encounter distribution of two random walkers on a finite one dimensional interval we analyse the first passage properties of two random walkers confined to a finite one dimensional domain for the case of absorbing boundaries at the endpoints of the interval we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries for the case of reflecting boundaries we obtain the mean first encounter time of the two particles our approach leads to closed form expressions that are more easily tractable than a previously derived solution in terms of the weierstrass elliptic function

sharp error bounds for the derivatives of lidstone spline interpolation ii abstract in this paper we shall derive explicit error estimates in l norm between a given function f x pc n a b 4 n 6 and its quintic lidstone spline interpolate the results obtained are then used to establish precise error bounds for the approximated and biquintic lidstone spline interpolates we also include applications to integral equations and boundary value problems as well as sufficient numerical examples which dwell upon the sharpness of the obtained results

on existence of positive solutions of sturm liouville boundary value problems for a nonlinear singular differential system abstract by employing the fixed point theorem of cone expansion and compression of norm type we investigate the existence of positive solutions of sturm liouville boundary value problems for a nonlinear singular differential system some well known results in the literature are generalized and improved an example is presented to illustrate the application of our main result

monotone convergence of iterative methods for right focal point boundary value problems abstract we provide sufficient conditions so that the picard iterative scheme for the right focal point boundary value problems converges monotonically an example which dwells upon the usefulness of this technique is also included

existence of positive solutions for a system of generalized lidstone problems in this paper we study the existence of positive solutions for the system of generalized lidstone problems for ordinary differential equations 1 mu 2 m f 1 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 1 nv 2 n f 2 t u u 1 m 1u 2 m 2 v v 1 n 1v 2 n 2 a 0u 2 i 0 b 0u 2 i 1 0 a 1u 2 i 1 b 1u 2 i 1 1 0 i 0 1 m 1 a 0v 2 j 0 b 0v 2 j 1 0 a 1v 2 j 1 b 1v 2 j 1 1 0 j 0 1 n 1 here f 1 f 2 c 0 1 xr m n r r 0 our hypotheses imposed on the nonlinearities f 1 and f 2 are formulated in terms of nonnegative matrices we use fixed point index theory to establish our main results based on a priori estimates of positive solutions

a singular boundary value problem for odd order differential equations abstract the odd order differential equation 1 nx 2n 1 f t x x 2n together with the lidstone boundary conditions x 2j 0 x 2j t 0 0 j n 1 and the next condition x 2n 0 0 is discussed here f satisfying the local caratheodory conditions can have singularities at the value zero of all its phase variables existence result for the above problem is proved by the general existence principle for singular boundary value problems

error inequalities for quintic and biquintic discrete hermite interpolation in this paper we shall develop a class of discrete hermite interpolates in one and two independent variables further we offer explicit error bounds in norm for the quintic and biquintic discrete hermite interpolates some numerical examples are included to illustrate the results obtained

on periodic discrete spline interpolation quintic and biquintic cases in this paper we develop a class of periodic discrete spline interpolates in one and two independent variables explicit error bounds are further derived for the periodic quintic and biquintic discrete spline interpolates we also present some numerical examples to illustrate the results obtained

error estimates for discrete spline interpolation in this paper we shall develop a class of discrete spline interpolates in one and two independent variables further explicit error bounds in norm are derived for the quintic and biquintic discrete spline interpolates we also present some numerical examples to illustrate the results obtained

a fourth order compact finite difference method for nonlinear higher order multi point boundary value problems a fourth order compact finite difference method is proposed for a class of nonlinear 2nth order multi point boundary value problems the multi point boundary condition under consideration includes various commonly discussed boundary conditions such as the three or four point boundary condition n 2 point boundary condition and 2 n m point boundary condition the existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term the convergence and the fourth order accuracy of the method are proved an efficient monotone iterative algorithm is developed for solving the resulting nonlinear finite difference systems various sufficient conditions for the construction of upper and lower solutions are obtained some applications and numerical results are given to demonstrate the high efficiency and advantages of this new approach

higher order lidstone boundary value problems for elliptic partial differential equations the aim of this paper is to show the existence and uniqueness of a solution for a class of 2nth order elliptic lidstone boundary value problems where the nonlinear functions depend on the higher order derivatives sufficient conditions are given for the existence and uniqueness of a solution it is also shown that there exist two sequences which converge monotonically from above and below respectively to the unique solution the approach to the problem is by the method of upper and lower solutions together with monotone iterative technique for nonquasimonotone functions all the results are directly applicable to 2nth order two point lidstone boundary value problems

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

two point higher order bvps with singularities in phase variables the existence of solutions for singular higher order differential equations with the lidstone or the n p boundary conditions is proved the right hand sides of differential equations can have singularities in the zero value of their phase variables and so higher derivatives of solutions changing their signs can pass through these singularities proofs are based on the method of a priori estimates the degree theory arguments and on vitali s convergence theorem

relational duals of the c means clustering algorithms abstract the hard and fuzzy c means algorithms are widely used effective tools for the problem of clustering n objects into hard or fuzzy groups of similar individuals when the data is available as object data consisting of a set of n feature vectors in rp however object data algorithms are not directly applicable when the n objects are implicitly described in terms of relational data which consists of a set of n2 measurements of relations between each of the pairs of objects new relational versions of the hard and fuzzy c means algorithms are presented here for the case when the relational data can reasonably be viewed as some measure of distance some convergence properties of the algorithms are given along with a numerical example

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

explicit error bounds for the derivatives of piecewise lidstone interpolation abstract the purpose of this paper is to provide explicit error bounds for the derivatives of piecewise lidstone interpolation in l and l2 norms the results obtained are best possible sharp and supplement those established in earlier papers

k means clustering based data detection and symbol timing recovery for burst mode optical receiver burst mode receivers are key components of optical transmission systems including passive optical networks and have received much attention in recent years we present new efficient methods for burst optical signal detection in burst mode data transmission using a modified k means clustering technique we also develop a data aided feedforward symbol timing recovery method based on a polynomial interpolation and maximum likelihood estimation theory a performance criterion considering the error caused by the interpolation approximation is derived for this method the proposed detection and timing recovery approaches can be implemented effectively and rapidly therefore they are very suitable for burst mode receivers we also provide some numerical examples to demonstrate the performance of the proposed methods

a parametric model for fusing heterogeneous fuzzy data presented is a model that integrates three data types numbers intervals and linguistic assessments data of these three types come from a variety of sensors one objective of sensor fusion models is to provide a common framework for data integration processing and interpretation that is what our model does we use a small set of artificial data to illustrate how problems as diverse as feature analysis clustering cluster validity and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model the effects of reparameterization on computational outputs are discussed numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types

polynomial approximation of cm functions by means of boundary values and applications a survey we collect classical and more recent results on polynomial approximation of sufficiently regular real functions defined in bounded closed intervals by means of boundary values only the problem is considered from the point of view of the existence of explicit formulas interpolation to boundary data bounds for the remainder and convergence of the polynomial series applications to some problems of numerical analysis are pointed out such as nonlinear equations numerical differentiation and integration formulas special associated differential boundary value problems some polynomial expansions for smooth enough functions defined in rectangles or in triangles of r 2 as well as in cuboids or in tetrahedrons in r 3 and their applications are also discussed

new neutrosophic approach to image segmentation neutrosophic set ns a part of neutrosophy theory studies the origin nature and scope of neutralities as well as their interactions with different ideational spectra ns is a formal framework that has been recently proposed however ns needs to be specified from a technical point of view for a given application or field we apply ns after defining some concepts and operations for image segmentation the image is transformed into the ns domain which is described using three membership sets t i and f the entropy in ns is defined and employed to evaluate the indeterminacy two operations a mean and b enhancement operations are proposed to reduce the set indeterminacy finally the proposed method is employed to perform image segmentation using a c means clustering we have conducted experiments on a variety of images the experimental results demonstrate that the proposed approach can segment the images automatically and effectively especially it can segment the clean images and the images having noise with different noise levels

explicit polynomial expansions of regular real functions by means of even order bernoulli polynomials and boundary values for a function f c2n 1 a b an explicit polynomial interpolant in a and in the even derivatives up to the order 2n 1 at the end points of the interval is derived explicit cauchy and peano representations and bounds for the error are given and the analysis of the remainder term allows to find sufficient conditions on f so that the polynomial approximant converges to f these results are applied to derive a new summation formula with application to rectangular quadrature rule the polynomial interpolant is related to a fairly interesting boundary value problem for odes we will exhibit solutions for this problem in some special situations

upper and lower solution methods for fully nonlinear boundary value problems abstract sufficient conditions are given for the existence of a solution of a fourth order nonlinear boundary value problem with nonlinear boundary conditions the conditions assume the existence of a strong upper solution lower solution pair a concept that is defined in the paper the differential equation has nonlinear dependence on all lower order derivatives of the unknown in particular appropriate nagumo conditions are obtained and employed

optimal error bounds for the derivatives of two point hermite interpolation abstract for the derivatives of the hermite polynomial interpolation of a function on the interval a b we obtain best possible uniform error estimates for this a new representation for the error function is developed

lidstone polynomials and boundary value problems abstract we define lidstone polynomials provide their explicit representations give their relations with bernoulli polynomials obtain best possible error estimates in lidstone interpolation and establish several best possible sharp inequalities which compare favourably with the known results next we use these results to study even order differential equations together with lidstone boundary conditions

reconstruction of a function from hermite birkhoff data abstract birkhoff or lacunary interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about some function and its derivatives a birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space in this paper we split up the initial problem in subproblems having a unique polynomial solution and use multinode rational basis functions in order to obtain a global interpolant

universality classes of first passage time distribution in confined media we study the first passage time fpt distribution to a target site for a random walker evolving in a bounded domain we show that in the limit of large volume of the confining domain this distribution falls into universality classes indexed by the walk dimension d w and the fractal dimension d f of the medium which have been recently identified previously benichou et al nat chem 2 472 2010 we present in this paper a complete derivation of these universal distributions discuss extensively the range of applicability of the results and extend the method to continuous time random walks this analysis puts forward the importance of the geometry and in particular the position of the starting point in first passage statistics analytical results are validated by numerical simulations applied to various models of transport in disordered media which illustrate the universality classes of the fpt distribution

existence of nodal solutions for lidstone eigenvalue problems abstract we are concerned with determining values of r for which there exist nodal solutions of the lidstone eigenvalue problem 1 m u 2 m x r a x f u x 0 x 1 u 2 i 0 u 2 i 1 0 i 0 1 2 m 1 the proof of our main result is based upon eigenvalue theory and bifurcation techniques

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

adaptive spatial information theoretic clustering for image segmentation the incorporation of spatial context into clustering algorithms for image segmentation has recently received a significant amount of attention many modified clustering algorithms have been proposed and proven to be effective for image segmentation in this paper we propose a different framework for incorporating spatial information with the aim of achieving robust and accurate segmentation in case of mixed noise without using experimentally set parameters based on the original robust information clustering ric algorithm called adaptive spatial information theoretic clustering asic algorithm the proposed objective function has a new dissimilarity measure and the weighting factor for neighborhood effect is fully adaptive to the image content it enhances the smoothness towards piecewise homogeneous segmentation and reduces the edge blurring effect furthermore a unique characteristic of the new information segmentation algorithm is that it has the capabilities to eliminate outliers at different stages of the asic algorithm these result in improved segmentation result by identifying and relabeling the outliers in a relatively stronger noisy environment comprehensive experiments and a new information theoretic proof are carried out to illustrate that our new algorithm can consistently improve the segmentation result while effectively handles the edge blurring effect the experimental results with both synthetic and real images demonstrate that the proposed method is effective and robust to mixed noise and the algorithm outperforms other popular spatial clustering variants

monotone iterative technique and positive solutions of lidstone boundary value problems the purpose of this paper is to investigate the existence and iteration of n symmetric positive solutions for lidstone boundary value problem 1 nw 2 n t f t w t 0

boundary type quadrature and boundary element method in this paper we apply a boundary type quadrature technique to derive a type of boundary element scheme which is used to solve the boundary value problems of partial differential equations numerical examples for solving the exterior boundary value problem of helmholtz equation by using the spline approximation and the spline wavelet approximation are given

convergence properties of the generalized fuzzy c means clustering algorithms fuzzy c means fcm clustering algorithms have been widely used to solve clustering problems yang and yu 1 extended these to optimization procedures with respect to any probability distribution they showed that the optimal cluster centers are the fixed points of these generalized fcm clustering algorithms the convergence properties of algorithms are the important theoretical issue in this paper we present convergence properties of the generalized fcm clustering algorithms these are global convergence local convergence and its rate of convergence

a new representation for the error function for the hermite interpolation and sharper pointwise and uniform error bounds for the derivatives let a a a r 2 2 be the given points and x e c a a n 2 2 be a given function satisfying the conditions a a j l j i 0 1 k j 1 2 r 1 1 where j kj r n let p r be the hermite interpolation polynomial of degree n 1 satisfying 1 1 for the error function e r x f p t everyone knows the integral representation in terms of peano s kernel green s function however the explicit representation of the green s function is unwieldy l 21 and hence except in some simple cases it cannot be used to obtain the bounds for the derivatives of e t the situation further worsens because the derivatives of the green s function change sign in the interval at a in fact even for the case n 6 r 2 k k 2 the computation is quite lengthy 3 the purpose of this paper is to give a new representation of the error function e t and use it to obtain pointwise as well as uniform error bounds for je k t 0 5 k 5 n 1 in terms of max ix t in

ncm neutrosophic c means clustering algorithm abstract in this paper a new clustering algorithm neutrosophic c means ncm is introduced for uncertain data clustering which is inspired from fuzzy c means and the neutrosophic set framework to derive such a structure a novel suitable objective function is defined and minimized and the clustering problem is formulated as a constrained minimization problem whose solution depends on the objective function in the objective function two new types of rejection have been introduced the ambiguity rejection which concerns the patterns lying near the cluster boundaries and the distance rejection dealing with patterns that are far away from all the clusters these measures are able to manage uncertainty due to imprecise and or incomplete definition of the clusters we conducted several experiments with synthetic and real data sets the results are encouraging and compared favorably with results from other methods as fcm pcm and fpcm algorithms on the same data sets finally the proposed method was applied into image segmentation algorithm the experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing

general type 2 fuzzy c means algorithm for uncertain fuzzy clustering pattern recognition in real world data is subject to various sources of uncertainty that should be appropriately managed the focus of this paper is the management of uncertainty associated with parameters of fuzzy clustering algorithms type 2 fuzzy sets t2 fss have received increased research interest over the past decade primarily due to their potential to model various uncertainties however because of the computational intensity of the processing of general t2 fuzzy sets gt2 fss only their constrained version i e the interval t2 it2 fss were typically used fortunately the recently introduced concepts of planes and zslices allow for efficient representation and computation with gt2 fss following this recent development this paper presents a novel approach for uncertain fuzzy clustering using the general type 2 fuzzy c means gt2 fcm algorithm the proposed method builds on top of the previously published it2 fcm algorithm which is extended via the planes representation theorem the fuzzifier parameter of the fcm algorithm can be expressed using linguistic terms such as small or high which are modeled as t1 fss this linguistic fuzzifier value is then used to construct the gt2 fcm cluster membership functions the linguistic uncertainty is transformed into uncertain fuzzy positions of the extracted clusters the gt2 fcm algorithm was found to balance the performance of t1 fcm algorithms in various uncertain pattern recognition tasks and to provide increased robustness in situations where noisy or insufficient training data are present

shape preserving approximations by polynomials and splines a review of shape preserving approximation methods and algorithms for approxi mating univariate functions or discrete data is given the notion of shape refers to the geometrical behavior of a function s or approximant s graph and usually includes positivity monotonicity and or convexity but in the recent literature the broader concept of shape also includes symmetry gen eralized convexity unimodality lipschitz property possessing peaks or discontinuities etc special stress is put on shape preserving interpolation methods by polynomials and splines of course this text has no pretensions to be complete geywords shape preserving approximation approximation of univariate functions approxima tion of discrete data shape preserving interpolation polynomial spline positivity monotonicity convexity generalized convexity unimodality lipschitz property

discrete polynomial interpolation green s functions maximum principles error bounds and boundary value problems abstract we construct discrete interpolating polynomials provide explicit representations of discrete green s functions give several identities and inequalities for these green s functions use the explicit forms of the interpolating polynomials and that of green s functions to establish several maximum principles further we obtain error bounds in discrete polynomial interpolation and use them to study existence and uniqueness of the discrete boundary value problems these bounds are also used to provide sufficient conditions for the convergence of the picard s method the approximate picard s method quasilinearization and the approximate quasilinearization the monotone convergence of the picard s iterative method is also analysed

ecmdd evidential c medoids clustering with multiple prototypes in this work a new prototype based clustering method named evidential c medoids ecmdd which belongs to the family of medoid based clustering for proximity data is proposed as an extension of fuzzy c medoids fcmdd on the theoretical framework of belief functions in the application of fcmdd and original ecmdd a single medoid prototype which is supposed to belong to the object set is utilized to represent one class for the sake of clarity this kind of ecmdd using a single medoid is denoted by secmdd in real clustering applications using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance in order to address this problem a variation of ecmdd using multiple weighted medoids denoted by wecmdd is presented unlike secmdd in wecmdd objects in each cluster carry various weights describing their degree of representativeness for that class this mechanism enables each class to be represented by more than one object experimental results in synthetic and real data sets clearly demonstrate the superiority of secmdd and wecmdd moreover the clustering results by wecmdd can provide richer information for the inner structure of the detected classes with the help of prototype weights

numerical methods for unilateral problems abstract the theory of variational inequalities besides being elegant and synthetic also provides a unified general framework for applying the numerical methods for solving many unrelated free boundary value problems in this paper we describe numerical experience on the use of variational inequalities and pade approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity like those describing the equilibrium configuration of an elastic beam stretched over an elastic obstacle in the case of a known obstacle these problems can be alternatively formulated as nonlinear boundary value problems without constraints for which the technique of pade approximants can be successfully employed the variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution

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

on the bivariate shepard lidstone operators we propose a new combination of the bivariate shepard operators coman and trimbitas 2001 2 by the three point lidstone polynomials introduced in costabile and dell accio 2005 7 the new combination inherits both degree of exactness and lidstone interpolation conditions at each node which characterize the interpolation polynomial these new operators find application to the scattered data interpolation problem when supplementary second order derivative data are given kraaijpoel and van leeuwen 2010 13 numerical comparison with other well known combinations is presented

the fuzzy c 2 means solving the ambiguity rejection in clustering abstract in this paper we deal with the clustering problem whose goal consists of computing a partition of a family of patterns into disjoint classes the method that we propose is formulated as a constrained minimization problem whose solution depends on a fuzzy objective function in which reject options are introduced two types of rejection have been included the ambiguity rejection which concerns patterns lying near the class boundaries and the distance rejection dealing with patterns that are far away from all the classes to compute these rejections we propose an extension of the fuzzy c means fcm algorithm of bezdek pattern recognition with fuzzy objective function algorithms plenum press new york 1981 this algorithm is called the fuzzy c 2 means fc 2m these measures allow to manage uncertainty due both to imprecise and incomplete definition of the classes the advantages of our method are 1 the degree of membership to the reject classes for a pattern xk are learned in the iterative clustering problem 2 it is not necessary to compute other characteristics to determine the reject and ambiguity degrees 3 the partial ambiguity rejections introduce a discounting process between the classical fcm membership functions in order to avoid the memberships to be spread across the classes 4 the membership functions are more immune to noise and correspond more closely to the notion of compatibility preliminary computational experiences on the developed algorithm are encouraging and compared favorably with results from other methods as fcm fpcm and f c 1 m fuzzy c 1 means clustering with solely distance rejection algorithms on the same data sets the differences in the performance can be attributed to the fact that ambiguous patterns are less accounted in for the computing of the centers

singular lidstone boundary value problem with given maximal values for solutions abstract the singular problem 1 nx 2n f t x x 2n 2 x 2j 0 x 2j t 0 0 j n 1 max x t 0 t t a depending on the parameter is considered here the positive caratheodory function f may be singular at the zero value of all its phase variables the paper presents conditions which guarantee that for any a 0 there exists a 0 such that the above problem with a has a solution x ac2n 1 0 t which is positive on 0 t the proofs are based on the regularization and sequential techniques and use the leray schauder degree and vitali s convergence theorem

on the construction of multi dimensional embedded cubature formulae in order to compute an integrali f one needs at least two cubature formulaeq j j 1 2 q 1 f q 2 f can be used as an error estimate for the less precise cubature formula in order to reduce the amount of work one can try to reuse some of the function evaluations needed forq 1 inq 2 the easiest way to construct embedded cubature formulae is start with a high degree formulaq 1 drop at least one knot and calculate the weights such that the new formulaq 2 is exact for as much monomials as possible we describe how such embedded formulae with positive weights can be found the disadvantage of such embedded cubature formulae is that there is in general a large difference in the degree of exactness of the two formulae in this paper we will explain how the high degree formula can be chosen to obtain an embedded pair of cubature formulae of degrees 2m 1 2m 1 the method works for all regions n n 2 we will also show the influence of structure on the cubature formulae

eigenvalues of lidstone boundary value problems we consider the following boundary value problem 1 ny 2 n lf t y n 1 t 0 1 y 2 i 0 y 2 i 1 0 0 0 the values of l are characterized so that the boundary value problem has a positive solution in addition we derive explicit intervals of l such that for any l in the interval existence of a positive solution of the boundary value problem is guaranteed several examples are also included to dwell upon the importance of the results obtained

nerf c means non euclidean relational fuzzy clustering abstract the relational fuzzy c means rfcm algorithm can be used to cluster a set of n objects described by pair wise dissimilarity values if and only if there exist n points in r n 1 whose squared euclidean distances precisely match the given dissimilarity data this strong restriction on the dissimilarity data renders rfcm inapplicable to most relational clustering problems this paper substantially improves rfcm by generalizing it to the case of arbitrary symmetric dissimilarity data the generalization is obtained using a computationally efficient modification of the existing algorithm that is equivalent to applying a spreading transformation to the dissimilarity data while the method given applies specifically to dissimilarity data a simple transformation can be used to convert similarity relations into dissimilarity data so the method is applicable to any numerical relational data that are positive reflexive or anti reflexive and symmetric numerical examples illustrate and compare the present approach to problems that can be studied with alternatives such as the linkage algorithms

mean first passage times in confined media from markovian to non markovian processes we review recent theoretical works that enable the accurate evaluation of the mean first passage time mfpt of a random walker to a target in confinement for markovian memory less and non markovian walkers for the markovian problem we present a general theory which allows one to accurately evaluate the mfpt and its extensions to related first passage observables such as splitting probabilities and occupation times we show that this analytical approach provides a universal scaling dependence of the mfpt on both the volume of the confining domain and the source target distance in the case of general scale invariant processes this analysis is applicable to a broad range of stochastic processes characterized by length scale invariant properties and reveals the key role that can be played by the starting position of the random walker we then present an extension to non markovian walks by taking the specific example of a tagged monomer of a polymer chain looking for a target in confinement we show that the mfpt can be calculated accurately by computing the distribution of the positions of all the monomers in the chain at the instant of reaction such a theory can be used to derive asymptotic relations that generalize the scaling dependence with the volume and the initial distance to the target derived for markovian walks finally we present an application of this theory to the problem of the first contact time between the two ends of a polymer chain and review the various theoretical approaches of this nonmarkovian problem

explicit error estimates for quintic and biquintic spline interpolation ii abstract the purpose of this paper is to provide explicit error estimates between a given function x t pc n a b 2 n 6 and its quintic spline interpolate s x t the results obtained are sharp and improve on or supplement those established by hall 1 and schultz 2 these results are then used to acquire precise error bounds for the approximated and biquintic spline interpolates sufficient numerical illustration which dwells upon the importance of the obtained results is also included

monotone convergence of iterative methods for n p and p n boundary value problems abstract we provide sufficient conditions so that the picard iterative scheme for n p and p n boundary value problems converges monotonically an example which illustrates the usefulness of this technique is also included

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

a unique multivariate hermite interpolant on the simplex abstract the objective of this paper is to construct a hermite interpolant for arbitrary regular simplices as simple and as well behaving as possible the presented interpolant is unique under the given conditions and has a polynomial degree of only 3 but is the identity for quadratic polynomials this property is not only nice but very useful for e g optimization last but not least the representation of the interpolant is quite simple and allows a fast implementation on a computer

centroid of a type 2 fuzzy set abstract in this paper we introduce the centroid and generalized centroid of a type 2 fuzzy set both of which are essential for implementing a type 2 fuzzy logic system and explain how to compute them for practical use we show how to compute the centroid of interval and gaussian type 2 fuzzy sets an exact computation procedure is provided for an interval type 2 set whereas an approximation is provided for both interval and gaussian type 2 sets examples are given that compare the exact computational results with the approximate results

ecm an evidential version of the fuzzy c means algorithm a new clustering method for object data called ecm evidential c means is introduced in the theoretical framework of belief functions it is based on the concept of credal partition extending those of hard fuzzy and possibilistic ones to derive such a structure a suitable objective function is minimized using an fcm like algorithm a validity index allowing the determination of the proper number of clusters is also proposed experiments with synthetic and real data sets show that the proposed algorithm can be considered as a promising tool in the field of exploratory statistics

on 2nth order lidstone boundary value problems this paper is concerned with the solutions of a class of 2nth order lidstone boundary value problems sufficient conditions for the existence and uniqueness of a solution are given a monotone iteration is developed so that the iteration sequence converges monotonically to a maximal or a minimal solution the approach to the problem is by the method of upper and lower solutions with a new maximum principle

the iterative solutions of 2nth order nonlinear multi point boundary value problems abstract the aim of this paper is to investigate the existence of iterative solutions for a class of 2 n th order nonlinear multi point boundary value problems the multi point boundary condition under consideration includes various commonly discussed boundary conditions such as three or four point boundary condition n 2 point boundary condition and 2 n m point boundary condition the existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique a monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution depending on whether the initial iteration is an upper solution or a lower solution two examples are presented to illustrate the results

axiomatic generalization of the membership degree weighting function for fuzzy c means clustering for decades practitioners have been using the center based partitional clustering algorithms like fuzzy c means fcm which rely on minimizing an objective function comprising of an appropriately weighted sum of distances of each data point from the cluster representatives numerous generalizations in terms of choice of the distance function have been introduced for fcm since its inception in a stark contrast to this fact to the best of our knowledge there has not been any significant effort to address the issue of convergence of the algorithm under the structured generalization of the weighting function here by generalization we mean replacing the conventional weighting function uijm where uij indicates the membership of data xi to cluster cj and m is the real valued fuzzifier with 1 m with a more general function g uij which can assume a wide variety of forms under some mild assumptions in this article for the first time we present a novel axiomatic development of the general weighting function based on the membership degrees we formulate the fuzzy clustering problem along with the intuitive justification of the technicalities behind the axiomatic approach we develop an alternative optimization ao procedure to solve the main clustering problem by solving the partial optimization problems in an iterative way the novelty of the article lies in the development of an axiomatic generalization of the weighting function of fcm formulation of an ao algorithm for the fuzzy clustering problem with the extension to this general class of weighting functions and a detailed convergence analysis of the proposed algorithm

a fourth order compact finite difference method for higher order lidstone boundary value problems a compact finite difference method is proposed for a general class of 2nth order lidstone boundary value problems the existence and uniqueness of the finite difference solution is investigated by the method of upper and lower solutions without any monotone requirement on the nonlinear term a monotone iteration process is provided for solving the resulting discrete system efficiently and a simple and easily verified condition is obtained to guarantee a geometric convergence of the iterations the convergence of the finite difference solution and the fourth order accuracy of the proposed method are proved numerical results demonstrate the high efficiency and advantages of this new approach

boundary value problems occurring in plate deflection theory abstract the paper deals with several iterative methods for solving some boundary value problems occurring in plate deflection theory making it possible to avoid the lengthy problem preparation which is required to solve these problems by finite difference methods

existence and uniqueness of positive solutions for a higher order boundary value problem the goal of this paper is to study the existence and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 n 1u 2 n 2 a 0u 2 i 0 email protected 0u 2 i 1 0 0 i 0 1 n 1 a 1u 2 i 1 email protected 1u 2 i 1 1 0 i 0 1 n 1 the krein rutman theorem and the krasnoselskii zabreiko fixed point theorem are the main tools that have been used to develop our work

survival probability of a brownian motion in a planar wedge of arbitrary angle we study the survival probability and the first passage time distribution for a brownian motion in a planar wedge with infinite absorbing edges we generalize existing results obtained for wedge angles of the form ensuremath pi n with n a positive integer to arbitrary angles which in particular cover the case of obtuse angles we give explicit and simple expressions of the survival probability and the first passage time distribution in which the difference between an arbitrary angle and a submultiple of ensuremath pi is contained in three additional terms as an application we obtain the short time development of the survival probability in a wedge of arbitrary angle

effects of confinement on the statistics of encounter times exact analytical results for random walks in a partitioned lattice we study the effects of temporarily and permanently confining domains on the statistics of first passage times in finite lattices in one and two dimensions we present exact results for the mean and variance of the first passage time between arbitrary sites in the following 1 a finite one dimensional lattice partitioned into temporarily confining domains and 2 a finite two dimensional lattice with reflecting boundaries for a single random walker and an immobile target in the one dimensional case we also present the full first passage time distribution via numerical inversion of laplace transforms

a possibilistic fuzzy c means clustering algorithm in 1997 we proposed the fuzzy possibilistic c means fpcm model and algorithm that generated both membership and typicality values when clustering unlabeled data fpcm constrains the typicality values so that the sum over all data points of typicalities to a cluster is one the row sum constraint produces unrealistic typicality values for large data sets in this paper we propose a new model called possibilistic fuzzy c means pfcm model pfcm produces memberships and possibilities simultaneously along with the usual point prototypes or cluster centers for each cluster pfcm is a hybridization of possibilistic c means pcm and fuzzy c means fcm that often avoids various problems of pcm fcm and fpcm pfcm solves the noise sensitivity defect of fcm overcomes the coincident clusters problem of pcm and eliminates the row sum constraints of fpcm we derive the first order necessary conditions for extrema of the pfcm objective function and use them as the basis for a standard alternating optimization approach to finding local minima of the pfcm objective functional several numerical examples are given that compare fcm and pcm to pfcm our examples show that pfcm compares favorably to both of the previous models since pfcm prototypes are less sensitive to outliers and can avoid coincident clusters pfcm is a strong candidate for fuzzy rule based system identification

upper and lower estimates for positive solutions of the higher order lidstone boundary value problem we consider the higher order lidstone boundary value problem new upper and lower estimates for positive solutions of the problem are obtained a discussion of the sharpness of the estimates is included

positive solutions of a 2nth order boundary value problem involving all derivatives via the order reduction method this paper is mainly concerned with the existence multiplicity and uniqueness of positive solutions for the 2nth order boundary value problem 1 nu 2 n f t u u 1 i 2 u i 1 n 1u 2 n 1 u 2 i 0 u 2 i 1 1 0 i 0 1 n 1 where n 2 and f c 0 1 xr 2 n r r 0 we first use the method of order reduction to transform the above problem into an equivalent initial value problem for a first order integro differential equation and then use the fixed point index theory to prove the existence multiplicity and uniqueness of positive solutions for the resulting problem based on a priori estimates achieved by developing spectral properties of associated parameterized linear integral operators finally as a byproduct our main results are applied for establishing the existence multiplicity and uniqueness of symmetric positive solutions for the lidstone problem involving all derivatives