owa operators and provide conditions under which the k conjunctive or k disjunctive character of an owa operator is retained by the suowa operators associated with it of particular interest is the case where the owa operator is located between two order statistics given that we can obtain suowa operators also located between the same order statistics likewise we show closed form expressions of k conjunctiveness and k disjunctiveness indices for some specific cases of suowa operators

fast solution of electromagnetic integral equations using adaptive wavelet packet transform the adaptive wavelet packet transform is applied to sparsify the moment matrices for the fast solution of electromagnetic integral equations in the algorithm a cost function is employed to adaptively select the optimal wavelet packet expansion testing functions to achieve the maximum sparsity possible in the resulting transformed system the search for the best wavelet packet basis and the moment matrix transformation are implemented by repeated two channel filtering of the original moment matrix with a pair of quadrature filters it is found that the sparsified matrix has above threshold elements that grow only as o n sup 1 4 for typical scatterers consequently the operations to solve the transformed moment equation using the conjugate gradient method scales as o n sup 1 4 the additional computational cost for carrying out the adaptive wavelet packet transform is evaluated and discussed

learning k maxitive fuzzy measures from data by mixed integer programming abstract fuzzy measures model interactions between the inputs in aggregation problems their complexity grows exponentially with the dimensionality of the problem and elicitation of fuzzy measure coefficients either from domain experts or from empirical data poses a significant challenge the notions of k additivity and k maxitivity simplify the fuzzy measures by limiting interactions to subsets of up to k elements learning fuzzy measures from data is an important elicitation technique which relies on solving an optimisation problem a heuristic learning algorithm to identify k maxitive fuzzy measures from the data on the basis of hlms heuristic least mean squares was recently presented in murillo et al 2017 11 we present an alternative formulation of the fitting problem which delivers a globally optimal solution through the solution of a mixed integer programming mip problem to deal with high computational cost of mip in moderate to large dimensions we also propose a simple mip relaxation technique which involves solving two related linear programming problems we also provide a linear programming formulation for fitting k tolerant fuzzy measures we discuss implementations of the fitting methods and present the results of numerical experiments

entropy of discrete choquet capacities we introduce a measure of entropy for any discrete choquet capacity and we interpret it in the setting of aggregation by the choquet integral

on the use of wavelet expansions in the method of moments em scattering an approach which incorporates the theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function which is often referred to as the mother wavelet the wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer the approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths using a galerkin method and subsequently applying a threshold procedure the moment method matrix is rendered sparsely populated the structure of the matrix reveals the localized scale fitting distribution long before the matrix equation is solved the performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double slot aperture

eigenvalues of a general class of boundary value problem with derivative dependent nonlinearity we consider a general class of boundary value problem bvp comprising the differential equation y m t f t y t y t y t y q t t 0 1 where 1 q m 1 and 0 together with multi point boundary conditions y 0 y 0 y 0 y q 1 0 0 a i y q t j y q 1 t j y m 1 t j 0 j r 0 1 i m q where 0 t 0 t 1 t r 1 particular cases of this general bvp include the well known abel gontscharoff focal m p sturm liouville and complementary lidstone bvps it is noted that bvps with derivative dependent nonlinear terms are less investigated in the literature due to technical difficulty in this paper a new technique is developed to characterize the eigenvalues so that the bvp has a positive solution explicit eigenvalue intervals are also established we include several well known examples in the literature to illustrate the results obtained

radon transforms on grassmann manifolds if n p q 1 the affine grassmann manifolds g p n of p planes and g q n of q planes in rn are dual homogeneous spaces of the euclidean motion group m n with g p n and g q n being incident if and only if meets at a right angle the resulting integral transform from functions on g p n to functions on g q n generalizes both the classical radon transform and its dual we show that this transform intertwines the actions of certain m n invariant differential operators on g p n and g q n and we prove an inversion formula for this transform when n is odd generalizing the radon inversion formula and obtaining in particular an inversion formula for the dual transform

2 additive capacity identification methods from multicriteria correlation preference information the essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity the 2 additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity besides the preference with respect to the decision criteria most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set which is a time consuming task for the decision maker in this paper we propose some models to identify 2 additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information mccpi the mccpi is a group of 2 d preference information which can be described and obtained by the refined diamond diagram the common principle of the proposed models is to minimize the different kinds of deviations between the mccpi and the most desired 2 additive capacity ies a multicriteria decision making example is presented to show the feasibility of the proposed methods and a 2 d scale of the mccpi is also introduced in the further discussion of the illustrative example

parametric characterization of aggregation functions the aim of this contribution is to find a common framework for parametric characterization of aggregation functions exploiting the notions of unipolar and bipolar parametric characterization and also unify the ideas of global and local parametric characterization we revise the known approaches to classification of aggregation functions in special classes in this framework and also propose some new parameters in classes of averaging conjunctive and disjunctive aggregation functions

radon transform on real complex and quaternionic grassmannians letgn k k be the grassmannian manifold of k dimensional k subspaces in k where k r c h is the field of real complex or quaternionic numbers for 1 k k n 1 we define the radon transform rf gn k k for functions f on gn k k as an integration over all when k k n we give an inversion formula in terms of the garding gindikin fractional integration and the cayley type differential operator on the symmetric cone of positive k k matrices over k this generalizes the recent results of grinberg rubin for real grassmannians

a variational method using fractional order hilbert spaces for tomographic reconstruction of blurred and noised binary images we provide in this article a refined functional analysis of the radon operator restricted to axisymmetric functions and show that it enjoys strong regularity properties in fractional order hilbert spaces this study is motivated by a problem of tomographic reconstruction of binary axially symmetric objects for which we have available one single blurred and noised snapshot we propose a variational approach to handle this problem consisting in solving a minimization problem settled in adapted fractional order hilbert spaces we show the existence of solutions and then derive first order necessary conditions for optimality in the form of optimality systems

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

a characterization of fourier and radon transforms on euclidean space we show that a continuous operator behaving under rotations positive dilations and translations like the fourier or the radon transform on r must be a constant multiple of one of these transforms we prove this characterization for various function spaces e g we characterize the fourier transform as an operator acting on spaces between 6d r and r on the other hand a counterexample shows that the radon transform is not determined by its behaviour above as an operator from r to s x r but we can characterize the radon trans form as an operator acting between r and s 1 x r the space of integrable distributions on s x r in the special case n our methods sharpen results of j l b cooper and h kober who characterize the fourier transform as an operator from lp r into lp r 1 s p z 2 introduction several authors have been concerned with the question whether an operator on function spaces on r is determined up to a constant multiple by its behaviour under rotations dilations and translations for instance stein 15 showed that the translation invariant hubert and riesz transforms on l2 can be characterized in such a way the fourier and radon transforms on r also have a well known simple be haviour under rotations positive dilations and translations in this article we prove that such a behaviour is characteristic an operator acting under those operations like the fourier or the radon transform is a constant multiple of one of these transforms in the case of the fourier transform for n 1 our methods e g determining homogeneous distributions by euler s equation sharpen results of cooper 1 and kober 10 who characterized by different methods the fourier transform as an operator from lp r into lp r 1 p 2 we also obtain connections to hardy 7 and plancherel 12 who looked for operators on l2 r behaving under dilations like the fourier transform further our characterizations can be used to obtain corresponding ones for operators related to the fourier and radon transforms our result implies the result on hilbert and riesz transforms mentioned above stein 15 we also remark that such characteristic properties can be applied to verify inversion formulas for the corresponding operator in the case of the radon

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

polynomial approximation to a non local boundary value problem in this paper we construct a special class of polynomials which converge uniformly to the solution of a non local boundary value problem nbvp the use of this special class is justified by the physics of the model which is described by this nbvp this nbvp has been studied by palamides et al 2009 in 2 where the existence of solutions is established

an axiomatic approach of the discrete sugeno integral as a tool to aggregate interacting criteria in a qualitative framework we present a model allowing us to aggregate decision criteria when the available information is of a qualitative nature the use of the sugeno integral as an aggregation function is justified by an axiomatic approach it is also shown that the mutual preferential independence of criteria reduces the sugeno integral to a dictatorial aggregation

norm estimates for k plane transforms and geometric inequalities abstract the article is devoted to remarkable interrelation between the norm estimates for k plane transforms in weighted and unweighted l p spaces and geometric integral inequalities for cross sections of measurable sets in r n a similar interrelation is studied for more general j plane to k plane transforms on affine grassmannians and their compact modifications the article contains a series of new integral geometric inequalities with sharp constants explicit equalities conjectures and open problems

on the range of the radon d plane transform and its dual we present direct group theoretic proofs of the range theorem for the radon d plane transform on r the original proof by richter involves extensive use of local coordinate calculations on g d n the grassmann manifold of affine a planes in r we show that moment conditions are not sufficient to describe this range when d n in contrast to the compactly supported case finally we show that the dual rf plane transform maps g g d n surjectively onto f r

wavelet like bases for thin wire integral equations in electromagnetics in this paper wavelets are used in solving by the method of moments a modified version of the thin wire electric field integral equation in frequency domain the time domain electromagnetic quantities are obtained by using the inverse discrete fast fourier transform the retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation the discretized model generated by applying the direct method of moments via point matching procedure results in a linear system with a dense matrix which have to be solved for each frequency of the fourier spectrum of the time domain impressed source therefore orthogonal wavelet like basis transform is used to sparsify the moment matrix in particular dyadic and m band wavelet transforms have been adopted so generating different sparse matrix structures this leads to an efficient solution in solving the resulting sparse matrix equation moreover a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed these numerical features are used in analyzing the transient behavior of a lightning protection system in particular the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation during its operation is focused the numerical results obtained by running a complex structure are discussed and the features of the used method are underlined

extreme points of some families of non additive measures non additive measures are a valuable tool to model many different problems arising in real situations however two important difficulties appear in their practical use the complexity of the measures and their identification from sample data for the first problem additional conditions are imposed leading to different subfamilies of non additive measures related to the second point in this paper we study the set of vertices of some families of non additive measures namely k additive measures and p symmetric measures these extreme points are necessary in order to properly apply a new method of identification of non additive measures based on genetic algorithms whose cross over operator is the convex combination we solve the problem through techniques of linear programming

radon transforms on affine grassmannians we develop an analytic approach to the radon transform f f f where f is a flinction on the affine grassmann manifold g n k of k dimensional planes in r n and is a k dimensional plane in the similar manifold g n k k k for f e l p g n k we prove that this transform is finite almost everywhere on g n k if and only if 1 n 1 and interpreted as a direct quasi orthogonal radon transform for another pair of affine grassmannians as a consequence we obtain that the radon transform and the dual radon transform are injective simultaneously if and only if k k n 1 the investigation is carried out for locally integrable and continuous functions satisfying natural weak conditions at infinity

generalized bonferroni mean operators in multi criteria aggregation in this paper we provide a systematic investigation of a family of composed aggregation functions which generalize the bonferroni mean such extensions of the bonferroni mean are capable of modeling the concepts of hard and soft partial conjunction and disjunction as well as that of k tolerance and k intolerance there are several interesting special cases with quite an intuitive interpretation for application

orbital parameters for induced and restricted representations general formulas for the spectral decomposition of both induced and restricted representations are laid out for the case of connected lie groups h c g the formulas which detail the actual spectrum the multiplicites and the spectral measure are in terms of the usual parameters in the so called orbit method a proof of these formulas is given in the nilpotent situation the proof is much simpler than a previously obtained proof using nilpotent algebraic geometry it is also capable of generalization to nonnilpotent groups with that in mind many new examples are presented for semisimple and symmetric homogeneous spaces also a start is made in the case of exponential solvable homogeneous spaces with the treatment of both normal and conormal subgroups

cone beam reconstruction with sources on a curve an inversion procedure is developed for reconstructing a function of compact support in mathbb r 3 from its divergent beam x ray transform with sources on a curve the results apply to many curves not satisfying the conditions of tuy siam j appl math 43 1983 pp 546 552 for example planar circles of sufficiently large radius in some cases estimates in sobolev norms are established for the inversion operator

dominance of capacities by k additive belief functions in this paper we deal with the set of k additive belief functions dominating a given capacity we follow the line introduced by chateauneuf and jaffray for dominating probabilities and continued by grabisch for general k additive measures first we show that the conditions for the general k additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid on the other hand we show that these conditions cannot be improved we solve this situation by imposing additional constraints on the dominating functions then we consider the more restrictive case of k additive belief functions in this case a similar result with stronger conditions is proved although better this result is not completely satisfactory and as before the conditions cannot be strengthened however when the initial capacity is a belief function we find a subfamily of the set of dominating k additive belief functions from which it is possible to derive any other dominant k additive belief function and such that the conditions are even more restrictive obtaining the natural extension of the result for probabilities finally we apply these results in the fields of social welfare theory and decision under risk