inverse scattering for surface impedance from phase less far field data we present a numerical comparison of a regularized newton type method and a direct method for reconstructing the surface impedance function of a three dimensional acoustic scatterer with known shape from the full far field pattern for scattering of one incident time harmonic plane wave furthermore we propose a modification of the newton type algorithm to recover a real valued surface impedance from phase less far field data numerical reconstructions illustrate the feasibility of the methods

analysis and simulation of fuzzy queues abstract the aim of this paper is to combine the ability of fuzzy sets to represent practical situations with the well known established traditional queuing approaches which are rigorous but the assumptions are frequently too far from reality it is shown that this approach can utilize the advantages of both the fuzzy and probability approaches to make the model more realistic and less restrictive both cut sets and the use of random variables to represent fuzzy numbers are investigated trapezoidal fuzzy numbers are used and the analytical and simulation results are discussed based on actual examples

on probability possibility transformations abstract a probability possibility transformation is a purely mechanical transformation of probabilistic support to possibilistic support and vice versa that is a conversion of the measure of support of one theory into that of the other that is independent of the problem domain in this paper it is shown that any bijective mapping between probability distributions and normalized possibility distributions that is symmetric and expansible cannot preserve the properties of projection noninteraction or conditionalization

the motivic fundamental group of p1 0 1 and the theorem of siegel in this paper we establish a link between the structure theory of the pro unipotent motivic fundamental group of the projective line minus three points and diophantine geometry in particular we give a p adic proof of siegel s theorem

inferring a possibility distribution from empirical data several transformations from probabilities to possibilities have been proposed in particular dubois and prade s procedure produces the most specific possibility distribution among the ones dominating a given probability distribution in this paper this method is generalized to the case where the probabilities are unknown the only information being a data sample represented by a histogram it is proposed to characterize the probabilities of the different classes by simultaneous confidence intervals with a given confidence level email protected from this imprecise specification a procedure for constructing a possibility distribution is described insuring that the resulting possibility distribution will dominate the true probability distribution in at least 100 email protected of the cases finally a simple efficient algorithm is given which makes the computations tractable even if the number of classes is high

the inverse scattering problem on a fixed energy level for the two dimensional schrodinger operator this paper contains a solution with complete proofs of the main problems of the inverse scattering at fixed energy e for the schrodinger two dimensional operator with decreasing coefficients uniqueness of the reconstruction a reconstruction procedure characterization of the scattering data most completed results are obtained under the condition of smallness of coefficients in comparison with the number e this paper develops and generalizes several preceded papers

local regularization for the nonlinear inverse autoconvolution problem we develop a local regularization theory for the nonlinear inverse autoconvolution problem unlike classical regularization techniques such as tikhonov regularization this theory provides regularization methods that preserve the causal nature of the autoconvolution problem allowing for fast sequential numerical solution cal o rn 2 r 2n flops where r ll n for the method discussed in this paper as applied to the nonlinear problem in comparison the cost for tikhonov regularization applied to a general linear problem is cal o n 3 flops we prove the convergence of the regularized solutions to the true solution as the noise level in the data shrinks to zero and supply convergence rates for the cases of both l 2 and continuous data we propose several regularization methods and provide a theoretical basis for their convergence of note is that this class of methods does not require an initial guess of the unknown solution our numerical results confirm the effectiveness of the methods with results comparing favorably to numerical examples found in the literature for the autoconvolution problem e g g fleischer r gorenflo and b hofmann zamm z angew math mech 79 1999 pp 149 159 for examples using tikhonov regularization with total variation constraints and j janno inverse problems 16 2000 pp 333 348 for examples using the method of lavrent ev this especially seems to be true when it comes to the recovery of sharp features in the unknown solution we also show the effectiveness of our method in cases not covered by the theory

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

methodology of linguistics evaluation in risk situations using fuzzy techniques abstract in this article the mathematical expression which determines the fuzzy weighted mean of a system in terms of a determined or specific configuration of estimates is studied its objective lies in obtaining fuzzy sets that are as close as possible to the natural expressions in systems which need an estimative calculation of risk whether it be of failure access or of any other type with incomplete and or unprecise data to do this the calculation fuzzy weighted mean of the fuzzy restriction associated with a system has been established as the proposed evaluation technique increasing the number of natural expressions and thus the number of fuzzy processes that are involved in the said calculation this increase has been achieved by analyzing all the possible results on the basis of the number of fuzzy sets in the numerator and denominator of the expression that denotes the fuzzy weighted mean of a system taking into account to what point of the calculation such an increase is feasible without impairing the resulting fuzzy set the importance of the resulting fuzzy set is the motivation behind effecting an enhancement process in this analytic phase since it determines a linguistic meaning that is taken as an element of comparison and reference for the obtention of the final natural expression the results of the proposed method have been verified by means of an interpreter which has been designed to deal with all the fuzzy operations which intervene in the different processes

on the instantiation of possibility distributions we investigate the problem of instantiating a variable whose value is uncertain but known to be constrained by a possibility distribution using a model based upon the dempster shafer belief structure we show that this problem of instantiation is analogous to a compound experiment in which we randomly select a subset and then perform a number of repeated experiments without replacement on this set the probability distribution resulting from this compound experiment leads to a random procedure for instantiating a possibility distribution

a note on the transformation of possibilistic information into probabilistic information for investment decisions abstract investment decisions of a firm take place in a highly competitive environment any attempt to capture the reality in such decisions often results in fuzzy information behaving like fuzzy restrictions but for decision making probabilistic data may be more effective rather than possibilistic data therefore possibilistic data need to be transformed into probabilistic data and this needs a suitable possibility probability consistency principle ppcp this note provides a ppcp and shows that under certain conditions fuzzy information about cashflows can be approximated by normal probability distribution then the tools of the probability theory can be applied for such decisions

reconstruction of the shape and surface impedance from acoustic scattering data for an arbitrary cylinder the inverse scattering for an obstacle d subset r 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary we construct some indicator functions for this inverse problem using the far field pattern directly without the necessity of transforming the far field to the near field based on careful singularity analysis these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the noncoated part of the boundary moreover an explicit representation formula for the surface impedance in the coated part of the boundary is also given our reconstruction scheme reveals that the coated part of the obstacle is less visible than the noncoated one which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave numerics are presented for the reconstruction formulas which show that both the boundary shape and the surface impedan

a uniqueness theorem for an inverse boundary value problem in electrical prospection we show that a near constant conductivity of a two dimensional body can be uniquely determined by steady state direct current measurements at the boundary mathematically we show that the coefficient in the operator is uniquely determined by its dirichlet integrals

fractional poincare and logarithmic sobolev inequalities for measure spaces abstract we prove generalizations of the poincare and logarithmic sobolev inequalities corresponding to the case of fractional derivatives in measure spaces with only a minimal amount of geometric structure the class of such spaces includes but is not limited to spaces of homogeneous type with doubling measures several examples and applications are given including poincare inequalities for graph laplacians fractional poincare inequalities of mouhot russ and sire 2011 17 and implications for recent work of the author and r m strain on the boltzmann collision operator gressman and strain 2010 2011 2011 9 10 11

quadratic chabauty for modular curves and modular forms of rank one in this paper we provide refined sufficient conditions for the quadratic chabauty method on a curve x to produce an effective finite set of points containing the rational points x mathbb q with the condition on the rank of the jacobian of x replaced by condition on the rank of a quotient of the jacobian plus an associated space of chow heegner points we then apply this condition to prove the effective finiteness of x mathbb q for any modular curve x x 0 n or x mathrm ns n of genus at least 2 with n prime the proof relies on the existence of a quotient of their jacobians whose mordell weil rank is equal to its dimension and at least 2 which is proven via analytic estimates for orders of vanishing of l functions of modular forms thanks to a kolyvagin logachev type result

the second rational homology group of the moduli space of curves with level structures abstract let be a finite index subgroup of the mapping class group of a closed genus g surface that contains the torelli group for instance can be the level l subgroup or the spin mapping class group we show that h 2 q q for g 5 a corollary of this is that the rational picard groups of the associated finite covers of the moduli space of curves are equal to q we also prove analogous results for surface with punctures and boundary components

after the fuzzy wave reached europe abstract we briefly describe the situation of the fuzzy community in europe before the fuzzy wave we show that there was a lot of expertise in almost all subareas of fuzzy logic then we describe some aspects of the fuzzy wave itself in particular fuzzy control and first generation fuzzy systems that played a role during the time the fuzzy wave reached europe we also make some remarks about european companies and their activities during this time then we discuss the situation after the fuzzy wave some aspects of second generation fuzzy systems the combination of fuzzy logic with other theories and techniques and some new application areas finally we will discuss the chances of fuzzy systems in europe in the future

a high order algorithm for obstacle scattering in three dimensions in this work we describe implement and analyse in detail a high order fully discrete spectral algorithm for solving the helmholtz equation exterior to a bounded sound soft sound hard or absorbing obstacle in three space dimensions with dirichlet neumann or robin impedance boundary conditions our algorithm may be thought of as a discrete glerkin method but it is also equivalent to a nystrom method after a simple transformation we test our algorithm with extensive computational experiments on a variety of three dimensional smooth and non smooth obstacles with conical singularities our tests include the computation of scattered and far fields induced by incident plane waves our method is shown to be very accurate for scattering from surfaces which are globally parameterised by spherical coordinates and tests show that it performs very much better than several of the well established fast algorithms for obstacle sattering on a range of such surfaces even some which are non smooth further we prove superalgebraic convergence of the scattered and far fields obtained using our algorithm in the case of smooth scatterers

phaseless inverse scattering problems in three dimensions three dimensional inverse scattering problems in the frequency domain are considered in the case when only the modulus of the scattered field is given while the phase is unknown uniqueness theorems are proved

on the sections of universal hyperelliptic curves abstract in this paper we will give an algebraic proof for determining the sections for the universal pointed hyperelliptic curves c h g n k h g n k when g 3 and the image of the l adic cyclotomic character g k z is infinite furthermore we will study the nonabelian phenomena associated to the universal hyperelliptic curves for example we will show that the section conjecture holds for c h g k h g k and the unipotent analogue of the conjecture holds for the pointed cases this work is an extension of hain s original work on the rational points of universal curves to the hyperelliptic case

fuzzy sets probability and measurement abstract in recent years the problem of uncertainty modeling has received much attention from scholars in artificial intelligence and decision theory various formal settings including but not restricted to fuzzy sets and possibility measures have been proposed based on different intuitions and dealing with various kinds of uncertain data the two main research directions are upper and lower probabilities which convey the idea of imprecisely estimated probability measures and distorted probabilities for the descriptive assessment of partial belief possibility measures and thereby fuzzy sets stand at the crossroads of these new approaches traditional views interpretive settings and canonical experiments for the measurement of probability such as frequentist approaches betting theories comparative uncertainty relations are currently extended to the generalized uncertainty measures these works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory conversely zadeh s logical point of view on fuzzy sets suggests a set theoretic perspective on uncertainty measures that brings together numerical quantification and logic

variation of mixed hodge structure i around 1970 griffiths introduced the notion of a variation of hodge structure on a complex manifold s see 17 w 2 it constitutes the axiomatization of the features possessed by the local systems of cohomology associated to a family of compact k ihler manifolds esp smooth projective varieties parametrized by s these are for a variation of hodge structure u of weight m 0 a locally constant sheaf u of q vector spaces or u of real vector spaces 1 hodge filtration horizontality a decreasing filtration o r of gs by holomorphic subbundles such that the evident connection v on takes o p into q 2 hodge decompositions if gs denotes the sheaf of functions on s and if

inverse scattering problem from an impedance obstacle via two steps method in this paper we deal with the inverse scattering problem for an impedance obstacle the aim is to recover both the impedance function and the scatterer simultaneously based on boundary integral equations our method splits the inverse problem into a well posed direct problem followed by a smaller ill posed problem which has advantages both in understanding the inverse problem and in the numerical reconstructions

phaseless inverse scattering and the phase problem in optics two related problems are considered i the inverse scattering problem for a potential v x supported on the half line x 0 when the given data is r k the amplitude of the reflection coefficient and ii determination of a function g t supported on the half line t 0 when the given data is g k the amplitude of the fourier transform of g under certain conditions on v or g uniqueness theorems are proved and computational methods are developed a numerical example of recovery of v x from r k is given

lattice valued fuzzy measure and lattice valued fuzzy integral abstract in this paper 1 the concepts of lattice valued fuzzy measure with no valuation property and lower resp upper lattice valued fuzzy integral are proposed which give the unified discription to the fuzzy measures and fuzzy integrals studied by delgado and moral qiao ralescu adams sugeno wang and zhang 2 some asymptotic structural characteristics of lattice valued fuzzy measures are introduced and some relations between them are given 3 some concepts of convergences for lattice valued functions are defined and riesz theorem egoroff s theorems and lebesgue s theorem for lattice valued measurable function are proved 4 the monotone increasing resp decreasing convergence theorem and almost resp pseudo almost everywhere convergence theorrem for lower resp upper lattice valued fuzzy integral are shown under some weak conditions

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

naive possibilistic classifiers for imprecise or uncertain numerical data in real world problems input data may be pervaded with uncertainty in this paper we investigate the behavior of naive possibilistic classifiers as a counterpart to naive bayesian ones for dealing with classification tasks in the presence of uncertainty for this purpose we extend possibilistic classifiers which have been recently adapted to numerical data in order to cope with uncertainty in data representation here the possibility distributions that are used are supposed to encode the family of gaussian probabilistic distributions that are compatible with the considered dataset we consider two types of uncertainty i the uncertainty associated with the class in the training set which is modeled by a possibility distribution over class labels and ii the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data moreover the approach takes into account the uncertainty about the estimation of the gaussian distribution parameters due to the limited amount of data available we first adapt the possibilistic classification model previously proposed for the certain case in order to accommodate the uncertainty about class labels then we propose an algorithm based on the extension principle to deal with imprecise attribute values the experiments reported show the interest of possibilistic classifiers for handling uncertainty in data in particular the probability to possibility transform based classifier shows a robust behavior when dealing with imperfect data

what does a probabilistic interpretation of fuzzy sets mean in this paper we propose a statistics model to better understand the probabilistic interpretation for fuzzy sets the model shows the relationship between the two kinds of statistics the set valued statistics for fuzzy sets and the conventional probability statistics for membership functions our model overcomes the shortcomings in previous approaches the results of this paper provide a theoretical interpretation to zadeh s insight that possibility relates to soft constraints restricting the values of language variables

fuzzy numbers from raw discrete data using linear regression this paper focuses on modelling fuzzy numbers with meaningful membership functions more precisely it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data in many applications input information is numerical and therefore particular fuzzy sets such as fuzzy numbers hold great interest and relevance in managing data imprecision and vagueness the proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression the technique is simple fast and effective preliminary tests are performed using different types of input data a gaussian function a sigmoidal function three datasets of synthetic discrete data and an histogram obtained from a colour satellite image

probabilities possibilities and fuzzy sets a formal analysis of probabilities possibilities and fuzzy sets is presented in this paper a number of theorems proved show the above measures have equal representational power when their domains are infinite however for finite domains it is proved that probabilities have a higher representational power than both possibilities and fuzzy sets the cost of this increased power is high computational complexity and reduced computational efficiency the resulting trade off of high complexity and representational power versus computational efficiency is discussed under the spectrum of experimental systems and applications

do inferential processes affect uncertainty frameworks this paper studies the connections among different comparative or numerical degrees of belief in particular we consider in turn a comparative probability or possibility on a given boolean algebra and we prove that their upper extensions to a different boolean algebra are respectively a comparative plausibility or possibility on the other hand in general the upper extension of a comparative necessity is simply a comparative capacity moreover by considering a suitable condition of weak logical independence between the two boolean algebras we prove that the upper ordinal relation is a comparative possibility in all the aforementioned cases we consider specifically also the lower ordinal relations since they may not be the comparative dual relation of the upper ones

recovering scattering obstacles by multi frequency phaseless far field data abstract it is well known that the modulus of the far field pattern or phaseless far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field so the shape but not the location of the obstacle can be recovered from the phaseless far field data this paper aims to devise an approach to break the translation invariance property of the phaseless far field pattern to this end we make use of the superposition of two plane waves rather than one plane wave as the incident field in this paper it is mathematically proved that the translation invariance property of the phaseless far field pattern can indeed be broken if superpositions of two plane waves are used as the incident fields for all wave numbers in a finite interval furthermore a recursive newton type iteration algorithm in frequencies is also developed to numerically recover both the location and the shape of the obstacle simultaneously from multi frequency phaseless far field data numerical examples are also carried out to illustrate the validity of the approach and the effectiveness of the inversion algorithm

combining uncertain information of differing modalities in this paper we consider approaches for combining separately possibilistic uncertainty probabilistic uncertainty and situations where both forms of uncertainty appear an approach to probability aggregation using rational consensus with equi weighting is developed this aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty the analysis is based on combinations of bounding cases of probability distributions measures of conflict and the effect on information are developed next possibility transformations are used and illustrated by three representative possibility cases the resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before finally a general approach to combining possibility distributions directly using quality criteria is described an example is provided to illustrate the basic possibility distribution aggregation fusion developed

a collaborative recommender system based on probabilistic inference from fuzzy observations the problem of building recommender systems has attracted considerable attention in recent years the objective of this paper is to automatically suggest and rank a list of new items to a user based on the past voting patterns of other users with similar tastes the proposed model can be considered as a soft computing based collaborative recommender system the combination of bayesian networks which enables an intuitive representation of the mechanisms that govern the relationships between the users and the fuzzy set theory enabling us to represent ambiguity or vagueness in the description of the ratings improves the accuracy of the system

reconstruction procedures for two inverse scattering problems without the phase information this is a continuation of two recent publications of the authors j inverse ill posed probl 23 2015 pp 415 426 j inverse ill posed probl 23 2015 pp 187 193 about reconstruction pr

rational points of universal curves in positive characteristics rational points of universal curves in positive characteristics by tatsunari watanabe department of mathematics duke university

recovering a polyhedral obstacle by a few backscattering measurements abstract we propose an inverse scattering scheme of recovering a polyhedral obstacle in r n n 2 3 by only a few high frequency acoustic backscattering measurements the obstacle could be sound soft or sound hard it is shown that the modulus of the far field pattern in the backscattering aperture possesses a certain local maximum behavior from which one can determine the exterior normal directions of the front sides faces then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions one can determine the exterior unit normal vector of each side face of the obstacle after the determination of the exterior unit normals the recovery is reduced to a finite dimensional problem of determining a location point of the obstacle and the distance of each side face away from the location point for the latter reconstruction we need to make use of the far field data with phases numerical experiments are also presented to illustrate the effectiveness of the proposed scheme

on the recovery of a 2 d function from the modulus of its fourier transform a uniqueness theorem is proven for the problem of the recovery of a complex valued compactly supported 2 d function from the modulus of its fourier transform an application to the phase problem in optics is discussed

on the issue of defuzzification and selection based on a fuzzy set abstract we are concerned with the problem of selecting a crisp element based on information provided by a fuzzy set a problem which manifests itself in the defuzzification step in fuzzy logic controllers we provide a unifying approach to this selection process among other characteristics this unification puts the defuzzification methods of mean of maxima and center of gravity in the same framework we show that this selection can be viewed as a three step operation transformation of the decision fuzzy set normalization to probability distribution selection based on the probability distribution a number of different procedures for selection are discussed

stability of schur functors abstract symplectic resp orthogonal schur functors are defined on a vector spacevwith a non degenerate skew symmetric resp symmetric bilinear form each of these functors determines an irreducible representation of s p v resp s o v we prove that if dim vis sufficiently large then the splitting into irreducible components of the composition of a symplectic orthogonal schur functor and an ordinary schur functor applied tovis independent of dim v we also prove the stability of the branching for the symplectic orthogonal schur functors

generalization of an invertible mapping between probability and possibility a discrete bijective mapping between probability and possibility is generalized to the continuous case in n dimensions the mapping contains a parametrical function which can be chosen such that the probability possibility consistency relation and the uncertainty invariance principle are fulfilled simultaneously

the determination of the surface impedance of a partially coated obstacle from far field data a variational method is given for determining the essential supremum of the surface impedance of a partiallycoated perfect conductor from a knowledge of the far field pattern of the time harmonic electric field at fixed frequency it is assumed that the shape of the scatterer has been determined e g bysolving the far field equation and using the linear sampling method numerical examples are given for the scalar case with constant surface impedance

entropy conserving probability transforms and the entailment principle our main result here is the development of a general procedure for transforming some initial probability distribution into a new probability distribution in a way that the resulting distribution has entropy at least as great as the original distribution a significant aspect of our approach is that it makes use of zadeh s entailment principle which is itself a general procedure for going from an initial possibility distribution to a new possibility distribution so that the resulting possibility has an uncertainty at least as great as the original