lower bounds for the perron root of a nonnegative matrix abstract new lower bounds frequently better than previous bounds and readily computable for the perron root r a of a nonnegative matrix a are obtained the theoretical comparison of new bounds with the known ones is supplemented with two numerical examples

on the best constants in inequalities of the markov and wirtinger types for polynomials on the half line abstract the main topic of the paper is best constants in markov type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves the norm is the l 2 norm with laguerre weight the leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term which is the operator norm of a volterra operator are given for best constants in inequalities of the wirtinger type the limit is computed and an asymptotic formula for the error term is presented

small mass expansion of functional determinants on the generalized cone in this paper we compute the small mass expansion for the functional determinant of a scalar laplacian defined on the bounded generalized cone in the framework of zeta function regularization we obtain an expression for the functional determinant valid in any dimension for both dirichlet and robin boundary conditions in terms of the spectral zeta function of the base manifold moreover as a particular case we specify the base to be a d dimensional sphere and present explicit results for d 2 3 4 5

numerical radius and zero pattern of matrices abstract let a be an n n complex matrix and r be the maximum size of its principal submatrices with no off diagonal zero entries suppose a has zero main diagonal and x is a unit n vector then letting a be the frobenius norm of a we show that a x x 2 1 1 2 r 1 2 n a 2 this inequality is tight within an additive term o r n 2 if the matrix a is hermitian then a x x 2 1 1 r a 2 this inequality is sharp moreover it implies the turan theorem for graphs

on the geometrical structure of symmetric matrices abstract the identity ray i for 0 can be seen as the center ray of the cone of symmetric and positive definite spd matrices in that sense the angle that any spd matrix forms with the identity plays a very important role to understand the geometrical structure of the cone in this work we extend this relationship and analyze the geometrical structure of symmetric matrices including the location of all orthogonal matrices not only the identity matrix this geometrical understanding leads to new results in the subspace of symmetric matrices we also extend some of the geometrical results for the case of general not necessarily symmetric nonsingular matrices

two soft thresholding based iterative algorithms for image deblurring iterative regularization algorithms such as the conjugate gradient algorithm for least squares problems cgls and the modified residual norm steepest descent mrnsd algorithm are popular tools for solving large scale linear systems arising from image deblurring problems these algorithms however are hindered by a semi convergence behavior in that the quality of the computed solution first increases and then decreases in this paper in order to overcome the semi convergence behavior we propose two iterative algorithms based on soft thresholding for image deblurring problems one of them combines cgls with a denoising technique like soft thresholding at each iteration and another combines mrnsd with soft thresholding in a similar way we prove the convergence of mrnsd and soft thresholding based algorithm numerical results show that the proposed algorithms overcome the semi convergence behavior and the restoration results are slightly better than those of cgls and mrnsd with their optimal stopping iterations

lower bounds for the spectral radius of a matrix abstract we develop lower bounds for the spectral radius of symmetric skew symmetric and arbitrary real matrices our approach utilizes the well known leverrier faddeev algorithm for calculating the coefficients of the characteristic polynomial of a matrix in conjunction with a theorem by lucas which states that the critical points of a polynomial lie within the convex hull of its roots our results generalize and simplify a proof recently published by tarazaga for a lower bound on the spectral radius of a symmetric positive definite matrix in addition we provide new lower bounds for the spectral radius of skew symmetric matrices we apply these results to a problem involving the stability of fixed points in recurrent neural networks

heat kernel coefficients of the laplace operator on the d dimensional ball we present a very quick and powerful method for the calculation of heat kernel coefficients it makes use of rather common ideas as integral representations of the spectral sum mellin transforms non trivial commutation of series and integrals and skillful analytic continuation of zeta functions on the complex plane we apply our method to the case of the heat kernel expansion of the laplace operator on a d dimensional ball with either dirichlet neumann or in general robin boundary conditions the final formulas are quite simple using this case as an example we illustrate in detail our scheme which serves for the calculation of an in principle arbitrary number of heat kernel coefficients in any situation when the basis functions are known we provide a complete list of new results for the coefficients b3 b10 corresponding to the d dimensional ball with all the mentioned boundary conditions and d 3 4 5

improving eigenvalue bounds using extra bounds abstract bounds for various functions of the eigenvalues of a hermitian matrix a based on the traces of a and a 2 are improved a technique is presented whereby these bounds can be improved by combining them with other bounds in particular the diagonal of a in conjunction with majorization is used to improve the bounds these bounds all require o n 2 multiplications

heat equation asymptotics for singular sturm liouville operators soit a c r a valeur reelle et l expression differentielle 7b t d x 2 a x x 2 1 x 2 d x 2 a x dans i 0 1 si a i 1 4 i 0 1 l extension de friedrichs t de 7b t c 0 i existe dans l 2 i et a un spectre ponctuel pur on etudie le developpement asymptotique de tr exp st quand s 0

geometrical properties of the frobenius condition number for positive definite matrices we study the geometrical properties of the frobenius condition number on the cone of symmetric and positive definite matrices this number related to the cosine of the angle between a given matrix and its inverse is equivalent to the classical 2 norm condition number but has a direct and natural geometrical interpretation in particular we establish bounds for the ratio between the angle that a matrix forms with the identity ray and the angle that the inverse of that matrix forms with the identity ray these bounds allow us to establish new lower bounds for the condition number that only require the trace and the frobenius norm of the matrix

new eigenvalue estimates for complex matrices abstract in a recent work 1 we have proved that all the eigenvalues j of a complex matrix a of order n lie in a disk with center at tr a n and radius n 1 n k 1 n k 2 tr a 2 n 1 2 in this paper we prove that the eigenvalues of a are contained in a rectangle with vertices on the boundary circle of the mentioned disk improving in this way the result in 1 we recall some inequalities which alloww us to bound the radius of the disk and the rectangle the bounds can be computed without knowing the eigenvalues of a

localization of eigenvalues in elliptic regions abstract we prove that the eigenvalues j of an n by n complex matrix a with its characteristic polynomial having real coefficients lie in the elliptic region defined by 2 tr a n 2 2 y 2 2 2 where n 1 n n 1 n re k 2 re te a 2 n 1 2 and n 1 n k 1 n im k 2 1 2 this region is intersected with the strip y 1 2 k 1 u im k 2 1 2 to obtain an improved eigenvalue localization region we also give bounds for the semiaxes which can be computed without knowing the eigenvalues of a when a has r n nonzero eigenvalues we obtain a smaller elliptic region containing such nonzero eigenvalues

smeared heat kernel coefficients on the ball and generalized cone we consider smeared zeta functions and heat kernel coefficients on the bounded generalized cone in arbitrary dimensions the specific case of a ball is analyzed in detail and used to restrict the form of the heat kernel coefficients an on smooth manifolds with boundary supplemented by conformal transformation techniques it is used to provide an effective scheme for the calculation of the an as an application the complete a5 2 coefficient is given

the spectral zeta function for laplace operators on warped product manifolds of the type i f n in this work we study the spectral zeta function associated with the laplace operator acting on scalar functions defined on a warped product of manifolds of the type i f n where i is an interval of the real line and n is a compact d dimensional riemannian manifold either with or without boundary starting from an integral representation of the spectral zeta function we find its analytic continuation by exploiting the wkb asymptotic expansion of the eigenfunctions of the laplace operator on m for which a detailed analysis is presented we apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion

eigenvalue estimates for symmetric matrices abstract we use the fact that the set of symmetric positive semidefinite matrices of order n form a cone with a special structure in order to find bounds for the eigenvalues of a symmetric matrix

the heat equation with singular coefficients the small time asymptotics of the kernel ofe th is defined and derived for h frac d 2 dx 2 frac kappa x 2 on 1 lemmas on singular asymptotics in the sense of distributions are formulated and used the results are applied to derive an index formula on 1

on the cone of positive semidefinite matrices abstract a survey of some general properties of the cone of positive semidefinite matrices its faces two isometric isomorphisms and linear transformations on it is given

bounds for eigenvalues using the trace and determinant abstract let a be a square matrix with real and positive eigenvalues 1 n 0 and let 1 k l n bounds for kl l and k l involving k l n tr a and det a only are presented

adjoints of elliptic cone operators we study the adjointness problem for the closed extensions of a general b elliptic operator a x diff m b m e 0 initially defined as an unbounded operator a c c m e x l 2 b m e x l 2 b m e inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the case where a is a symmetric semibounded operator is of particular interest and we give a complete description of the domain of the friedrichs extension of such an operator

more estimates for eigenvalues and singular values abstract there is an interesting relation between the angle that a matrix forms with the identity and its eigenvalues then we show for symmetric matrices that some information about the matrix can be known if the angle is computed a lower bound for the maximum eigenvalue is obtained for symmetric positive semidefinite matrices this inequality and the upper bound for eigenvalues given in 5 provide us an interval in which must lie the maximum eigenvalue finally some results from 5 and the first part of this paper are generalized for the non symmetric case

the resolvent expansion for second order regular singular operators abstract the paper gives a scheme for computing the asymptotics of tr e tl as t 0 where l is an elliptic operator of the form l d 2 x 2 a x and a x is a family of operators satisfying appropriate ellipticity and smoothness conditions a principle example is the laplace operator for a manifold with an asymptotically conic singularity the expansion has the usual terms away from the singularity appropriately regularized at x 0 plus singular contributions determined by the function of a 0 1 4 1 2 applications to index theorems are given in a subsequent paper

equalization of nonlinear time varying channels using type 2 fuzzy adaptive filters presents a kind of adaptive filter type 2 fuzzy adaptive filter faf one that is realized using an unnormalized type 2 takagi sugeno kang tsk fuzzy logic system fls we apply this filter to equalization of a nonlinear time varying channel and demonstrate that it can implement the bayesian equalizer for such a channel has a simple structure and provides fast inference a clustering method is used to adaptively design the parameters of the faf two structures are used for the equalizer transversal equalizer te and decision feedback equalizer dfe a decision tree structure is used to implement the decision feedback equalizer in which each leaf of the tree is a type 2 faf this dfe vastly reduces computational complexity as compared to a te simulation results show that equalizers based on type 2 fafs perform much better than nearest neighbor classifiers nnc or equalizers based on type 1 fafs

spectral geometry of singular riemannian spaces on considere la trace du noyau de la chaleur et l application de la methode de l equation de la chaleur au theoreme d indice pour la caracteristique d euler et des complexes signatures

kronecker product approximations for image restoration with whole sample symmetric boundary conditions reflexive boundary conditions bcs assume that the array values outside the viewable region are given by a symmetry of the array values inside the reflection guarantees the continuity of the image in fact there are usually two choices for the symmetry symmetry around the meshpoint and symmetry around the midpoint the first is called whole sample symmetry in signal and image processing the second is half sample many researchers have developed some fast algorithms for the problems of image restoration with the half sample symmetric bcs over the years however little attention has been given to the whole sample symmetric bcs in this paper we consider the use of the whole sample symmetric boundary conditions in image restoration the blurring matrices constructed from the point spread functions psfs for the bcs have block toeplitz plus pseudohankel with toeplitz plus pseudohankel blocks structures recently regardless of symmetric properties of the psfs a technique of kronecker product approximations was successfully applied to restore images with the zero bcs half sample symmetric bcs and anti reflexive bcs respectively all these results extend quite naturally to the whole sample symmetric bcs since the resulting matrices have similar structures it is interesting to note that when the size of the true psf is small the computational complexity of the algorithm obtained for the kronecker product approximation of the resulting matrix in this paper is very small it is clear that in this case all calculations in the algorithm are implemented only at the upper left corner submatrices of the big matrices finally detailed experimental results reporting the performance of the proposed algorithm are presented

resolvents of elliptic cone operators we prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions this is achieved by the construction of a suitable parametrix and reduction to the boundary special attention is devoted to the clarification of the analytic structure of the resolvent

on the resolvent and spectral functions of a second order differential operator with a regular singularity we consider the resolvent of a second order differential operator with a regular singularity admitting a family of self adjoint extensions we find that the asymptotic expansion for the resolvent in the general case presents unusual powers of which depend on the singularity the consequences for the pole structure of the function and for the small t asymptotic expansion of the heat kernel are also discussed

conical casimir pistons with hybrid boundary conditions in this paper we compute the casimir energy and force for massless scalar fields endowed with hybrid boundary conditions in the setting of the bounded generalized cone by using spectral zeta function regularization methods we obtain explicit expressions for the casimir energy and force in arbitrary dimensions in terms of the zeta function defined on the piston our general formulas are subsequently specialized to the case in which the piston is modeled by a d dimensional sphere in this particular situation explicit results are given for d 2 3 4 5

on the structure of the set of symmetric matrices with the perron frobenius property abstract in this paper we explore the geometry of the set of symmetric perron frobenius matrices whose spectral radius is an eigenvalue with a nonnegative associated eigenvector we prove that the set which is not convex is star convex with the identity matrix as the center we also describe a few aspects of the geometric structure of the set

a fuzzy noise reduction method for color images a new fuzzy filter is presented for the reduction of additive noise for digital color images the filter consists of two subfilters the first subfilter computes fuzzy distances between the color components of the central pixel and its neighborhood these distances determine in what degree each component should be corrected all performed corrections preserve the color component distances the goal of the second subfilter is to correct the pixels where the color components differences are corrupted so much that they appear as outliers in comparison to their environment experimental results show the feasibility of the proposed approach we compare with other noise reduction methods by numerical measures and visual observations we also illustrate the performance of the proposed method as preprocessing step for edge detection

on self adjoint boundary conditions for singular sturm liouville operators bounded from below abstract we extend the classical boundary values 0 1 g a w u a 0 g a lim x a g x u a 0 x g 1 a p g a w u a 0 g a lim x a g x g a u a 0 x u a 0 x for regular sturm liouville operators associated with differential expressions of the type r x 1 d d x p x d d x q x for a e x a b r to the case where is singular on a b r and the associated minimal operator t m i n is bounded from below here u a 0 and u a 0 denote suitably normalized principal and nonprincipal solutions of u 0 u for appropriate 0 r respectively our approach to deriving the analog of 0 1 in the singular context employing principal and nonprincipal solutions of u 0 u is closely related to a seminal 1992 paper by niessen and zettl 58 we also recall the well known fact that the analog of the boundary values in 0 1 characterizes all self adjoint extensions of t m i n in the singular case in a manner familiar from the regular case we briefly discuss the singular weyl titchmarsh kodaira m function and finally illustrate the theory in some detail with the examples of the bessel legendre and kummer resp laguerre operators

fuzzy random impulse noise reduction method a new two step fuzzy filter that adopts a fuzzy logic approach for the enhancement of images corrupted with impulse noise is presented in this paper the filtering method entitled as fuzzy random impulse noise reduction method frinr consists of a fuzzy detection mechanism and a fuzzy filtering method to remove random valued impulse noise from corrupted images based on the criteria of peak signal to noise ratio psnr and subjective evaluations we have found experimentally that the proposed method provides a significant improvement on other state of the art methods

heat kernel coefficients for laplace operators on the spherical suspension in this paper we compute the coefficients of the heat kernel asymptotic expansion for laplace operators acting on scalar functions defined on the so called spherical suspension or riemann cap subjected to dirichlet boundary conditions by utilizing a contour integral representation of the spectral zeta function for the laplacian on the spherical suspension we find its analytic continuation in the complex plane and its associated meromorphic structure thanks to the well known relation between the zeta function and the heat kernel obtainable via mellin transform we compute the coefficients of the asymptotic expansion in arbitrary dimensions the particular case of a d dimensional sphere as the base manifold is studied as well and the first few heat kernel coefficients are given explicitly

on a 50 savings in the computation of the centroid of a symmetrical interval type 2 fuzzy set computing the centroid of a type 2 fuzzy set t2 fs is an important operation for such sets for an interval t2 fs the centroid can be computed by using two iterative procedures that were developed by karnik and mendel 2 in this paper we prove that if the footprint of uncertainty for an interval t2 fs is symmetrical about the primary variable y at y m then the centroid is also symmetrical about y m and its defuzzified value equals m as a consequence of this computation of the centroid for such a t2 fs is reduced by 50 and the importance of obtaining a non symmetrical interval t2 fs prior to defuzzification is demonstrated

designing of a type 2 fuzzy logic filter for improving edge preserving restoration of interlaced to progressive conversion this paper focuses on recently advanced fuzzy models and the application of type 2 fuzzy sets in video deinterlacing the final goal of the proposed deinterlacing algorithm is to exactly determine an unknown pixel value while preserving the edges and details of the image to begin we will discuss some artefacts of spatial temporal and spatio temporal domain deinterlacing methods in order to address the aforementioned issues we adopted type 2 fuzzy sets concepts to design a weight evaluating approach in the proposed method the upper and lower fuzzy membership functions of the type 2 fuzzy logic filters are derived from the type 1 or primary fuzzy membership function the weights from upper and lower membership functions are considered to be multiplied with the candidate deinterlaced pixels experimental results proved that the performance of the proposed method was superior both objectively and subjectively to other different conventional deinterlacing methods moreover the proposed method preserved the smoothness of the original image edges and produced a high quality progressive image

topological indices of the line graph of subdivision graphs and their schur bounds in this paper we investigate topological indices of the line graphs of the tadpole graphs wheel graphs and ladder graphs using the subdivision concept which generalize the results of ranjini et al 2011 in addition we present the schur bound for the general sum connectivity co index

bounds for singular values using traces abstract bounds for the singular values ratios of singular values and rank of a square matrix a involving tr a tr a 2 and tr a h a are presented some of the results are analogous to the well known bounds for the eigenvalues ratios of eigenvalues and rank of a involving tr a and tr a 2

lower bounds for the smallest singular value abstract let a aij be an n n complex matrix suppose that g a the undirected graph of a has no isolated vertex let e be the set of edges of g a we prove that the smallest singular value of a n satisfies n min ij i j e where gij ai aj ai aj 2 ri ci rj cj 1 2 2 with ai aii and ri ci are the ith deleted absolute row sum and column sum of a respectively the result simplifies and improves that of johnson and szulc n mini j ij see 1

a decreasing sequence of eigenvalue localization regions abstract we construct a decreasing sequence of rectangles rp in such a way that all the eigenvalues of a complex matrix a are contained in each rectangle when a is a matrix with real spectrum or a normal matrix each rp can be obtained without knowing the eigenvalues of a

a decreasing sequence of upper bounds for the perron root abstract we obtain a decreasing sequence of upper bounds for the perron root of a nonnegative matrix these upper bounds are new and readily computable for any nonnegative matrix with zero trace the mentioned sequence converges to the perron root we apply these results to the adjacency matrix of a graph

zeta function on surfaces of revolution in this paper we applied the contour integral method for the zeta function associated with a differential operator to the laplacian on a surface of revolution using the wkb expansion we calculated the residues and values of the zeta function at several important points the results agree with those obtained from the heat kernel expansion we also obtained a closed form formula for the determinant of the laplacian on such a surface

locally estimated heterogeneity property and its fuzzy filter application for deinterlacing this paper presents an intra field scanning format conversion method using two filters bilinear filter bf and fuzzy based weighted average filter fwaf the proposed method is intended for black and white images luminance component of yiq color space or each color component of rgb color space we start from the notion that pixels to be interpolated can be classified into two areas based on local variance homogeneous and heterogeneous areas according to the local variance criteria we apply the fwaf to the heterogeneous area and the bf to the homogeneous one producing good visual results our fwaf consists of an intensity similarity filter and a geometric closeness filter the latter is used to populate the heterogeneous area with the missing lines due to its high deinterlacing precision our experimental results show that the proposed approach provides satisfactory performances in terms of both objective metrics and visual image quality we used parameter tuning on our training set to explore the relationship between objective quality and computational complexity we report on how to achieve good performance or the best quality speed tradeoff using the methods researched

heat kernels and functional determinants on the generalized cone we consider zeta functions and heat kernel expansions on the bounded generalized cone in arbitrary dimensions using an improved calculational technique the specific case of a global monopole is analysed in detail and some restrictions thereby placed on thea 5 2 coefficient the computation of functional determinants is also addressed general formulas are given and known results are incidentally and rapidly reproduced

unusual poles of the ζ functions for some regular singular differential operators we consider the resolvent of a system of first order differential operators with a regular singularity admitting a family of self adjoint extensions we find that the asymptotic expansion for the resolvent in the general case presents powers of which depend on the singularity and can take even irrational values the consequences for the pole structure of the corresponding and functions are also discussed

zeta function of self adjoint operators on surfaces of revolution in this article we analyze the zeta function for the laplace operator on a surface of revolution a variety of boundary conditions separated and unseparated are considered formulas for several residues and values of the zeta function as well as for the determinant of the laplacian are obtained the analysis is based upon contour integration techniques in combination with a wkb analysis of solutions of related initial value problems

an efficient centroid type reduction strategy for general type 2 fuzzy logic system in this paper an efficient centroid type reduction strategy for general type 2 fuzzy set is introduced this strategy makes use of the result of a plane representation and performs the centroid type reduction on each a plane simulations show that it usually needs only several resolution of a value such that the defuzzified value converges to a real value consequently comparing with the exhaustive computation approach this approach can tremendously decrease the computation complexity from exponential into linear

experimental study of intelligent controllers under uncertainty using type 1 and type 2 fuzzy logic uncertainty is an inherent part in control systems used in real world applications the use of new methods for handling incomplete information is of fundamental importance type 1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems type 2 fuzzy sets that are used in type 2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom this paper deals with the design of control systems using type 2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements environmental noise etc the experimental results are divided in two classes in the first class simulations of a feedback control system for a non linear plant using type 1 and type 2 fuzzy logic controllers are presented a comparative analysis of the systems response in both cases was performed with and without the presence of uncertainty for the second class a non linear identification problem for time series prediction is presented based on the experimental results the conclusion is that the best results are obtained using type 2 fuzzy systems

zeta function determinant of the laplace operator on the d dimensional ball we present a direct approach for the calculation of functional determinants of the laplace operator on balls dirichlet and robin boundary conditions are considered using this approach formulas for any value of the dimension d of the ball can be obtained quite easily explicit results are presented here for dimensionsd 2 3 4 5 and 6

design of interval type 2 fuzzy sliding mode controller in this paper an interval type 2 fuzzy sliding mode controller it2fsmc is proposed for linear and nonlinear systems the proposed it2fsmc is a combination of the interval type 2 fuzzy logic control it2flc and the sliding mode control smc which inherits the benefits of these two methods the objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed loop system the lyapunov stability method is adopted to verify the stability of the interval type 2 fuzzy sliding mode controller system the design procedure of the it2fsmc is explored in detail a typical second order linear interval system with 50 parameter variations an inverted pendulum with variation of pole characteristics and a duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method the simulation results show that the it2fsmc achieves the best tracking performance in comparison with the type 1 fuzzy logic controller t1flc the it2flc and the type 1 fuzzy sliding mode controller t1fsmc

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

matricial inner products and pointed cones of hermitian preserving linear transformations abstract let be a conjugate homogeneous reflector on a vector space v over r or c with p a pointed cone contained in spec v a mapping on v v whose range is contained in p which generalizes the usual inner product properties is called a vectorial inner product a certain family of these vectorial inner products on matrices which we call matricial inner products is used to generate a set of pointed cones in the ambient space of hermitian preserving linear transformations some basic results on these cones including psd psd and c p and on the partial orders that they induce are given

characterizations and lower bounds for the spread of a normal matrix abstract the spread of an n n matrix a with eigenvalues 1 n is defined by spr a max j k j k we prove that if a is normal then spr a max x ax y ay x y c n x y 1 max x ay y ax x y c n x y 1 re x y 0 max x ay y ax x y c n x y 1 x y 0 max spr z a z a 2 z c z 1 2 max x a 2 x x ax 2 x a ax x ax 2 1 2 x c n x 1 we also present several lower bounds for spr a given by these characterizations

a fuzzy edge dependent motion adaptive algorithm for de interlacing de interlacing algorithms are required to convert interlaced video into progressive scan format they perform an interpolation technique which doubles the vertical sampling density this paper presents a de interlacing algorithm which employs fuzzy logic to adapt the interpolation strategy to the presence of motion and edges extensive simulations of video sequences prove the advantages of this novel approach

neuro fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets abstract this paper presents the results of using type 2 fuzzy sets to assist in the pre processing of data for use with neuro fuzzy clustering for classification of sports injuries in the lower leg this research is concerned with the analysis of bone scans from stress related injuries to the tibia of particular interest is whether neural network based clustering techniques can help the consultant in classifying the images the work was motivated by the situation where there is a relatively small amount of relevant data and difficulties are faced by consultants in classifying the various types of injuries for this particular problem the consultant s interpretation of the image lends itself to representation using type 2 fuzzy sets this research sets out to address whether with fuzzy neuro clustering techniques some insights may be provided to the consultant that they can use along with their experience and knowledge the results of this approach indicate that the use of neural clustering using a type 2 representation can improve the classification of shin images

fuzzy relation equations for coding decoding processes of images and videos we adopt fuzzy relation equations with continuous triangular norms for compression decompression processes of grey images colour images in the rgb space and frames of videos by comparing the results of the reconstructed images with standard methods like jpeg and mpeg 4 any image is subdivided in blocks and each block is coded decoded using arbitrary fuzzy sets as coders in the fuzzy equations we evaluate the peak signal to noise ratio psnr on the decompressed images for several values of the compression rates as measure of the quality of images and frames reconstructed the original frames of a video are classified in intra frames and predictive frames by using a similarity measure based on the well known lukasiewicz t norm

hybrid learning mechanism for interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems a proposed learning methodology based on a hybrid mechanism for training interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems uses a recursive square root filter to tune the type 1 consequent parameters and the steepest descent method to tune the interval type 2 antecedent parameters the proposed hybrid learning algorithm changes the interval type 2 model parameters adaptively to minimize some criterion function as new information becomes available and to match desired input output data pairs its antecedent sets are type 2 fuzzy sets its consequent sets are type 1 fuzzy sets and its inputs are interval type 2 non singleton fuzzy numbers with uncertain standard deviations as reported in the literature the performance indices of hybrid models have proved to be better than those of the individual training mechanisms used alone comparison with non hybrid interval a2 c1 type 2 takagi sugeno kang fuzzy logic systems and with non hybrid a1 c0 type 1 takagi sugeno kang fuzzy logic systems shows that the proposed hybrid mechanism is a well performing non linear adaptive method that enables the interval type 2 fuzzy model to match an unknown non linear mapping and to converge very fast experiments were carried out involving the application of the hybrid interval a2 c1 type 2 non singleton type 2 takagi sugeno kang fuzzy logic systems for modeling and prediction of the scale breaker entry temperature in a hot strip mill for three different types of coils the results demonstrate how the interval type 2 fuzzy system learns from selected input output data pairs and improves its performance as hybrid training progresses

on the uniform asymptotic expansion of the legendre functions a uniform expansion of the legendre functions of large indices is considered by using the wkb approach we obtain the recurrent formula for the coefficients of uniform expansion and compare them with the uniform expansion of the bessel function

zeta determinant for laplace operators on riemann caps the goal of this paper is to compute the zeta function determinant for the massive laplacian on riemann caps or spherical suspensions these manifolds are defined as compact and boundaryless d dimensional manifolds deformed by a singular riemannian structure the deformed spheres considered previously in the literature belong to this class after presenting the geometry and discussing the spectrum of the laplacian we illustrate a method to compute its zeta regularized determinant the special case of the deformed sphere is recovered as a limit of our general formulas

applications of type 2 fuzzy logic systems to forecasting of time series abstract in this paper we begin with a type 1 fuzzy logic system fls trained with noisy data we then demonstrate how information about the noise in the training data can be incorporated into a type 2 fls which can be used to obtain bounds within which the true noisefree output is likely to lie we do this with the example of a one step predictor for the mackey glass chaotic time series m c mackey l glass oscillation and chaos in physiological control systems science 197 1977 287 280 we also demonstrate how a type 2 fls can be used to obtain better predictions than those obtained with a type 1 fls

new results about the centroid of an interval type 2 fuzzy set including the centroid of a fuzzy granule the centroid of an interval type 2 fuzzy set it2 fs provides a measure of the uncertainty of such a fs its calculation is very widely used in interval type 2 fuzzy logic systems in this paper we present properties about the centroid of an it2 fs we also illustrate many of the general results for a t2 fuzzy granule fg in order to develop some understanding about the uncertainty of the fg in terms of its vertical and horizontal dimensions at present the t2 fg is the only it2 fs for which it is possible to obtain closed form formulas for the centroid and those formulas are in this paper

upper bounds for singular values abstract let a be an n n matrix with singular values 1 n if 1 r n then r min h s r h where sr is the set of n n matrices h such that rank a h r 1 and denotes the spectral norm i e the largest singular value we find upper bounds for r by choosing h suitably

normalized frobenius condition number of the orthogonal projections of the identity abstract this paper deals with the orthogonal projection in the frobenius sense a n of the identity matrix i onto the matrix subspace a s a r n n s being an arbitrary subspace of r n n lower and upper bounds on the normalized frobenius condition number of matrix a n are given furthermore for every matrix subspace s r n n a new index f a s which generalizes the normalized frobenius condition number of matrix a is defined and analyzed

inequalities for the numerical radius the norm and the maximum of the real part of bounded linear operators in hilbert spaces some inequalities for the numerical radius the operator norm and the maximum of the real part of bounded linear operators in hilbert spaces under suitable assumptions for the involved operator are given

bounds for ratios of eigenvalues using traces abstract let a be an n n matrix with real eigenvalues 1 n and let 1 k l n bounds involving tr a and tr a 2 are introduced for k l k l k l and k k n l 1 l 2 k 2 k n l 1 2 l also included are conditions for l 0 and for k l 0

bounds for the spectral radius and the largest singular value abstract we derive an increasing sequence of lower bounds for the spectral radius of a matrix with real spectrum and progressively improved bounds for the largest singular value of a complex matrix we also find estimates for the rank of normal matrices with real spectrum and for the rank of normal nonnegative matrices including some sufficient condition for such matrices to be invertible

lower bounds for the numerical radius abstract let a be a complex n n matrix we find lower bounds for its numerical radius r a max x ax x c n x x 1 first we choose x satisfying x x 1 and compute x ax we also improve the simple bound so obtained second we apply r a max z a z a 2 z c z 1 where denotes the largest eigenvalue