sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

on viewing fuzzy measures as fuzzy subsets we introduce the concept of a fuzzy measure discuss some of their basic properties and look at some notable examples we introduce a correspondence between a fuzzy measure on x and a fuzzy subset over the power set of x these fuzzy subsets are required to have special properties on the space 2x and we refer to these as measure type fuzzy sets we take advantage of this correspondence between a fuzzy measure and a fuzzy set to suggest the formulation of various set operations on fuzzy measures

m quantile models for small area estimation small area estimation techniques are employed when sample data are insufficient for acceptably precise direct estimation in domains of interest these techniques typically rely on regression models that use both covariates and random effects to explain variation between domains however such models also depend on strong distributional assumptions require a formal specification of the random part of the model and do not easily allow for outlier robust inference we describe a new approach to small area estimation that is based on modelling quantile like parameters of the conditional distribution of the target variable given the covariates this avoids the problems associated with specification of random effects allowing inter domain differences to be characterized by the variation of area specific m quantile coefficients the proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area specific parameters including that of the quantiles of the distribution of the target variable in the different small areas results from two simulation studies comparing the performance of the m quantile modelling approach with more traditional mixed model approaches are also provided

existence of bubbling solutions for chern simons model on a torus we study the existence of bubbling solutions for the the following chern simons higgs equation delta u frac1 varepsilon 2 rm e u 1 rm e u 4 pi sum i 1 2k delta p i quad text in omega where is a torus if k 1 for any critical point q of the associated sum of the green functions we introduce a quantity d q see 1 11 below we show that for any non degenerate critical point q with d q 0 the above problem has a solution ue satisfying that e 0 ue blows up at q the calculations in this paper also show that if a sequence of solutions ue blows up at q as e 0 then q must be a critical point of the associated sum of the green functions and d q leqq 0 so the condition d q 0 is almost necessary to obtain our result we also construct solutions with k bubbles for k geqq 2

maximal solution of the liouville equation in doubly connected domains abstract in this paper we consider the liouville equation u 2 e u 0 with dirichlet boundary conditions in a two dimensional doubly connected domain we show that there exists a simple closed curve such that for a sequence n 0 and a sequence of solutions u n it holds u n log 1 n h where h is a harmonic function in and n 2 log 1 n e u n d x 8 c where c is a constant depending on the conformal class of only

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

the estimation of the mean squared error of small area estimators abstract small area estimation has received considerable attention in recent years because of a growing demand for reliable small area statistics the direct survey estimators based only on the data from a given small area or small domain are likely to yield unacceptably large standard errors because of small sample size in the domain therefore alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency these estimators use models either implicitly or explicitly that connect the small areas through supplementary e g census and administrative data for example simple synthetic estimators are based on implicit modeling in this article three small area models of battese harter and fuller 1988 dempster rubin and tsutakawa 1981 and fay and herriot 1979 are investigated these models are all special cases of a general mixed linear model involving fixed and random effects and a small area mean can be expr

singular mean field equations on compact riemann surfaces for a general class of elliptic pde s in mean field form on compact riemann surfaces with exponential nonlinearity we address the question of the existence of solutions with concentrated nonlinear term which in view of the applications are physically of definite interest in the model we also include the possible presence of singular sources in the form of dirac masses which makes the problem more difficult to attack

on the mean field equation with variable intensities on pierced domains abstract we consider the two dimensional mean field equation of the equilibrium turbulence with variable intensities and dirichlet boundary condition on a pierced domain u 1 v 1 e u v 1 e u d x 2 v 2 e u v 2 e u d x in i 1 m b i i u 0 on where b i i is a ball centered at i with radius i is a positive parameter and v 1 v 2 0 are smooth potentials when 1 8 m 1 and 2 2 8 m m 1 with m 1 0 1 m there exist radii 1 m small enough such that the problem has a solution which blows up positively and negatively at the points 1 m 1 and m 1 1 m respectively as the radii approach zero

controlling the bias of robust small area estimators sinha rao 2009 proposed estimation procedures designed for small area means based on robustified maximum likelihood estimators and robust empirical best linear unbiased predictors their methods are of the plug in type and may be biased bias corrected estimators have been proposed by chambers et al 2013 here we investigate two new approaches one relying on the work of chambers 1986 and the second using the concept of conditional bias to measure the influence of units in the population these two classes of estimators also include correction terms for the bias but are both fully bias corrected in the sense that the corrections account for the potential impact of the other domains on the small area of interest monte carlo simulations suggest that the sinha rao method and the bias adjusted estimator of chambers et al 2013 may exhibit a large bias while the new procedures often offer lower bias and mean squared error a parametric bootstrap procedure is considered for constructing confidence intervals copyright 2013 oxford university press

a note on the conditional probability of fuzzy subsets of a continuous domain abstract the notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets the definition is motivated by considering a possible mechanism by which an intelligent agent could extend set theoretic operations to fuzzy sets this same mechanism also suggests an alternative definition for the conditional probability of fuzzy sets it is noted that this definition is probability possibility consistent and it is shown that in the case where the probability distribution on the domain has a density function then the conditional probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g this result is used to develop an analytical method for calculating conditional probabilities of fuzzy subsets of the reals where the membership functions of f and g and the density function are continuous piecewise linear functions such a method has applications to the development of a general semantic unification in fril

an improved geometric inequality via vanishing moments with applications to singular liouville equations we consider a class of singular liouville equations on compact surfaces motivated by the study of electroweak and self dual chern simons theories the gaussian curvature prescription with conical singularities and onsager s description of turbulence we analyse the problem of existence variationally and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the moser trudinger inequality and in turn to lower bounds on the euler lagrange functional we then discuss existence and non existence results

bias robust estimation in finite populations using nonparametric calibration a standard problem in sample survey inference is that of predicting the finite population total h of a function h y of a random variable y the model based approach to this problem first defines a working model for y and then predicts h by estimating its expectation under conditional on the sample values of y this approach leads to biased predictions if is incorrect we explore an automatic solution to this misspecification bias that uses nonparametric regression to define a robust but inefficient predictor of h and then calibrates this predictor for its bias under an application to prediction of the finite population distribution function of a population of australian beef farms is presented

robust restricted maximum likelihood in mixed linear models summary definitions of robust maximum likelihood robust ml and robust restricted maximum likelihood robust reml are introduced and the definitions are applied to data from biological and chemical experiments a simulation study is undertaken to investigate the asymptotic properties of robust ml and robust reml in small samples and to examine the advantages of using robust methods 1 introduction and definitions linear models with multiple sources of error are widely used in designed experiments across many scientific fields an example of such an experiment is described by patterson and nabugoomu 1992 from patterson and silvey 1980 six varieties of wheat were grown at ten centres that formed a sample of the main types of growing area for wheat in scotland and the yields in tonnes hectare were recorded the experiment is unbalanced because of 60 possible variety centre combinations only 46 were used at seven centres four varieties were grown and at the remaining three centres all six varieties were grown in this paper we fit the simplest mixed linear model proposed for this data by patterson and nabugoomu namely

elliptic functions green functions and the mean field equations on tori we show that the green functions on flat tori can have either 3 or 5 critical points only there does not seem to be any direct method to attack this problem instead we have to employ sophisticated non linear partial differential equations to study it we also study the distribution of number of critical points over the moduli space of flat tori through deformations the functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori the general picture is also emerged though some of the necessary technicality is still to de developed 1 introduction and statement of results the study of geometric or analytic problems on two dimensional tori is the same as the study of problems on r 2 with doubly periodic data such situations occur naturally in sciences and mathematics since early days the mathematical foundation of elliptic functions was subsequently devel oped in the 19th century it turns out that these special functions are rather deep objects by themselves tori of different shape may result in very dif ferent behavior of the elliptic functions and their associated objects arith metic on elliptic curves is perhaps the eldest and the most vivid example in this paper we show that this is also the case for certain non linear par tial differential equations indeed researches on doubly periodic problems in mathematical physics or differential equations often restrict the study to rectangular tori for simplicity this leaves the impression that the theory for general tori may resemble much the same way as for the rectangular case however this turns out to be false we will show that the solvability of themean field equation dependson the shape of the green function which in turn depends on the geometry of the tori in an essential way recall that the green function g z w on a flat torus t c z 1 z 2 is the unique function on t t which satisfies zg z w w z 1 t

outlier robust small area estimation recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data this naturally leads down to the idea of an outlier robust bias correction for these estimators in this paper we develop this idea and also propose two different analytical mean squared error estimators for the ensuring bias corrected outlier robust estimators simulations based on realistic outlier contaminated data show that the proposed bias correction often leads to more efficient estimators furthermore the proposed mean squared error estimators appear to perform well with a variety of outlier robust smal area estimators

mean squared error of estimation or prediction under a general linear model abstract the problem considered is that of predicting a linear combination of the fixed and random effects of a mixed effects linear model more generally the problem considered is that of predicting an unobservable random variable from a set of observable random variables the best linear unbiased predictor depends on parameters which generally are unknown various exact or approximate expressions are given for the mean squared error mse of the predictor obtained by replacing the unknown parameters with estimates several estimators of the mse are investigated

possibility versus probability the main objective of this note is to try to indicate that a possibility distribution at least in some applications can be interpreted as a family of probabilities possibly subjective an advantage of the latter interpretation is that subsequent derivations can be made by well proven probabilistic arguments rather than relying on an intuition concerning the properties of possibility distributions which is not well developed multistate reliability theory is given as an example of an area of application where the probabilistic approach seems far superior

the use of a fuzzy decision making method in a large scale computer system choice problem abstract we recently proposed a fuzzy decision making method for multiple objectives problems in an uncertain and ill defined environment this paper presents a real and large scale application of the method the problem is to decide what sort of computer system for research and education should be renewed in the department of computer engineering one member of a renewal committee appears as a decision maker after describing the outline of the fuzzy decision making method the decision analysis process objective hierarchy identification of decision maker s preference structure rating and ranking of alternatives and sensitivity analysis is presented

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

a note on the operativeness of neyman pearson tests with fuzzy information abstract in a previous paper we have studied the extension of the neyman pearson optimality criterion of testing statistical hypotheses when the available experimental information involves fuzzy imprecision this extension usually becomes unmanageable for small samples nevertheless we will verify that when the sample size is large enough the application of the central limit theorem determines an operative extension

reliability estimation and design with insufficient data based on possibility theory early in the engineering design cycle it is difficult to quantify product reliability or compliance to performance targets because of insufficient data or information for modeling the uncertainties design decisions are therefore based on fuzzy information that is vague imprecise qualitative linguistic or incomplete the uncertain information is usually available as intervals with lower and upper limits in this work the possibility theory is used to assess design reliability with incomplete information the possibility theory can be viewed as a variant of fuzzy set theory the formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures a computationally efficient and accurate hybrid global local optimization approach is subsequently described for calculating the confidence level of fuzzy response the method combines the advantages of the commonly used vertex and discretization methods subsequently the possibility theory is used in design a possibility based design optimization method is proposed where all design constraints are expressed in a possibilistic way it is shown that the method gives a conservative solution compared with all conventional reliability based designs obtained with different probability distributions finally a general possibility based design optimization method which handles a combination of random and possibilistic design variables is presented several numerical examples demonstrate the application of possibility theory in design

a fuzzy decision making method and its application to a company choice problem abstract we propose a fuzzy decision making method for multiobjective decision problems its main features are the use of fuzzy connectives to represent the decision maker s preference structure and fuzzy probability to express imprecise and uncertain outcomes the preference structure is extracted through interaction between the decision maker and a computer the fuzzy connectives adopted here are zimmermann s operation and its two extensions the extended operations describe the preference structure better than the operation the proposed method consists of the following five steps 1 1 identification of the problem 2 2 a questionnaire process 3 3 parameter identification 4 4 evaluations of alternatives 5 5 aggregated rating and ranking of alternatives finally an application of this method to a company choice problem is presented

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

concentrating solutions for an exponential nonlinearity with robin boundary condition abstract we study the following robin boundary value problem 0 1 u 2 u p 1 e u p 0 u 0 in u n u 0 on where is a bounded domain in r 2 with smooth boundary as 0 and simultaneously 0 p 2 by using a lyapunov schmidt reduction procedure we extend for the whole range of exponents 0 p 2 the results of davila and topp 2012 who constructed bubbling solutions to problem 0 1 for p 1

standard errors of prediction in generalized linear mixed models abstract the unconditional mean squared error of prediction umsep is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in the classical normal theory mixed model but the umsep is inappropriate for generalized linear mixed models where the conditional variance of the random effects depends on the data when the random effects describe variation between independent small domains and domain specific prediction is of interest we propose a conditional mean squared error of prediction cmsep as a general measure of prediction variance the cmsep is shown to be the sum of the conditional variance and a positive correction that accounts for the sampling variability of parameter estimates we derive a second order correct estimate of the cmsep that consists of three components a a plug in estimate of the conditional variance b a plug in estimate of a taylor series approximation to the correction term and c a bootstrap estimate of

generic multiplicity for a scalar field equation on compact surfaces we prove generic multiplicity of solutions for a scalar field equation on compact surfaces via morse inequalities in particular our result improves significantly the multiplicity estimate which can be deduced from the degree counting formula in chen and lin 2003 12 related results are derived for the prescribed q curvature equation

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

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

vagueness and bayesian probability this paper is a response to michael laviolette and john w seaman jr s ibid vol 2 no 1 p 4 1994 position paper the efficacy of fuzzy representations of uncertainty which criticizes fuzzy representations of uncertainty and suggests that bayesian probability can do better the commenter argues that the author s make some misleading comments about bayesian probability and he briefly discusses the problem of giving a satisfactory interpretation of membership functions

bubbling solutions for relativistic abelian chern simons model on a torus we prove the existence of bubbling solutions for the following chern simons higgs equation delta u frac 1 varepsilon 2 e u 1 e u 4 pi sum j 1 n delta p j quad rm in omega where is a torus we show that if n 4 and p 1 p j j 2 n then for small e 0 the above problem has a solution u e and as e 0 u e blows up at the vertex point p 1 and satisfies frac 1 varepsilon 2 e u 1 e u to 4 pi n delta p 1 this is the first result for the existence of a solution which blows up at a vertex point

uniqueness and symmetry results for solutions of a mean field equation on 2 via a new bubbling phenomenon motivated by the study of gauge field vortices we consider a mean field equation on the standard two sphere involving a dirac distribution supported at a point p of s 2 as needed for the applications we show that solutions concentrate exactly at p for some limiting value of a given parameter we use this fact to obtain symmetry about the axis op and uniqueness property for the solution the presence of the dirac measure makes such a task particularly delicate indeed we need to rule out the possibility that after blow up in a suitable scale the solution sequence may admit a double peak profile described in terms of appropriate limiting problems for instance we need to account for the presence of non axially symmetric solutions in such limiting problems in this process we establish a symmetry result about a maximal circle through p and its antipodal point p that applies to more general situations where the full axial symmetry cannot be expected

existence of conformal metrics with constant q curvature given a compact four dimensional manifold we prove existence of conformal metrics with constant q curvature under generic assumptions the problem amounts to solving a fourth order nonlinear elliptic equation with variational structure since the corresponding euler functional is in general unbounded from above and from below we employ topological methods and min max schemes jointly with the compactness result of 35

sampling fuzzy discretization and signal reconstruction abstract the sampling theorem provides the condition under which a continuous time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time it gives a condition for the signal reconstruction problem the importance of this theorem pertains to the necessity of knowing when a continuous time signal is uniquely represented by its discrete version so that continuous time signals can be properly converted and handled by sampled data systems like digital computers the problem of the equivalence between either continuous time or discrete time signals and their fuzzy descriptions is analyzed here this encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled data systems such as fuzzy filters fuzzy models or fuzzy controllers a necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces furthermore a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed the discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning

outlier robust finite population estimation abstract outliers in sample data are a perennial problem for applied survey statisticians moreover it is a problem for which traditional sample survey theory offers no real solution beyond the sensible advice that such sample elements should not be weighted to their fullest extent in estimation sample outliers can be identified as of two basic types here we are concerned with the first type which may conveniently be termed representative outliers these are sample elements with values that have been correctly recorded and that cannot be assumed to be unique that is there is no good reason to assume there are no more similar outliers in the nonsampled part of the target population the remaining sample outliers which by default are termed nonrepresentative are sample elements whose data values are incorrect or unique in some sense methods for dealing with these nonrepresentative outliers lie basically within the scope of survey editing and imputation theory and are therefore not considered in

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

efficiencies of two stage systems with fuzzy data two stage dea data envelopment analysis models show the performance of individual processes and thus are more informative than the conventional one stage models for making decisions this paper extends this approach from deterministic to uncertain situations where the observations are represented by fuzzy numbers the extension principle is utilized to develop a pair of two level mathematical programs to calculate the lower and upper bounds of the a cut of the fuzzy efficiency by enumerating various values of a the membership functions of fuzzy efficiencies are constructed numerically it is found that the property of the system efficiency being equal to the product of the two process efficiencies which holds for the deterministic case also holds for the fuzzy case this property can be generalized to series systems with more than two processes an example of non life insurance companies in taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy

bias calibrated estimation from sample surveys containing outliers we discuss the problem of estimating finite population parameters on the basis of a sample containing representative outliers we clarify the motivation for chambers s bias calibrated estimator of the population total and show that bias calibration is a key idea in constructing estimators of finite population parameters we then link the problem of estimating the population total to distribution function or quantile estimation and explore a methodology based on the use of chambers s estimator we also propose methodology based on the use of robust estimates and a bias calibrated form of the chambers and dunstan estimator of the population distribution function this proposal leads to a bias calibrated estimator of the population total which is an alternative to that of chambers we present a small simulation study to illustrate the utility of these estimators

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

parametric bootstrap approximation to the distribution of eblup and related prediction intervals in linear mixed models empirical best linear unbiased prediction eblup method uses a linear mixed model in combining information from different sources of information this method is particularly useful in small area problems the variability of an eblup is traditionally measured by the mean squared prediction error mspe and interval estimates are generally constructed using estimates of the mspe such methods have shortcomings like under coverage or over coverage excessive length and lack of interpretability we propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled eblup the bootstrap histogram is highly accurate and differs from the true eblup distribution by only o d 3 n 3 2 where d is the number of parameters and n the number of observations this result is used to obtain highly accurate prediction intervals simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models

robust estimation of variance components outliers may occur with respect to any of the random components in the mixed linear model a procedure for limiting the influence of these outliers on the estimates of the model parameters is described given the variances or estimates of them the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects as appropriate and winsorized the robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of huber s proposal 2 a numerical example illustrates the use of the methodology both as a diagnostic and as an estimation tool

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

user preferences discovery using fuzzy models user preferences discovery aims to learn the patterns of user preferences for various services or items such as movies preferences discovery is essential to the development of intelligent personalization applications based on decision and utility theories traditional approaches to preferences discovery explicitly query users about the behavior of value function or utility of every outcome with respect to each decision criterion consequently these approaches are generally error prone and labor intensive although implicit elicitation approaches have been proposed to address the above limitations extent approaches largely ignore multi valued nature of item features and uncertainty associated with item features and user preferences to address uncertainty due to vagueness and imprecision this research proposed a general framework for preferences discovery based on fuzzy set theories in addition new fuzzy models were created for preferences discovery and representation further an algorithm was developed to predict user preferences with uncertainty and visualization of item features user feedback and the discovered preferences helped improve the interpretation of the discovered knowledge the results of the simulation evaluation using a benchmark movie dataset revealed that the proposed preference discovery method 1 doubled the accuracy of preference discovery as compared to random prediction and 2 outperformed conventional techniques in making movie recommendation these findings suggest that fuzzy models are effective for preferences patterns discovery and personalized recommendation application

topological degree for a mean field equation on riemann surfaces we consider the following mean field equations 0 1 where m is a compact riemann surface with volume 1 h is a positive continuous function on m is a real number 0 2 and where is a bounded smooth domain h is a c1 positive function on and based on our previous analytic work 14 we prove among other things that the degree counting formula for 0 1 is given by for 8m 8 m 1 2003 wiley periodicals inc

bubbling solutions for moser trudinger type equations on compact riemann surfaces abstract we study an elliptic equation related to the moser trudinger inequality on a compact riemann surface s g g u u e u 2 1 s s u e u 2 d v g 0 in s s u d v g 0 where 0 is a small parameter s is the area of s g is the laplace beltrami operator and d v g is the area element given any integer k 1 under general conditions on s we find a bubbling solution u which blows up at exactly k points in s as 0 when s is a flat two torus in rectangular form we find that either seven or nine families of such solutions do exist for k 2 in particular in any square flat two torus actually nine families of bubbling solutions with two bubbling points do exist if s is a riemann surface with non constant robin s function then at least two bubbling solutions with k 1 exists

two dimensional euler flows with concentrated vorticities for a planar model of euler flows proposed by tur and yanovsky 2004 we construct a family of velocity fields w e for a fluid in a bounded region with concentrated vorticities e for e 0 small more precisely given a positive integer and a sufficiently small complex number a we find a family of stream functions e which solve the liouville equation with dirac mass source e e 2 e e 4 pa e in e 0 on for a suitable point p p a e the vorticities e e concentrate in the sense that 1 e 4 pa e 8 1 j 1 pa e a j 0 as e 0 j 1 where the satellites a 1 a 1 denote the complex 1 roots of a the point p a e lies close to a zero point of a vector field explicitly built upon derivatives of order 1 of the regular part of green s function of the domain