new bounds for the first inequality of ostrowski gruss type and applications abstract some new bounds for the first inequality of ostrowski gruss type are derived these new bounds can be much better than some recently obtained bounds applications in numerical integration are also given

computing nonnegative rank factorizations abstract the existence of nonnegative generalized inverses in terms of nonnegative rank factorizations is considered an algorithm is presented which computes a nonnegative rank factorization of a nonnegative matrix when a nonnegative 1 inverse exists

what tasks can be performed with an uncalibrated stereo vision system this article studies the following question when is it possible to decide on the basis of images of point features observed by an imprecisely modeled two camera stereo vision system whether or not a prescribed robot positioning task has been precisely accomplished results are shown for three camera model classes injective cameras weakly calibrated projective cameras and uncalibrated projective cameras in particular given a weakly calibrated stereo pair it is shown that a positioning task can be precisely accomplished if and only if the task specification is invariant to projective transformations it is shown that injective and uncalibrated projective cameras can accomplish fewer tasks but are still able to accomplish tasks involving point coincidences the same formal framework is applied to the problem of determining the set of tasks which can be precisely accomplished with the well known position based control architecture it is shown that for any class of camera models the set of tasks which can be precisely accomplished using a position based control architecture is a subset of the complete set of tasks which can be decided on the set but includes all positioning tasks based on point coincidences two ways of extending the idea of position based control to accomplish more tasks are also presented

self calibration from one circular motion sequence and two images this paper describes a new method for self calibration of camera with constant internal parameters under circular motion using one sequence and two images captured with different camera orientations unlike the previous method in which three circular motion sequences are needed with known motion the new method computes the rotation angles and the projective reconstructions of the sequence and the images with circular constraint enforced which is called a circular projective reconstruction using a factorization based method it is then shown that the images of the circular points of each circular projective reconstruction can be readily obtained subsequently the image of the absolute conic and the calibration matrix of the camera can be determined experiments on both synthetic and real image sequence are given showing the accuracy and robustness of the new algorithm

on sharp inequalities of simpson type and ostrowski type in two independent variables in this paper two sharp inequalities are derived the first is a sharp simpson inequality and the second is a sharp inequality of ostrowski type in two independent variables

self calibration under the cayley framework the cayley framework here is meant to tackle the vision problems under the infinite cayley transformation ict its main advantage lies in its numerical stability in this work the stratified self calibration under the cayley framework is investigated it is well known that the main difficulty of the stratified self calibration in multiple view geometry is to upgrade a projective reconstruction to an affine one in other words to estimate the unknown 3 vector of the plane at infinity called the normal vector to our knowledge without any prior knowledge about the scene or the camera motion the only available constraint on a moving camera with constant intrinsic parameters is the well known modulus constraint in the literature do other kinds of constraints exist if yes what they are how could they be used in this work such questions will be systematically investigated under the cayley framework our key contributions include 1 the original projective expression of the ict is simplified and a new projective expression is derived to make the upgrade easier from a projective reconstruction to a metric reconstruction 2 the constraints on the normal vector are systematically investigated for two views two constraints on the normal vector are derived one of them is the well known modulus constraint while the other is a new inequality constraint there are only these two constraints for two views for three views besides the constraints for two views two groups of new constraints are derived and each of them contains three constraints in other words there are 12 constraints in total for three views 3 based on our projective expression and these constraints a stratified cayley algorithm and a total cayley algorithm are proposed for the metric reconstruction from images it is experimentally shown that they both improve significantly the numerical stability of the classical algorithms compared with the global optimal algorithm under the infinite homography framework the cayley algorithms have comparable calibration accuracy but substantially reduce the computational load

a geometric treatment of generalized inverses and semigroups of nonnegative matrices abstract the purpose of this paper is to provide a unified treatment from the geometric viewpoint of the following closely related aspects of nonnegative matrices nonnegative matrices with nonnegative generalized inverses of various kinds nonnegative rank factorization regular elements green s relations and maximal subgroups of the semigroups of nonnegative matrices stochastic matrices column stochastic matrices and doubly stochastic matrices

on the optimal constants of ostrowski like inequalities involving n knots we compute the optimal constants of ostrowski like inequalities involving n knots given by huy and ngo

modulus of continuity of the canonic brownian motion on the group of diffeomorphisms of the circle abstract an explicit modulus of holder continuity is given for the flow associated to the canonic brownian motion on the diffeomorphism group of the circle

ray saliency bottom up visual saliency for a rotating and zooming camera we extend the classical notion of computational visual saliency to multi image data collected using a stationary pan tilt zoom ptz camera by introducing the concept of consistency the requirement that the set of generated saliency maps should each assign the same saliency value to unique regions of the environment that appear in more than one image we show that processing each image independently will often fail to provide a consistent measure of saliency and that using an image mosaic to quantify saliency suffers from several drawbacks we then propose ray saliency and an immediate extension approximate ray saliency a mosaic free method for calculating a consistent measure of bottom up saliency experimental results demonstrating the effectiveness of the proposed approach are presented

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

a reverse hadamard inequality abstract let u be an n n unitary matrix with determinant equal to 1 let a be an n n real matrix with rank a 2 and entries satisfying aij 1 for 1 i j n then it follows that det a u 1 this reversal of the hadamard inequality can be obtained easily from an old result of fiedler in this article we present a different proof of this fact and discuss its ramifications

self calibration of stationary cameras a new practical method is given for the self calibration of a camera in this method at least three images are taken from the same point in space with different orientations of the camera and calibration is computed from an analysis of point matches between the images the method requires no knowledge of the orientations of the camera calibration is based on the image correspondences only this method differs fundamentally from previous results by maybank and faugeras on self calibration using the epipolar structure of image pairs in the method of this paper there is no epipolar structure since all images are taken from the same point in space and so maybank and faugeras s method does not apply since the images are all taken from the same point in space determination of point matches is considerably easier than for images taken with a moving camera since problems of occlusion or change of aspect or illumination do not occur a non iterative calibration algorithm is given that works with any number of images an iterative refinement method that may be used with noisy data is also described the algorithm is implemented and validated on several sets of synthetic and real image data

the nonnegative rank factorizations of nonnegative matrices abstract let a p m n r the set of all m n nonnegative matrices having the same rank r for matrices a in p m n n we introduce the concepts of a has only trivial nonnegative rank factorizations and a can have nontrivial nonnegative rank factorizations correspondingly the set p m n n is divided into two disjoint subsets p 1 and p 2 such that p 1 p 2 p m n n it happens that the concept of a has only trivial nonnegative rank factorizations is a generalization of a is prime in p n n n we characterize the sets p 1 and p 2 some of our results generalize some theorems in the paper of daniel j richman and hans schneider 9

an iterative method for solving nonlinear equations an iterative method for finding a solution of the equation f x 0 is presented the method is based on some specially derived quadrature rules it is shown that the method can give better results than the newton method

a note on some ostrowski like type inequalities abstract error estimate plays an important role for numerical integration some ostrowski like type inequalities concerning a new type of quadrature formula are established recently by huy and ngo 2009 2010 6 7 in this note improvement and extension to these inequalities are given

improvement of some inequalities of euler gruss type abstract we prove an inequality of gruss type and use it to improve strictly some general euler gruss type inequalities all improved inequalities are sharp

new bounds for moments of continuous random variables in this paper some gruss and ostrowski gruss type inequalities are applied to estimate the moments of continuous random variables whose probability density function is in l p space some results of kumar are generalized p kumar inequalities involving moments of a continuous random variable defined over a finite interval comput math appl 48 2004 257 273 p kumar the ostrowski type moment integral inequalities and moment bounds for continuous random variables comput math appl 49 2005 1929 1940

generalized gronwall bellman type delay dynamic inequalities on time scales and their applications abstract in this paper we establish some new gronwall bellman type delay dynamic inequalities on time scales which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales our results generalize the main results of ou iang l ou iang the boundedness of solutions of linear differential equations y a t y 0 shuxue jinzhan 3 1957 409 415 jiang f c jiang f w meng explicit bounds on some new nonlinear integral inequality with delay j comput appl math 205 2007 479 486 and yuan z l yuan x w yuan f w meng some new delay integral inequalities and their applications appl math comput 208 2009 231 237

remarks on ostrowski like inequalities abstract we show the error inequalities on quadrature formulas obtained by huy and ngo can be improved if m is even

a probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix the perspective projections of n physical points on two views stereovision are constrained as soon as n 8 however to prove in practice the existence of a rigid motion between two images more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches in this paper we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points n and the accuracy of the matches this criterion yields an objective way to compare say precise matches of a few points and approximate matches of a lot of points it gives a yes no answer to the question could this rigid points correspondence have occurred by chance since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired it also yields absolute accuracy requirements for rigidity detection in the case of non matched points and optimal values of n depending on the expected accuracy of the matches and on the proportion of outliers we use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90 of outliers which outperforms the best currently known methods like m estimators lmeds classical ransac and tensor voting

general euler ostrowski formulae and applications to quadratures the aim of this paper is to generalize inequality f x 1 b a ab f s1 ds1 f b f a b a x a b 2 f b f a 2 b a x2 a b x a2 b2 4ab 6 f b a 3 6i x a b a obtained in a aglic aljinovic m matic j pecaric improvements of some ostrowski type inequalities j comput anal appl in press and therefore obtain a generalization and improvement of inequality f x 1 b a ab f s1 ds1 f b f a b a x a b 2 f b f a 2 b a x2 a b x a2 b2 4ab 6 f a x b a 3 obtained in g a anastassiou univariate ostrowski inequalities revisited monatsh math 135 2002 175 189 to do this first we derive general euler ostrowski formulae which generalize extended euler formulae obtained in lj dedic m matic j pecaric on generalizations of ostrowski inequality via some euler type identities math inequal appl 3 3 2000 337 353 the main novelty is that a remainder is expressed in terms of bn x mt which enables us to obtain a vide variety of quadrature formulae such as trapezoid midpoint bitrapezoid twopoint formulae and their multipoint generalizations

improvement of some ostrowski gruss type inequalities abstract in this paper we improve and further generalize some ostrowski gruss type inequalities involving bounded once and twice differentiable mappings

non negative matrix factorization revisited uniqueness and algorithm for symmetric decomposition non negative matrix factorization nmf has found numerous applications due to its ability to provide interpretable decompositions perhaps surprisingly existing results regarding its uniqueness properties are rather limited and there is much room for improvement in terms of algorithms as well uniqueness aspects of nmf are revisited here from a geometrical point of view both symmetric and asymmetric nmf are considered the former being tantamount to element wise non negative square root factorization of positive semidefinite matrices new uniqueness results are derived e g it is shown that a sufficient condition for uniqueness is that the conic hull of the latent factors is a superset of a particular second order cone checking this condition is shown to be np complete yet this and other results offer insights on the role of latent sparsity in this context on the computational side a new algorithm for symmetric nmf is proposed which is very different from existing ones it alternates between procrustes rotation and projection onto the non negative orthant to find a non negative matrix close to the span of the dominant subspace simulation results show promising performance with respect to the state of art finally the new algorithm is applied to a clustering problem for co authorship data yielding meaningful and interpretable results

a representation of the peano kernel for some quadrature rules and applications a general interpolating formula is established from this formula all newton cotes quadrature rules of the closed type can be derived some corrected interpolating polynomials are also derived and used for obtaining corresponding quadrature rules a new effective representation of the peano kernel is derived estimation of errors for these quadrature rules is established

some generalized ostrowski gruss type integral inequalities in this paper we establish some new ostrowski gruss type integral inequalities involving k 1 interior points in 1d case which are generalizations of some known results in the literature and one of which is sharp then we deduce an ostrowski gruss type integral inequality in 2d case involving k 1 2 interior points for the first time we also present one application on the estimate of error bound for numerical integration formula in which a sharp error bound for a new numerical integration formula is provided by the results established

some ostrowski gruss type inequalities and applications new generalizations of ostrowski gruss type inequalities for functions of lipschitzian type are established applications for cumulative distribution functions are given

computing symmetric nonnegative rank factorizations an algorithm is described for the nonnegative rank factorization nrf of some completely positive cp matrices whose rank is equal to their cp rank the algorithm can compute the symmetric nrf of any nonnegative symmetric rank r matrix that contains a diagonal principal submatrix of that rank and size with leading cost o rm2 operations in the dense case the algorithm is based on geometric considerations and is easy to implement the implications for matrix graphs are also discussed

a note to inequalities of euler gruss type following the main ideas of wang 1 we generalize matie s results and establish our inequalities for functions with n t h derivatives of bounded p variation all of our error bounds are sharp in the sense that they cannot be replaced by smaller ones

a new inequality of ostrowski gruss type and applications to some numerical quadrature rules in this paper we derive some gruss and ostrowski gruss type inequalities for functions in l p spaces as applications we provide some new estimates for the error in some numerical integration rules in particular we deal with the mid point and trapezoid quadrature rules

spherical mosaics with quaternions and dense correlation we describe an algorithm for generating spherical mosaics from a collection of images acquired from a common optical center the algorithm takes as input an arbitrary number of partially overlapping images an adjacency map relating the images initial estimates of the rotations relating each image to a specified base image and approximate internal calibration information for the camera the algorithm s output is a rotation relating each image to the base image and revised estimates of the camera s internal parameters our algorithm is novel in the following respects first it requires no user input our image capture instrumentation provides both an adjacency map for the mosaic and an initial rotation estimate for each image second it optimizes an objective function based on a global correlation of overlapping image regions third our representation of rotations significantly increases the accuracy of the optimization finally our representation and use of adjacency information guarantees globally consistent rotation estimates the algorithm has proved effective on a collection of nearly four thousand images acquired from more than eighty distinct optical centers the experimental results demonstrate that the described global optimization strategy is superior to non global aggregation of pair wise correlation terms and that it successfully generates high quality mosaics despite significant error in initial rotation estimates

using geometric constraints through parallelepipeds for calibration and 3d modeling this paper concerns the incorporation of geometric information in camera calibration and 3d modeling using geometric constraints enables more stable results and allows us to perform tasks with fewer images our approach is motivated and developed within a framework of semi automatic 3d modeling where the user defines geometric primitives and constraints between them in this paper first a duality that exists between the shape parameters of a parallelepiped and the intrinsic parameters of a camera is described then a factorization based algorithm exploiting this relation is developed using images of parallelepipeds it allows us to simultaneously calibrate cameras recover shapes of parallelepipeds and estimate the relative pose of all entities besides geometric constraints expressed via parallelepipeds our approach simultaneously takes into account the usual self calibration constraints on cameras the proposed algorithm is completed by a study of the singular cases of the calibration method a complete method for the reconstruction of scene primitives that are not modeled by parallelepipeds is also briefly described the proposed methods are validated by various experiments with real and simulated data for single view as well as multiview cases

cayley transformation and numerical stability of calibration equation the application of cayley transformation to enhance the numerical stability of camera calibration is investigated first a new calibration equation called the standard calibration equation is introduced using the cayley transformation and its analytical solution is obtained the standard calibration equation is equivalent to the classical calibration equation but it exhibits remarkable better numerical stability second a one parameter calibration family called the cayley calibration family which is equivalent to the standard calibration equation is obtained using also the cayley transformation and it is found that this family is composed of those infinite homographies whose rotation has the same axis with the rotation between the two given views the condition number of equations in the cayley calibration family varies with the parameter value and an algorithm to determine the best parameter value is provided third the generalized cayley calibration families equivalent to the standard calibration equation are also introduced via generalized cayley transformations an example of the generalized cayley transformations is illustrated called the s cayley calibration family as in the cayley calibration family the numerical stability of equations in a generalized cayley calibration family also depends on the parameter value in addition a more generic calibration family is also proposed and it is proved that the standard calibration equation the cayley calibration family and the s cayley calibration family are all some special cases of this generic calibration family

sharp inequalities of simpson type and ostrowski type two sharp inequalities are derived the first is a sharp simpson s inequality and the second is a sharp inequality of ostrowski type the mentioned inequalities give error bounds for some known quadrature rules these results enlarge applicability email protected the corresponding quadrature rules with respect to the obtained error bounds applications in numerical integration are also given

some remarks on a conjecture of boyle and handelman abstract boyle and handelman have conjectured that whenever a is an n n nonnegative matrix with rank a r and perron root 1 the inequality det i ta n r r 1r holds for all real numbers satisfying 1 we introduce an analogous conjecture involving nonnegative central class functions on the permutation group sn the analogue of the rank condition in this context is a condition on the support of the nonabelian fourier transform of the central function we are able to establish that both conjectures are true in case 2r n

a new ostrowski gruss inequality involving 3n knots abstract this is the fifth and last in our series of notes concerning some classical inequalities such as the ostrowski simpson iyengar and ostrowski gruss inequalities in r in the last note we propose an improvement of the ostrowski gruss inequality which involves 3 n knots where n 1 is an arbitrary numbers more precisely suppose that x k k 1 n 0 1 y k k 1 n 0 1 and k k 1 n 0 n are arbitrary sequences with k 1 n k n and k 1 n k x k n 2 the main result of the present paper is to estimate 1 n k 1 n k f a b a y k 1 b a a b f t d t f b f a n k 1 n k y k x k in terms of either f or f unlike the standard ostrowski gruss inequality and its known variants which basically estimate f x a b f t d t b a in terms of a correction term as a linear polynomial of x and some derivatives of f our estimate allows us to freely replace f x and the correction term by using 3 n knots x k k 1 n y k k 1 n and k k 1 n as far as we know this is the first result involving the ostrowski gruss inequality with three sequences of parameters

on some generalizations of an ostrowski gruss type integral inequality in this paper we improve and extend a new ostrowski gruss type integral inequality obtained recently by feng and meng 2012 26 to be precise we show that a condition imposed on the inequality can be removed furthermore we provide a two dimensional generalization of this ostrowski gruss type inequality which is sharp

a generalization of the corrected midpoint trapezoid rule and error bounds a generalization of the corrected midpoint trapezoid rule is derived various error bounds for this generalization are established

bounds for the chebyshev functional and applications to the weighted integral formulae the aim of this paper is to provide some error estimates for the general weighted n point quadrature formulae by using some inequalities for the chebyshev functional the above results are applied to obtain some new bounds for the gauss chebyshev formulae of the first and the second kind

weighted quadrature rules via gruss type inequalities for weighted lp spaces new estimates of gruss type for weighted ebysev functional in weighted lp spaces are presented by using the sonin s identity these results are applied to obtain new ostrowski type inequalities and further to weighted numerical rules for functions whose derivative belongs to weighted lp spaces

the nmf problem and lattice subspaces abstract suppose that a is a nonnegative n m real matrix the nmf problem is the determination of two nonnegative real matrices f v so that a f v with intermediate dimension p smaller than m i n n m in this article we present a general method for the determination of two nonnegative real factors f v of a based on the theory of lattice subspaces and positive bases

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

motion of points and lines in the uncalibrated case in the present paper we address the problem of computing structure and motion given a set point and or line correspondences in a monocular image sequence when the camera is not calibrated

an ostrowski gruss type inequality on time scales we derive a new inequality of ostrowski gruss type on time scales by using the gruss inequality on time scales and thus unify corresponding continuous and discrete versions we also apply our result to the quantum calculus case

some integral inequalities for functions with n 1 st derivatives of bounded variation in this paper we generalize cerone s results and a unified treatment of error estimates for a general inequality satisfying f n 1 being of bounded variation is presented we derive the estimates for the remainder terms of the mid point trapezoid and simpson formulas all constants of the errors are sharp applications in numerical integration are also given

a nonconvex splitting method for symmetric nonnegative matrix factorization convergence analysis and optimality symmetric nonnegative matrix factorization symnmf has important applications in data analytics problems such as document clustering community detection and image segmentation in this paper we propose a novel nonconvex variable splitting method for solving symnmf the proposed algorithm is guaranteed to converge to the set of karush kuhn tucker kkt points of the nonconvex symnmf problem furthermore it achieves a global sublinear convergence rate we also show that the algorithm can be efficiently implemented in parallel further sufficient conditions are provided that guarantee the global and local optimality of the obtained solutions extensive numerical results performed on both synthetic and real datasets suggest that the proposed algorithm converges quickly to a local minimum solution

improvement and further generalization of inequalities of ostrowski gruss type abstract we improve some inequalities of ostrowski gruss type and further generalize them we apply the obtained results to the estimation of error bounds for some numerical quadrature rules also some bounds for the differences of some special means are discussed

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

a unified approach to some inequalities of ostrowski gruss type based on the euler maclaurin formula in the spirit of 1 we provide a unified approach to some inequalities of ostrowski gruss type which include some existing results as special cases some illustrative examples are also included

a method for solving nonlinear equations a method for finding a solution of the equation f x 0 is presented the method is based on some specially derived quadrature rules it is shown that the method can give better results than the newton method

a new way to think about ostrowski like type inequalities in this present paper by considering some known inequalities of ostrowski like type we propose a new way to treat a class of ostrowski like type inequalities involving n points and m th derivative to be precise the following inequality email protected a bf x email protected i 1nf a x i b a 2m 54 b a m 1 m 1 s s holds where email protected sup a x bf m x email protected inf a x bf m x and for suitable x 1 x 2 x n it is worth noticing that n m are arbitrary numbers this means that the estimate in is more accurate when m is large enough our approach is also elementary

the ostrowski s integral inequality for lipschitzian mappings and applications abstract a generalization of ostrowski s inequality for lipschitzian mappings and applications in numerical analysis and for euler s beta function are given

stereo calibration from rigid motions we describe a method for calibrating a stereo pair of cameras using general or planar motions the method consists of upgrading a 3d projective representation to affine and to euclidean without any knowledge neither about the motion parameters nor about the 3d layout we investigate the algebraic properties relating projective representation to the plane at infinity and to the intrinsic camera parameters when the camera pair is considered as a moving rigid body we show that all the computations can be carried out using standard linear resolutions techniques an error analysis reveals the relative importance of the various steps of the calibration process projective to affine and affine to metric upgrades extensive experiments performed with calibrated and natural data confirm the error analysis as well as the sensitivity study performed with simulated data

on euler trapezoid formulae modified versions of the euler trapezoid formula for functions whose derivatives are either functions of bounded variation or lipschitzian functions or functions in l p spaces are given the results are applied to quadrature formulae

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities

on the nonnegative rank of euclidean distance matrices abstract the euclidean distance matrix for n distinct points in r r is generically of rank r 2 it is shown in this paper via a geometric argument that its nonnegative rank for the case r 1 is generically n

a sharp estimate for the peano error representation we provide a sharp estimate of the peano error representation formula for linear functionals as applications we obtain sharp estimates for the remainder term in general quadrature formulae and expand some ostrowski like type inequalities to linear functionals the new approach extends and unifies many earlier results on the subject dragomir and wang 1997 cheng 2001 matic 2003 vong 2011 gonska et al 2012