a new gradient descent approach for local learning of fuzzy neural models the majority of reported learning methods for takagi sugeno kang tsk fuzzy neural models to date mainly focus on improvement of their accuracy however one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behavior when all the rules are aggregated to produce the overall system output this is one of the distinctive characteristics from black box models such as neural networks therefore how to find a desirable set of fuzzy partitions and hence identify the corresponding consequent models which can be directly explained in terms of system behavior presents a critical step in fuzzy neural modeling in this paper a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed unlike the conventional two stage optimization procedure widely practiced in the field where the two sets of parameters are optimized separately the consequent parameters are transformed into a dependent set on the premise parameters thereby enabling the introduction of a new integrated gradient descent learning approach thus a new jacobian matrix is proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second order levenberg marquardt optimization method several other interpretability issues regarding the fuzzy neural model are also discussed and integrated into this new learning approach numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm and compared with the results from some well known methods

tyz expansion for the kepler manifold the main goal of the paper is to address the issue of the existence of kempf s distortion function and the tian yau zelditch tyz asymptotic expansion for the kepler manifold an important example of non compact manifold motivated by the recent results for compact manifolds we construct kempf s distortion function and derive a precise tyz asymptotic expansion for the kepler manifold we get an exact formula finite asymptotic expansion of n 1 terms and exponentially small error terms uniformly with respect to the discrete quantization parameter m rightarrow infty hbar m 1 rightarrow 0 standing for planck s constant and x rightarrow infty x in mathbb c n moreover the coefficients are calculated explicitly and they turned out to be homogeneous functions with respect to the polar radius in the kepler manifold we show that our estimates are sharp by analyzing the nonharmonic behaviour of tm for m rightarrow infty the arguments of the proofs combine geometrical methods quantization tools and functional analytic techniques for investigating asymptotic expansions in the framework of analytic gevrey spaces

moment maps scalar curvature and quantization of kahler manifolds building on donaldson s work on constant scalar curvature metrics we study the space of regular kahler metrics e i e those for which deformation quantization has been defined by cahen gutt and rawnsley after giving in sects 2 and 3 a review of donaldson s moment map approach we study the essential uniqueness of balanced basis i e of coherent states in a more general setting theorem 2 5 we then study the space e in sect 4 and we show in sect 5 how all the tools needed can be defined also in the case of non compact manifolds

submanifolds of cartan hartogs domains and complex euclidean spaces abstract we study the non existence of common submanifolds of a complex euclidean space and a cartan hartogs domain equipped with their canonical metrics

fully nonlinear fourth order equations with functional boundary conditions abstract the aim of this paper consists in to give sufficient conditions to ensure the existence and location of the solutions of a nonlinear fully fourth order equation with functional boundary conditions the arguments make use of the upper and lower solutions method a laplacian operator and a fixed point theorem an application of the beam theory to a nonlinear continuous model of the human spine allows to estimate its deformation under some loading forces

scalar curvature and projective embeddings i we prove that a metric of constant scalar curvature on a polarised kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings satisfying a condition introduced by h luo this gives as a corollary the uniqueness of constant scalar curvature kahler metrics in a given rational cohomology class the proof uses results in the literature on the asymptotics of the bergman kernel the arguments are presented in a general framework involving moment maps for two different group actions

fixed sign solutions of second order difference equations with neumann boundary conditions in this paper we study the existence of solution of the nonlinear second order difference problem with neumann boundary conditions assuming the existence of a pair of ordered lower and upper solutions and we obtain optimal existence results for the case and even for to this end we do an exhaustive study of the values of the real parameters and for which the associated green s function to the linear operator l u u 2 2 u 1 u with neumann boundary conditions has fixed sign

kahler einstein submanifolds of the infinite dimensional projective space this paper consists of two main results in the first one we describe all kahler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the wallach set of the domain in the second one we exhibit an example of complete and non homogeneous kahler einstein metric with negative scalar curvature which admits a kahler immersion into the infinite dimensional complex projective space

an output constrained clustering approach for the identification of fuzzy systems and fuzzy granular systems this paper presents an output constrained clustering approach for fuzzy system identification and fuzzy granular system identification the approach is unlike most existing clustering algorithms for structure identification of fuzzy systems where the focus is on input or combined input output clustering the output constrained clustering algorithm divides the output space into several partitions and each output partition is considered to be a constraint then input data are projected into clusters that are based on the input distribution constrained by the output partitions by introducing the key concept of separability of a set of clusters within each output constraint the proposed approach automatically finds an appropriate small and efficient number of clusters for each output constraint to have an appropriate small and efficient number of clusters in each output constraint results in a more compact final system structure and better accuracy this better performance is illustrated by experiments using benchmark function approximation and dynamic system identification

nonresonance conditions for generalised ϕ laplacian problems with jumping nonlinearities abstract we consider the boundary value problem 0 1 x u x u x f x u x u x a e x 0 1 0 2 c 00 u 0 c 01 u 0 c 10 u 1 c 11 u 1 where c j 0 c j 1 0 for each j 0 1 and f 0 1 r 2 r are caratheodory functions with suitable additional properties the differential operator generated by the left hand side of 0 1 together with the boundary conditions 0 2 is a generalisation of the usual p laplacian and also of the so called laplacian which corresponds to x s t t with an odd increasing homeomorphism for the p laplacian problem and more particularly the semilinear case p 2 nonresonance conditions which ensure the solvability of the problem 0 1 0 2 have been obtained in terms of either eigenvalues for non jumping f or the fucik spectrum or half eigenvalues for jumping f of the p laplacian in this paper under suitable growth conditions on and f we extend these conditions to the general problem 0 1 0 2

fuzzy rough nearest neighbor algorithms in classification in this paper classification efficiency of the conventional k nearest neighbor algorithm is enhanced by exploiting fuzzy rough uncertainty the simplicity and nonparametric characteristics of the conventional k nearest neighbor algorithm remain intact in the proposed algorithm unlike the conventional one the proposed algorithm does not need to know the optimal value of k moreover the generated class confidence values which are interpreted in terms of fuzzy rough ownership values do not necessarily sum up to one consequently the proposed algorithm can distinguish between equal evidence and ignorance and thus the semantics of the class confidence values becomes richer it is shown that the proposed classifier generalizes the conventional and fuzzy knn algorithms the efficacy of the proposed approach is discussed on real data sets

radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems this paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network rbfnn after a nonparametric approximate model of the system is constructed from a priori experiments or simulations a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations the procedures for both training and state estimation are described along with discussions on approximation error nonlinear systems with linear output equations are considered as a special case of the general formulation finally applications of the proposed rbfnn to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method

fixed sign solutions of a system of higher order difference equations abstract we consider the following system m u i k f i k u 1 k u 2 k u n k 0 k 0 1 t j u i 0 0 0 j m 3 i m 2 u i 0 i m 1 u i 0 0 i m 2 u i t 1 i m 1 u i t 1 0 i 1 2 n where m 2 t m 1 and for each 1 i n i 0 i 0 i 0 i i and i i t 1 i i i i 0 criteria are offered for the existence of single and double fixed sign solutions of the system

positive periodic solutions for nonlinear difference equations with periodic coefficients abstract we prove the existence of positive solutions of second order nonlinear difference equations on a finite discrete segment with periodic boundary conditions obtained results yield positive periodic solutions of the equation on the whole discrete axis provided that the coefficients are periodic

the bergman kernel function and proper holomorphic mappings it is proved that a proper holomorphic mapping f between bounded complete reinhardt domains extends holomorphically past the boundary and that if in addition f 1 0 01 then f is a polynomial mapping the proof is accomplished via a transformation rule for the bergman kernel function under proper holomorphic mappings

the design methodology of radial basis function neural networks based on fuzzy k nearest neighbors approach various approaches to partitioning of high dimensional input space have been studied with the intent of developing homogeneous clusters formed over input and output spaces of variables encountered in system modeling in this study we propose a new design methodology of a fuzzy model where the input space is partitioned by making use of some classification algorithm especially fuzzy k nearest neighbors k nn classifier being guided by some auxiliary information granules formed in the output space this classifier being regarded in the context of this design as a supervision mechanism is used to capture the distribution of data over the output space this type of supervision is beneficial when developing the structure in the input space it is demonstrated that data involved in a partition constructed by the fuzzy k nn method realized in the input space show a high level of homogeneity with regard to the data present in the output space this enhances the performance of the fuzzy rule based model whose premises in the rules involve partitions formed by the fuzzy k nn the design is illustrated with the aid of numeric examples that also provide a detailed insight into the performance of the fuzzy models and quantify several crucial design issues

a novel training algorithm for rbf neural network using a hybrid fuzzy clustering approach this paper introduces a novel clustering based algorithm to train gaussian type radial basis function neural networks in contrast to existing approaches we develop a specialized learning strategy that combines the merits of fuzzy and crisp clustering crisp clustering is a fast process yet very sensitive to initialization on the other hand fuzzy clustering reduces the dependency on initialization however it constitutes a slow learning process the proposed strategy aims to search for a trade off among these two potentially different effects the produced clusters possess fuzzy and crisp areas and therefore the final result is a hybrid partition where the fuzzy and crisp conditions coexist the hybrid clusters are directly involved in the estimation process of the neural network s parameters specifically the center elements of the basis functions coincide with cluster centers while the respective widths are calculated by taking into account the topology of the hybrid clusters to this end the network s design becomes a fast and efficient procedure the proposed method is successfully applied to a number of experimental cases where the produced networks prove to be highly accurate and compact in size

an efficient immune based symbiotic particle swarm optimization learning algorithm for tsk type neuro fuzzy networks design in this paper we propose a new learning algorithm that can be used to design tsk type neuro fuzzy networks though there has been a great deal of interest in the use of immune algorithms ias for computer science and engineering in terms of fundamental methodologies they are not dramatically different from other algorithms in order to enhance the ia performance we propose the immune based symbiotic particle swarm optimization ispso for use in tsk type neuro fuzzy networks for solving the prediction and skin color detection problems the proposed ispso embeds the symbiotic evolution scheme in an ia and utilizes particle swarm optimization pso to improve the mutation mechanism in order to avoid trapping in a local optimal solution and to ensure the search capability of a near global optimal solution mutation plays an important role therefore we employed the advantages of pso to improve the mutation mechanism and used a method that introduces chaotic mapping with certainty ergodicity and the stochastic property into pso to improve global convergence unlike the ia that uses each individual in a population as a full solution to a problem symbiotic evolution assumes that each individual in a population represents only a partial solution to a problem complex solutions combine several individuals in the population

existence theorems for second order discrete boundary value problems abstract this article is concerned with the existence of solutions of boundary value problems for nonlinear second order difference equations of the type p n x n 1 q n x n f n x n where 0 is the ratio of odd positive integers p n and q n are real sequences the authors apply the linking theorem and the mountain pass lemma in the critical point theory and give some new results for the existence of solutions

monotone iterative method for the second order three point boundary value problem with upper and lower solutions in the reversed order abstract this article introduces a new concept of upper and lower solutions and studies the existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order the sufficient conditions for the existence and uniqueness of solutions are obtained by using the monotone iterative method meantime the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution are given some results of previous literature are extended and improved a numerical example is also included to illustrate the effectiveness of the proposed results

existence and uniqueness of solutions of second order three point boundary value problems with upper and lower solutions in the reversed order abstract this paper studies the existence and uniqueness of solutions of second order three point boundary value problems with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence and uniqueness of solutions by use of the monotone iterative method and gives the iterative sequence for solving a solution and its error estimate formula under the condition of unique solution

rule based modeling of nonlinear relationships we discuss a problem of rule based fuzzy modeling of multiple input single output nonlinear relationships f r sub n spl rarr r the model under investigation is viewed as a collection of conditional statements if state spl omega then y g sub i x at i 1 2 n with spl omega sub i being a fuzzy relation defined in the space of the input variables in contrast to the commonly encountered identification approach based exclusively upon discrete experimental data the one proposed in this study is concerned with the rule based modeling exploiting the available nonlinear input output relationship the main thrust is in the development of a relevant fuzzy partition of the input variables we introduce and study criteria of separability and variability as the key means guiding a distribution and granularity of the linguistic labels forming the condition part of the local models

a hierarchical fuzzy clustering approach to fuzzy modeling abstract this paper introduces a new method for fuzzy modeling based on a hierarchical fuzzy clustering scheme the method consists of a sequence of steps aiming towards developing a takagi sugeno ts fuzzy model of optimal structure where the fuzzy sets in the premise part are of gaussian type starting from an initial ordinary fuzzy partition of the input space the algorithm performs a nearest neighbor search and groups the original input training data into a number of clusters the centers of these clusters are further processed using an optimal fuzzy clustering technique which is based on the weighted fuzzy c means algorithm the resulted optimal fuzzy partition defines the number of fuzzy rules and provides an initial estimation for the system parameters which in a next step are fine tuned using the well known gradient descend algorithm the proposed method is successfully applied to three test examples where the produced fuzzy models prove to be very accurate as well as compact in size

a self adaptive neural fuzzy network with group based symbiotic evolution and its prediction applications in this paper we propose a self adaptive neural fuzzy network with group based symbiotic evolution sanfn gse method a self adaptive learning algorithm consists of two major components first a self clustering algorithm sca identifies a parsimonious internal structure an internal structure is said to be parsimonious in the sense that the number of clusters fuzzy rules is equal to the true number of clusters in a given training data set the proposed sca is an online method and is a distance based connectionist clustering method unlike the traditional cluster techniques that only consider the total variation to updates the only one mean and deviation the proposed sca method considers the variation of each dimension for the input data second a group based symbiotic evolution learning gse method is used to adjust the parameters for the desired outputs the gse method is different from traditional gas genetic algorithms with each chromosome in the gse method representing a fuzzy system moreover in the gse method there are several groups in the population each group represents a set of the chromosomes that belong to a cluster computing by the sca in this paper we used numerical time series examples one step ahead prediction mackey glass chaotic time series and sunspot number forecasting to evaluate the proposed sanfn gse model the performance of the sanfn gse model compares excellently with other existing models in our time series simulations

rigidity of proper holomorphic mappings between certain unbounded non hyperbolic domains abstract the fock bargmann hartogs domain d n m 0 in c n m is defined by the inequality w 2 e z 2 where z w c n c m which is an unbounded non hyperbolic domain in c n m recently yamamori gave an explicit formula for the bergman kernel of the fock bargmann hartogs domains in terms of the polylogarithm functions and kim ninh yamamori determined the automorphism group of the domain d n m in this article we obtain rigidity results on proper holomorphic mappings between two equidimensional fock bargmann hartogs domains our rigidity result implies that any proper holomorphic self mapping on the fock bargmann hartogs domain d n m with m 2 must be an automorphism

on singular functional nonsmooth and implicit phi laplacian initial and boundary value problems in this paper we apply fixed point results for mappings in partially ordered spaces to derive existence results for extremal solutions of phi laplacian initial and boundary value problems the considered problems can be singular functional discontinuous nonlocal and implicit concrete examples are also solved

balanced metrics on cartan and cartan hartogs domains this paper consists of two results dealing with balanced metrics in donaldson terminology on noncompact complex manifolds in the first one we describe all balanced metrics on cartan domains in the second one we show that the only cartan hartogs domain which admits a balanced metric is the complex hyperbolic space by combining these results with those obtained in loi and zedda mathematische annalen 2011 to appear we also provide the first example of complete kahler einstein and projectively induced metric g such that g is not balanced for all 0

using radial basis functions to approximate a function and its error bounds a novel network called the validity index network vi net is presented the vi net derived from radial basis function networks fits functions and calculates confidence intervals for its predictions indicating local regions of poor fit and extrapolation

evolving space filling curves to distribute radial basis functions over an input space an evolutionary neural network training algorithm is proposed for radial basis function rbf networks the locations of basis function centers are not directly encoded in a genetic string but are governed by space filling curves whose parameters evolve genetically this encoding causes each group of codetermined basis functions to evolve to fit a region of the input space a network produced from this encoding is evaluated by training its output connections only networks produced by this evolutionary algorithm appear to have better generalization performance on the mackey glass time series than corresponding networks whose centers are determined by k means clustering

on the proper holomorphic equivalence for a class of pseudoconvex domains a complete and explicit description of the holomorphic proper mappings between weakly pseudoconvex domains of the class ap see below is given the study of proper holomorphic mappings i e holomorphic mappings which antitransform compact sets into compact sets 1 f d d2 d1 d2 c cn n 1 between bounded pseudoconvex domains with smooth boundary has had recently a considerable impulse and has been applied mainly to investigate a under which hypothesis there is no obstruction for the existence of such an f b the regularity up to the boundary of 1 c for which domains proper means in effect biholomorphic the first class of problems has been taken into consideration for instance in 8 5 4 and a typical result is for example that a strictly pseudoconvex domain cannot be mapped properly onto a weakly pseudoconvex domain about b see for instance 4 2 3 and the bibliography there included the property enunciated in c has been proved in the case d d2 unit ball see 1 and 9 when d and d2 are strictly pseudoconvex domains with in addition d2 simply connected see 7 and 4 and in the case d d2 and strictly pseudoconvex see 7 the aim of this note is to look at questions of type a and c above posed for the following class of weakly pseudoconvex domains ap z 1j z2p lzn 2pn p pn e z n precisely we prove theorem in order for a proper holomorphic mapping from ap onto a q to exist it is necessary and sufficient that plq p llql pnlqn e z furthermore assuming the only proper holomorphic mapping between a p and a q is up to biholomorphisms of a q f z zfl l zpnqn received by the editors october 25 1982 and in revised form march 29 1983 1980 mathematics subject classification primary 32h99 secondary 32f15 work performed with finanical aid from m p i di1984 american mathematical society 0002 9947 84 1 00 25 per page

existence and approximation of solutions for first order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions abstract this paper is devoted to the study of the existence of solutions of first order difference equations verifying nonlinear conditions that involve the global behavior of the solution we prove that the existence of lower and upper solutions warrants the existence of such solutions lying in the sector formed by the mentioned functions we also can prove that some classical results for differential equations are not true in general for this case

a further result on the oscillation of delay difference equations in this paper we are concerned with the delay difference equations of the form yn 1 yn pnyn k 0 n 0 1 2 where pn 0 and k is a positive integer we prove by using a new technique that n 0 i nn kpi ln i nn k pi 1 sign i nn k pi i n 1n k pi ln i n 1n k pi 1 sign i n 1n k pi guarantees that all solutions of equation oscillate which improves many previous well known results in particular our theorems also fit the case where n 1i n kpi kk 1 k 1 k 1 in addition we present a nonoscillation sufficient condition for equation

boundary value problems involving upper and lower solutions in reverse order in this paper we discuss the existence of extreme solutions of the boundary value problem for a class of first order functional equations with a nonlinear boundary condition in the presence of a lower solution a and an upper solution b with email protected email protected we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique

monotone method for the neumann problem with lower and upper solutions in the reverse order this work is devoted to the study of the existence and approximation of solutions of the problem u f t u u u a u b 0 in the presence of lower and upper solutions in the reverse order to this end we prove anti maximum principles for the nonlinear operator u 2k u email protected

proper self maps of weakly pseudoconvex domains this theorem was proved by burns and shnider i 5 in the case that d is strongly pseudoconvex in the more general case pin6uk 1 9 corollary 2 has reduced the problem of showing that a proper mapping f d d is biholomorphic to proving that f is unbranched i e that det f 0 our interest in the theorem above stems from the fact that if f d t d 2 is a proper holomorphic mapping of a weakly pseudoconvex domain d 1 onto a second domain dz it is possible for f to branch if d1 d 2 this is contrary to what may occur if d 1 is assumed to be strongly pseudoconvex see alexander 1 pin6uk 9 10 fornaess 1 8 bell 1 3 diederich and fornaess 1 7 it has recently been proved in 1 4 and in i 6 that the mapping f in the theorem extends smoothly to this fact is basic to our proof the theorem may be shown to remain valid if 112 is replaced by a stein manifold see 2 but si ace the arguments of 4 and 6 do not carry over automatically to this case the methods used in 1 2 are more technical

extremal solutions for nonlinear functional ϕ laplacian impulsive equations abstract in this paper we deal with some nonlinear laplacian second order boundary value problems with impulses subject to a general type of boundary value conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type the impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear in both cases functional dependence on the solution is allowed

the monotone method for periodic differential equations with the non well ordered upper and lower solutions in this paper we consider the following periodic problem x t g t x t x t a e t a b x a x b x a x b the unique solution is obtained by constructing an auxiliary periodic system with bounded solutions and proving these bounds to be equal in which case they are the expected unique solution

systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions abstract this paper is concerned with the existence of solutions for systems of first order impulsive functional differential equations with deviating arguments and nonlinear boundary conditions by establishing new comparison results and applying the monotone iterative technique we obtain the sufficient conditions for the existence of extremal system of solutions

a positive operator approach to the neumann problem for a second order ordinary differential equation abstract in this paper the solvability of the second order neumann problem u t cu t f t u t 0 qquad u 0 a u r b is studied we suppose that there is a lower solution and an upper solution in the reversed order and we obtain optimal conditions infto assure the existence of a solution lying between and

extraction of fuzzy rules from support vector machines the relationship between support vector machines svms and takagi sugeno kang tsk fuzzy systems is shown an exact representation of svms as tsk fuzzy systems is given for every used kernel function restricted methods to extract rules from svms have been previously published their limitations are surpassed with the presented extraction method the behavior of svms is explained by means of fuzzy logic and the interpretability of the system is improved by introducing the l fuzzy rule based system l frbs the l frbs exactly approximates the svm s decision boundary and its rules and membership functions are very simple aggregating the antecedents with uninorms as compensation operators the rules of the l frbs are limited to two and the number of fuzzy propositions in each rule only depends on the cardinality of the set of support vectors for that reason the l frbs overcomes the course of dimensionality and problems with high dimensional data sets are easily solved with the l frbs

evolutionary fuzzy modeling this study is concerned with a general methodology of identification of fuzzy models unlike numeric models fuzzy models operate at a level of information granules fuzzy sets and this aspect brings up an important design requirement of transparency of the model we propose a three phase development framework by distinguishing between structural and parametric optimization processes the underlying topology of the model dwells on fuzzy neural networks architectures governed by fuzzy logic and equipped with parametric flexibility two general optimization mechanisms are explored the structural optimization is realized via genetic programming whereas for the ensuing detailed parametric optimization we proceed with gradient based learning the main advantages of this approach are discussed in detail the study is illustrated with the aid of a numeric example that provides a detailed insight into the performance of the fuzzy models and quantifies crucial design issues

extremal solutions for the difference φ laplacian problem with nonlinear functional boundary conditions abstract in this paper we study the existence and approximation of the extremal solutions for the laplacian problem lying between a pair of a lower solution and an upper solution such that we consider general boundary functional conditions that include classical ones as separated or periodic

rigidity of proper holomorphic mappings between nonequidimensional bounded symmetric domains we prove that any proper holomorphic mapping from d p p 1 i to d p p i p geq 3 is necessarily a totally geodesic isometric embedding with respect to their bergman metrics and therefore is the standard linear embedding up to their automorphisms the proof of the main result in this paper will be achieved by a differential geometric study of a special class of complex geodesic curves on the bounded symmetric domains with respect to their bergman metrics

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

on sturm liouville boundary value problems for second order nonlinear functional finite difference equations motivated by the interesting paper i karaca discrete third order three point boundary value problem j comput appl math 205 2007 458 468 this paper is concerned with a class of boundary value problems for second order functional difference equations sufficient conditions for the existence of at least one solution of a sturm liouville boundary value problem for second order nonlinear functional difference equations are established we allow f to be at most linear superlinear or sublinear in obtained results

an online self constructing neural fuzzy inference network and its applications a self constructing neural fuzzy inference network sonfin with online learning ability is proposed in this paper the sonfin is inherently a modified takagi sugeno kang tsk type fuzzy rule based model possessing neural network learning ability there are no rules initially in the sonfin they are created and adapted as online learning proceeds via simultaneous structure and parameter identification in the structure identification of the precondition part the input space is partitioned in a flexible way according to an aligned clustering based algorithm as to the structure identification of the consequent part only a singleton value selected by a clustering method is assigned to each rule initially afterwards some additional significant terms selected via a projection based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds the combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network a main feature of the sonfin in the parameter identification the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm to enhance the knowledge representation ability of the sonfin a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved

building an interpretable fuzzy rule base from data using orthogonal least squares application to a depollution problem in many fields where human understanding plays a crucial role such as bioprocesses the capacity of extracting knowledge from data is of critical importance within this framework fuzzy learning methods if properly used can greatly help human experts amongst these methods the aim of orthogonal transformations which have been proven to be mathematically robust is to build rules from a set of training data and to select the most important ones by linear regression or rank revealing techniques the ols algorithm is a good representative of those methods however it was originally designed so that it only cared about numerical performance thus we propose some modifications of the original method to take interpretability into account after recalling the original algorithm this paper presents the changes made to the original method then discusses some results obtained from benchmark problems finally the algorithm is applied to a real world fault detection depollution problem

extremal solutions for third order nonlinear problems with upper and lower solutions in reversed order abstract this paper deals with the existence of extremal solutions for the third order nonlinear boundary value problem u t f t u t t a b u a a u a b u b c in the presence of a pair of lower and upper solutions in reversed order here r r is an increasing homeomorphism f a b r r is a carathedory function and a b c r the proof follows from monotone iterative techniques which are based on suitable anti maximum principles for adequate operators to deduce such results we study some related problems coupled with boundary value conditions of the form p 0 u a q 0 u a a p 1 u b q 1 u b b u a c and u a a u a b u b c

boundary value problem for first order impulsive functional integro differential equations this paper investigates extremal solutions of the boundary value problem for impulsive functional integro differential equations with nonlinear boundary conditions and deviating arguments in the presence of a lower solution u and an upper solution v with u v existence of extremal solutions is proved by establishing a new comparison principle and using the monotone iterative technique

oscillation of two dimensional difference systems abstract the authors consider the nonlinear two dimensional difference system x n b n g y n y n 1 a n f x n n n o no no 1 where n 0 n 1 2 a n and b n n n n 0 are real sequences and f g r r are continuous with uf u 0 and ug u 0 for u 0 a solution x n y n of the system is oscillatory if both components are oscillatory the authors obtain sufficient conditions for all solutions of the system to be oscillatory some of their results allow a n to oscillate examples to illustrate the results are included

on the existence of positive solutions of p laplacian difference equations in this paper by means of fixed point theorem in a cone the existence of positive solutions of p laplacian difference equations is considered

a new approach to fuzzy modeling this paper proposes a new approach to fuzzy modeling the suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as takagi and sugeno s model 1985 because it has the same structure as that of takagi and sugeno s model it is also as easy to implement as sugeno and yasukawa s model 1993 because its identification mimics the simple identification procedure of sugeno and yasukawa s model the suggested algorithm is composed of two steps coarse tuning and fine tuning in coarse tuning fuzzy c regression model fcrm clustering is used which is a modified version of fuzzy c means fcm in fine tuning gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models finally some examples are given to demonstrate the validity of this algorithm

existence and uniqueness results for some nonlinear boundary value problems u a s u b s0 dirichlet 2 u9 a s u9 b s 0 neumann 3 u a s u b and u9 a s u9 b periodic 4 w x here f r a r is an odd increasing homeomorphism k a b a r and w x 2 py2 f a b r a r equation 1 with f s s s s where p 1 and k t s n y 1 rt arises in the study of radial solutions for the p laplacian equation on an annular domain in n dimensions py2 n div u u q f x u u s 0 a x b x g r 5 w x and has been studied extensively see for instance 1 4 6 in this paper we shall establish existence results for 1 with each of the above boundary conditions 2 3 and 4 under various growth conditions on f in particular our results give the existence of radial solutions

on canonical metrics on cartan hartogs domains the cartan hartogs domains are defined as a class of hartogs type domains over irreducible bounded symmetric domains the purpose of this paper is twofold firstly for a cartan hartogs domain omega b d 0 mu endowed with the canonical metric g mu we obtain an explicit formula for the bergman kernel of the weighted hilbert space mathcal h alpha of square integrable holomorphic functions on left omega b d 0 mu g mu right with the weight exp alpha varphi where varphi is a globally defined kahler potential for g mu for alpha 0 and furthermore we give an explicit expression of the rawnsley s varepsilon function expansion for left omega b d 0 mu g mu right secondly using the explicit expression of the rawnsley s varepsilon function expansion we show that the coefficient a 2 of the rawnsley s varepsilon function expansion for the cartan hartogs domain left omega b d 0 mu g mu right is constant on omega b d 0 mu if and only if left omega b d 0 mu g mu right is biholomorphically isometric to the complex hyperbolic space so we give an affirmative answer to a conjecture raised by m zedda

extremal solutions for the first order impulsive functional differential equations with upper and lower solutions in reversed order this paper studies the existence of solutions of first order impulsive functional differential equations with lower and upper solutions in the reversed order obtains the sufficient conditions for the existence of solutions by establishing a new comparison principle and using the monotone iterative technique a concrete example is presented and solved to illustrate the obtained results

kernelized fuzzy attribute c means clustering algorithm a novel kernelized fuzzy attribute c means clustering algorithm is proposed in this paper since attribute means clustering algorithm is an extension of fuzzy c means algorithm with weighting exponent m 2 and fuzzy attribute c means clustering is a general type of attribute c means clustering with weighting exponent m 1 we modify the distance in fuzzy attribute c means clustering algorithm with kernel induced distance and obtain kernelized fuzzy attribute c means clustering algorithm kernelized fuzzy attribute c means clustering algorithm is a natural generalization of kernelized fuzzy c means algorithm with stable function experimental results on standard iris database and tumor normal gene chip expression data demonstrate that kernelized fuzzy attribute c means clustering algorithm with gaussian radial basis kernel function and cauchy stable function is more effective and robust than fuzzy c means fuzzy attribute c means clustering and kernelized fuzzy c means as well

rigidity of proper holomorphic mappings between equidimensional hua domains hua domain named after chinese mathematician loo keng hua is defined as a domain in mathbb c n fibered over an irreducible bounded symmetric domain omega subset mathbb c d with the fiber over z in omega being a n d dimensional generalized complex ellipsoid sigma z in general a hua domain is a nonhomogeneous bounded pseudoconvex domain without smooth boundary the purpose of this paper is twofold firstly we obtain what seems to be the first rigidity results on proper holomorphic mappings between two equidimensional hua domains secondly we determine the explicit form of the biholomorphisms between two equidimensional hua domains as a special conclusion of this paper we completely describe the group of holomorphic automorphisms of the hua domain

function spaces and reproducing kernels on bounded symmetric domains there are several natural hilbert spaces of holomorphic functions on a bounded symmetric domain such are the bergman type spaces on which the holomorphic discrete series operates and the hardy type spaces which are related to the analytic continuation of the holomorphic discrete series also closely related is the bergmann space of entire functions on the ambient which arises as the closure of the polynomials with respect to a natural inner product the space of holomorphic polynomials decomposes into irreducible subspaces under the action of the isotropy group k of the domain the main facts about this decomposition were proved by schmid 21 for another proof see 22 each irreducible subspace contains a unique normalized l invariant spherical polynomial where l is the isotropy group of the shilov boundary in k our first main result is the explicit computation of the norms of the spherical polynomials with respect to each of the hilbert spaces considered for the domains of classical type they were considered by hua 9 and for some of the hilbert spaces this was done before by upmeier 24 using different methods for certain others there are partial results in 22 we are able to do this in a fairly simple unified way by making strong use of gindikin s generalized gamma function s next we obtain a description of the reproducing kernels of the k irreducible subspaces in each of our hilbert spaces and an expansion in terms of these for

a methodology for automated fuzzy model generation in this paper we propose a generic methodology for the automated generation of fuzzy models the methodology is realized in three stages initially a crisp model is created and in the second stage it is transformed to a fuzzy one in the third stage all parameters entering the fuzzy model are optimized the proposed methodology is novel and generic since it can integrate alternative techniques in each of its stages a specific realization of this methodology is implemented using decision trees for the creation of the crisp model the sigmoid function the min max operators and the maximum defuzzifier for the transformation of the crisp model into a fuzzy one and four different optimization strategies including global and local optimization techniques as well as hybrid approaches the proposed methodology presents several advantages and novelties the transformation of the crisp model to the respective fuzzy one is straightforward ensuring its full automated nature and it introduces a set of parameters expressing the importance of each fuzzy rule the above realization is extensively evaluated using several benchmark data sets from the uci machine learning repository and the obtained results indicate its high efficiency

on training rbf neural networks using input output fuzzy clustering and particle swarm optimization this paper elaborates on the use of particle swarm optimization in training gaussian type radial basis function neural networks under the umbrella of input output fuzzy clustering the problem being investigated concerns the selection of basis function centers that contribute most in network s performance given that the clustering process in the input space is guided by the clustering in the output space to accomplish this task we quantify the effect of the input space fuzzy partition upon network s square error in terms of an objective function that describes the ability of the partition to accurately reconstruct the input training samples we then theoretically prove that the minimization of the above function acts to minimize an upper bound of the network s square error therefore the resulting solution corresponds to a minimal square error while at the same time it maintains the structure of the input data due to the peculiarity of the aforementioned objective function we treat it as the fitness function used by the particle swarm optimizer the proposed methodology encompasses three design steps the first step implements an independent fuzzy clustering in the output space to obtain a set of cluster centers in the second step unlike other approaches the above centers are directly involved in the estimation of the membership degrees in the input output space in the third step these membership degrees are used by the particle swarm optimizer in order to obtain optimal values for the centers to summarize the novelty of our contribution lies in a the way we handle the information flow from output to input space and b the way we handle the effect of the input space partition upon network s performance the experiments indicate that the fitness function decreases as the number of hidden node increases finally a comparison between the proposed method and other sophisticated approaches shows its statistically significant superiority

oscillation and nonoscillation for second order linear difference equations new oscillation and nonoscillation theorems are obtained for the second order linear difference equation 2xn 1 pnxn 0 where if pn n 1 is a real sequence with pn 0

radial balanced metrics on the unit ball of the kepler manifold abstract we show that there is no radial balanced metric on the unit ball of the kepler manifold with not too wild boundary behavior additionally we identify explicitly the weights corresponding to radial metrics with such boundary behavior which satisfy the balanced condition as far as germs at the boundary are concerned related results for poincare metrics are also established

existence and comparison results for difference φ laplacian boundary value problems with lower and upper solutions in reverse order abstract this paper is devoted to the study of the existence and comparison results for nonlinear difference laplacian problems with mixed dirichlet neumann and periodic boundary value conditions we deduce existence of extremal solutions of periodic and neumann boundary value problems lying between a pair of lower and upper solutions given in reverse order we prove the optimality of some assumptions in