the units of a ring spectrum and a logarithmic cohomology operation recall that if r is a commutative ring then the set r r of invertible elements of r is naturally an abelian group under multiplication this construction is a functor from commutative rings to abelian groups in general there is no obvious relation between the additive group of a ring r and the multiplicative group of units r however under certain circumstances one can define a homomorphism from a subgroup of r to a suitable completion of r e g the natural logarithm q 0 r or the p adic logarithm 1 pzp zp the logarithmic cohomology operation is a homotopy theoretic analogue of the above where r is a commutative s algebra and completion is bousfield localization with respect to a morava k theory the purpose of this paper is to give a formula for the logarithmic operation in certain contexts in terms of power operations before giving our results we briefly explain some of the concepts involved

invariant character recognition with zernike and orthogonal fourier mellin moments abstract in this paper we consider the use of orthogonal moments for invariant classification of alphanumeric characters of different size in addition to the zernike and pseudo zernike moments zms and pzms which have been previously proposed for invariant character recognition a new method of combining orthogonal fourier mellin moments ofmms with centroid bounding circle scaling is introduced which is shown to be useful in characterizing images with large variability through extensive experimentation using zms and ofmms as features different scaling methodologies and classifiers it is shown that ofmms give the best overall performance in terms of both image reconstruction and classification accuracy

adams filtration and generalized hurewicz maps for infinite loopspaces we study the hurewicz map begin aligned h pi x rightarrow r omega infty x end aligned where omega infty x is the 0th space of a spectrum x and r is the generalized homology theory associated to a connective commutative s algebra r we prove that the decreasing filtration of the domain associated to an r based adams resolution is compatible with a filtration of the range associated to the augmentation ideal filtration of the augmented commutative s algebra sigma infty omega infty x the proof of our main theorem makes much use of composition properties of this filtration and its interaction with topological andre quillen homology an application is a connectivity theorem localize away from p 1 and suppose x is c 1 connected with c 0 if alpha in pi x has adams filtration s and alpha cp s then h alpha 0 in r omega infty x when specialized to mod p homology this implies a finiteness theorem if h x mathbb z p is finitely presented as a module over the steenrod algebra then the image of the hurewicz map in h omega infty x mathbb z p is finite we illustrate these theorems with calculations of the mod 2 hurewicz image of bo its connected covers and omega infty tmf and the mod p hurewicz image of all the spaces in the bp and bp langle n rangle spectra en route we get new proofs of theorems of milnor and wilson in the special case when x is the suspension spectrum of a space z and r h mathbb z 2 we recover results announced by lannes and zarati in the 1980s relating the adams filtration of pi s z to dyer lashof length in h qz mathbb z 2 and generalize them to all primes p for any x we also get parallel results for the hurewicz map for morava e theory where pi x is now given the adams novikov filtration

multichannel interpolation of nonuniform samples with application to image recovery abstract the multichannel trigonometric reconstruction from uniform samples was proposed recently it not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according to the types and amounts of the collected samples the paper presents the theory of multichannel interpolation from nonuniform samples two distinct models of nonuniform sampling patterns are considered namely recurrent and generic nonuniform sampling each model involves two types of samples nonuniform samples of the observed signal and its derivatives numerical examples and quantitative error analysis are provided to demonstrate the effectiveness of the proposed algorithms additionally the proposed algorithms for recovering highly corrupted images are also investigated in comparison with the median filter and the shepard interpolation the proposed algorithms produce superior results with lower errors

hkr characters p divisible groups and the generalized chern character in this paper we describe the generalized chern character of classifying spaces of finite groups in terms of hopkins kuhn ravenel generalized group characters for this purpose we study the p divisible group and its level structures associated with the k n localization of the n 1 st morava e theory

general servomechanism problems for distributed parameter systems abstract this paper investigates a general servomechanism problem for distributed parameter systems the systems are described by linear differential equations in a banach space applicable to both parabolic and hyperbolic equations a feedback control law is determined in order to stabilize the resultant controlled system exponentially or strongly and regulate output to reference outputs asymptotically in spite of un measurable arbitrary disturbances it is noted that the disturbances and the reference outputs treated here both belong to general classes

computation of transmission zeros for distributed parameter systems the transmission zeros for a class of distributed parameter systems are defined as the limit points of the spectrum as the feedback gain increases to infinity a simple criterion which characterizes the transmission zeros different from the system operators spectrum is found the case when the transmission zeros belong to the spectrum is also discussed the presented theory is clarified with an example

distributed feedback design for systems governed by the wave equation this article deals with the geometric control of a one dimensional non autonomous linear wave equation the idea consists in reducing the wave equation to a set of first order linear hyperbolic equations then based on geometric control concepts a distributed control law that enforces the exponential stability and output tracking in the closed loop system is designed the presented control approach is applied to obtain a distributed control law that brings a stretched uniform string modelled by a wave equation with dirichlet boundary conditions to rest in infinite time by considering the displacement of the middle point of the string as the controlled output the controller performances have been evaluated in simulation by considering both tracking and disturbance rejection problems the robustness of the controller has also been studied when the string tension is subjected to sudden variations

generalized artin and brauer induction for compact lie groups let g be a compact lie group we present two induction theorems for certain generalized g equivariant cohomology theories the theory applies to g equivariant k theory k g and to the borel cohomology associated with any complex oriented cohomology theory the coefficient ring of k g is the representation ring r g of g when g is a finite group the induction theorems for k g coincide with the classical artin and brauer induction theorems for r g

image analysis by circularly semi orthogonal moments various types of circularly orthogonal moments have been widely used for image reconstruction and rotation invariant classification however they suffer from two errors namely numerical integration error and geometric error which affect their reconstruction capability and pattern recognition accuracy in this paper a novel category of circular moments named circularly semi orthogonal moments is proposed in the proposed moment a set of orthogonal basis functions modulated by a negative power exponential envelope is utilized as the radial basis function for a given degree n the radial basis function possesses more compact bandwidth less cutoff frequency and more zeros compared with the frequently used circularly orthogonal moments including zernike and orthogonal fourier mellin moments and so the circularly semi orthogonal moment calculated with the zeroth order approximation is more robust to numerical error than the frequently used circularly orthogonal moments furthermore the capability of the semi orthogonal moment to describe high spatial frequency components of images is relatively higher than that of the frequently used circularly orthogonal moments experimental results demonstrate that the semi orthogonal moments calculated with the zeroth order approximation perform better than the frequently used circularly orthogonal moments in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions it is also shown that the proposed high order moments are more numerically stable than the circularly orthogonal moments a kind of circular moments named circularly semi orthogonal moment is proposed it outperforms in image reconstruction over the circularly orthogonal moments it performs better in invariant image recognition under noisy and smooth distortions

classification of invariant image representations using a neural network a neural network nn based approach for classification of images represented by translation scale and rotation invariant features is presented the utilized network is a multilayer perceptron mlp classifier with one hidden layer back propagation learning is used for its training two types of features are used moment invariants derived from geometrical moments of the image and features based on zernlike moments which are the mapping of the image onto a set of complex orthogonal polynomials the performance of the mlp is compared to the bayes nearest neighbor and minimum mean distance statistical classifiers through extensive experimentation with noiseless as well as noisy binary images of all english characters 26 classes the following conclusions are reached 1 the mlp outperforms the other three classifiers especially when noise is present 2 the nearest neighbor classifier performs about the same as the nn for the noiseless case 3 the nn can do well even with a very small number of training samples 4 the nn has a good degree of fault tolerance and 5 the zernlike moment based features possess strong class separability power and are more powerful than moment invariants

generalized dual hahn moment invariants in this work we introduce a generalized expression of the weighted dual hahn moment invariants up to any order and for any value of their parameters in order for the proposed invariants to be formed the weighted dual hahn moments up to any order and for any value of their parameters are expressed as a linear combination of geometric ones for this reason a formula expressing the nth degree dual hahn polynomial for any value of its parameters as a linear combination of monomials c r x r is proved in addition a recurrent relation for the fast computation of the aforementioned monomials coefficients c r is also given moreover normalization aspects of the generalized weighted dual hahn moment invariants are discussed while a modification of them is proposed in order to avoid their numerical instabilities finally experimental results and classification scenarios including datasets of natural scenes evaluate the proposed methodology

on the rigidity theorems of witten in this paper we prove the rigidity theorems predicted by witten in 1986 about the index of certain elliptic operators on manifolds with an s1 action w witten s insight was the culmination of an interesting interchange of ideas between him and hopkins landweber ochanine and stong for the detailed history we refer the reader to la the present account is essentially a reinterpretation of the second author s taubes t original proof of the theorem the senior author s contribution was solely to notice that the rather densely written arguments of the original manuscript could be formulated in terms of the well known fixed point formulae of equivariant index theory and equivariant cohomology in this context the final proof then appears in direct lineage of the atiyah hirzebruch theorem concerning the vanishing of the a genus of spin manifolds admitting a circle action a h and of the even older idea of lusztig concerning circle actions in the complex case there remains however the beautiful physics inspired novelty of connecting these techniques with elliptic function theory

a uniqueness theorem for stable homotopy theory roughly speaking the stable homotopy category of algebraic topology is obtained from the homotopy category of topological spaces by inverting the suspension functor yielding a linear approximation to the homotopy category of spaces the isomorphism classes of objects in the stable homotopy category represent the generalized cohomology theories defined by the eilenberg steenrod axioms es45 without the dimension axiom which distinguishes ordinary from generalized cohomology theories the first construction of the full stable homotopy category was given by boardman b69 nowadays manymodels for the stable homotopy category are known most of which have the additional structure of a closed model category in the sense of quillen q67 in m83 h r margolis introduced a short list of axioms and conjectured that they characterize the stable homotopy category up to an equivalence of categories in theorem 3 2 we prove that these axioms do uniquely specify the stable homotopy category whenever there is some underlying quillen model category we also prove amore structured version theuniqueness theorembelow which states that the model category of spectra itself is uniquely determined by certain equivalent conditions up to so called quillen equivalence of

self similarity inspired local descriptor for non rigid multi modal image registration the self similarity inspired local descriptor is proposed for non rigid multi modal registration the zernike moments is introduced into the proposed method to explore rotational self similarity the effective computation of self similarity based both intensities and edge texture features of the multi modal images is utilized in the proposed method the proposed method can achieve higher registration accuracy than the other state of the art image representation based registration methods non rigid multi modal image registration plays an important role in medical image analysis it remains a challenging problem due to the significant intensity distortion and the non rigid transformation between images existing registration methods based on the information theoretic measures and image representations cannot address this problem effectively in this paper we have proposed a novel self similarity inspired local descriptor to determine the similarity metrics a key component in image registration the self similarity is determined based on the zernike moments of image patches in a local neighborhood and it is utilized to generate the local descriptor the euclidean distance between the local descriptors computed in the reference and moving images is used as the similarity metrics distinctively the proposed local descriptor can provide an effective representation of complicated image features due to its robustness to noise and rotational invariance which provides the proposed method with good registration performance extensive experiments on both simulated and real multi modal image datasets demonstrate that the proposed method has higher registration accuracy appreciated by the target registration error tre than the state of the art registration methods based on the normalized mutual information nmi the sum of squared differences on entropy images essd the weber local descriptor wld and the modality independent neighborhood descriptor mind

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

s 1 actions and elliptic genera a proof is given of witten s conjectures for the rigidity of the index of the dirac ramond operator on the loop space of a spin manifold which admits ans1 symmetry

the transmission zeros of systems with delays in this paper we study the properties of the zeros of a system with general delays in the input state and control variables the main result of this paper shows that the zeros of the transfer function are always zeros of the system matrix with of at least the same multiplicity moreover when the system is canonical the zeros of the system matrix are zeros of the transfer function with the same multiplicity

inner products of 2 representations abstract we define and calculate inner products of 2 representations along the way we prove that the categorical trace t r of 24 sec 3 is multiplicative with respect to various notions of categorical tensor product and we identify the center of the category of equivariant objects we discuss applications ranging from schur s result about the number of irreducible projective representations to a formula for the hochschild cohomology of a global quotient orbifold

on systems with spectral cluster points and their relation to h p spaces in this paper we continue our investigation of the general theory of root locus for distributed parameter systems which we began in banks ans abbasi ghelmansarai 1983a 1983b in the latter paper we considered the root locus of systems whose defining operator had a spectrum which did not cluster at any point of the plane and we obtained a generalisation of the classical theory by considering generalised poles and zero s

invariant zeros of siso infinite dimensional systems the zeros of a finite dimensional system can be characterised in terms of the eigenvalues of an operator on the largest closed feedback invariant subspace this characterisation is also valid for infinite dimensional systems provided that a largest closed feedback invariant subspace exists we generalise this characterisation of the zeros to the case when the largest closed feedback invariant subspace does not exist we give an example which shows that the choice of domain of the operator on this invariant subspace is crucial to this characterisation

nilpotence and descent in equivariant stable homotopy theory abstract let g be a finite group and let f be a family of subgroups of g we introduce a class of g equivariant spectra that we call f nilpotent this definition fits into the general theory of torsion complete and nilpotent objects in a symmetric monoidal stable category with which we begin we then develop some of the basic properties of f nilpotent g spectra which are explored further in the sequel to this paper in the rest of the paper we prove several general structure theorems for categories of module spectra over objects such as equivariant real and complex k theory and borel equivariant mu using these structure theorems and a technique with the flag variety dating back to quillen we then show that large classes of equivariant cohomology theories for which a type of complex orientability holds are nilpotent for the family of abelian subgroups in particular we prove that equivariant real and complex k theory as well as the borel equivariant versions of complex oriented theories have this property

the goodwillie tower of the identity functor and the unstable periodic homotopy of spheres we investigate goodwillie s taylor tower of the identity functor from spaces to spaces more specifically we reformulate johnson s description of the goodwillie derivatives of the identity and prove that in the case of an odd dimensional sphere the only layers in the tower that are not contractible are those indexed by powers of a prime moreover in the case of a sphere the tower is finite in v k periodic homotopy

zernike functions rigged hilbert spaces and potential applications we revise the symmetries of the zernike polynomials that determine the lie algebra su 1 1 su 1 1 we show how they induce discrete as well as continuous bases that coexist in the framework of rigged hilbert spaces we also discuss some other interesting properties of zernike polynomials and zernike functions one of the areas of interest of zernike functions has been their applications in optics here we suggest that operators on the spaces of zernike functions may play a role in optical image processing we revise the symmetries of the zernike polynomials that determine the lie algebra su 1 1 su 1 1 we show how they induce discrete as well as continuous bases that coexist in the framework of rigged hilbert spaces we also discuss some other interesting properties of zernike polynomials and zernike functions one of the areas of interest of zernike functions has been their applications in optics here we suggest that operators on the spaces of zernike functions may play a role in optical image processing

orthogonal variant moments features in image analysis moments are statistical measures used to obtain relevant information about a certain object under study e g signals images or waveforms e g to describe the shape of an object to be recognized by a pattern recognition system invariant moments e g the hu invariant set are a special kind of these statistical measures designed to remain constant after some transformations such as object rotation scaling translation or image illumination changes in order to e g improve the reliability of a pattern recognition system the classical moment invariants methodology is based on the determination of a set of transformations or perturbations for which the system must remain unaltered although very well established the classical moment invariants theory has been mainly used for processing single static images i e snapshots and the use of image moments to analyze images sequences or video from a dynamic point of view has not been sufficiently explored and is a subject of much interest nowadays in this paper we propose the use of variant moments as an alternative to the classical approach this approach presents clear differences compared to the classical moment invariants approach that in specific domains have important advantages the difference between the classical invariant and the proposed variant approach is mainly but not solely conceptual invariants are sensitive to any image change or perturbation for which they are not invariant so any unexpected perturbation will affect the measurements i e is subject to uncertainty on the contrary a variant moment is designed to be sensitive to a specific perturbation i e to measure a transformation not to be invariant to it and thus if the specific perturbation occurs it will be measured hence any unexpected disturbance will not affect the objective of the measurement confronting thus uncertainty furthermore given the fact that the proposed variant moments are orthogonal i e uncorrelated it is possible to considerably reduce the total inherent uncertainty the presented approach has been applied to interesting open problems in computer vision such as shape analysis image segmentation tracking object deformations and object motion tracking obtaining encouraging results and proving the effectiveness of the proposed approach

tate cohomology and periodic localization of polynomial functors in this paper we show that goodwillie calculus as applied to functors from stable homotopy to itself interacts in striking ways with chromatic aspects of the stable category localized at a fixed prime p let t n be the telescope of a v n self map of a finite s module of type n the periodicity theorem of hopkins and smith implies that the bousfield localization functor associated to t n is independent of choices goodwillie s general theory says that to any homotopy functor f from s modules to s modules there is an associated tower under f p d f such that f p d f is the universal arrow to a d excisive functor our first main theorem says that p d f pd 1f always admits a homotopy section after localization with respect to t n and so also after localization with respect to morava k theory k n thus after periodic localization polynomial functors split as the product of their homogeneous factors this theorem follows from our second main theorem which is equivalent to the following for any finite group g the tate spectrum mathcal t g t n is weakly contractible this strengthens and extends previous theorems of greenlees sadofsky hovey sadofsky and mahowald shick the periodicity theorem is used in an essential way in our proof the connection between the two theorems is via a reformulation of a result of mccarthy on dual calculus

root locii for systems defined on hilbert spaces the root locus is an important tool for analyzing the stability and time constants of linear finite dimensional systems as a parameter often the gain is varied however many systems are modelled by partial differential equations or delay equations these systems evolve on an infinite dimensional space and their transfer functions are not rational in this paper a rigorous definition of the root locus for infinite dimensional systems is given and it is shown that the root locus is well defined for a large class of infinite dimensional systems as for finite dimensional systems any limit point of a branch of the root locus is a zero however the asymptotic behavior can be quite different from that for finite dimensional systems this point is illustrated with a number of examples it is shown that the familiar pole zero interlacing property for collocated systems with a hermitian state matrix extends to infinite dimensional systems with self adjoint generator this interlacing property is also shown to hold for collocated systems with a skew adjoint generator

some properties of the frequency domain description of boundary control systems abstract in this paper we make use of the semigroup approach to study a boundary control system with possibly unbounded output operator input and output functions take values in finite dimensional spaces we define the class of modally canonical systems and we show that a system of this class which satisfies suitable conditions can equivalently be described by the system operator matrix as well as by the transfer function the implications of the canonicity assumption on the structure of the system are examined

accurate calculation of zernike moments zernike moments zms are very effective global image descriptors which are used in many digital image processing applications the digitization process compromises the accuracy of the moments and therefore several of its properties are affected there are two major discretization errors namely the geometric error and numerical integration error in this paper we propose two new algorithms which eliminate these errors the first algorithm performs the exact computation of geometric moments gms over a unit disk and then uses gms to zms relationship to compute the latter this algorithm is computationally more expensive and it becomes numerically instable for higher order moments therefore we develop a second algorithm based on gaussian quadrature numerical integration the second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of gaussian quadrature numerical integration increases the proposed algorithms are observed to provide very accurate zms which result in improved image reconstruction reduction in reconstruction error and improvement in rotation and scale invariance exhaustive experiments are provided to support improved accuracy of zms and time complexity analysis is performed for the existing and the proposed methods

lifting homotopy t algebra maps to strict maps abstract the settings for homotopical algebra categories such as simplicial groups simplicial rings a spaces e ring spectra etc are often equivalent to categories of algebras over some monad or triple t in such cases t is acting on a nice simplicial model category in such a way that t descends to a monad on the homotopy category and defines a category of homotopy t algebras in this setting there is a forgetful functor from the homotopy category of t algebras to the category of homotopy t algebras under suitable hypotheses we provide an obstruction theory in the form of a bousfield kan spectral sequence for lifting a homotopy t algebra map to a strict map of t algebras once we have a map of t algebras to serve as a basepoint the spectral sequence computes the homotopy groups of the space of t algebra maps and the edge homomorphism on 0 is the aforementioned forgetful functor we discuss a variety of settings in which the required hypotheses are satisfied including monads arising from algebraic theories and operads we also give sufficient conditions for the e 2 term to be calculable in terms of quillen cohomology groups we provide worked examples in g spaces g spectra rational e algebras and a algebras explicit calculations connected to rational unstable homotopy theory show that the forgetful functor from the homotopy category of e ring spectra to the category of h ring spectra is generally neither full nor faithful we also apply a result of the second named author and nick kuhn to compute the homotopy type of the space e coker j l k 2 r

poincare koszul duality we prove a duality for factorization homology which generalizes both usual poincare duality for manifolds and koszul duality for mathcal e n algebras the duality has application to the hochschild homology of associative algebras and enveloping algebras of lie algebras we interpret our result at the level of topological quantum field theory

stereo effect of image converted from planar research on planar to stereo image conversion has significant theoretical and practical implications for image processing in this paper we use a method which segments an image into sub blocks to perform this kind of conversion parameters such as random variables are used for conversion control we use two quantitative criteria cross entropy and root mean square error to evaluate the stereo effect furthermore the stereo effect that the random variables create is discussed the results of the experiment show that i when all random variables have the same distribution different values of these random variables only slightly affect the stereo effect and ii when different distributions are applied to the random variables the cross entropies or root mean square errors are slightly different which indicates different distributions have a small influence on the stereo effect generally we recommend normal distribution for better stereo effect in most cases

moment based local image watermarking via genetic optimization a totally optimized image watermarking methodology that manages to enhance its local behaviour by applying the krawtchouk moments is presented through this paper the introduced technique is making use of a simple genetic algorithm in order to optimize the set of parameters that significantly influences the locality properties alongside with the overall performance of the watermarking procedure herein the watermarking process is tackled as an optimization procedure in this context the appropriate set of configuration parameters is being searched for ensuring high quality watermarked images and low bit error rates at the extraction stage for this purpose several traditional and newly introduced image quality measures are used in order to quantify the influence of the examined set of parameters as far as the quality of the watermarked image and the accuracy of the extracted watermark are concerned the proposed method produces watermarked images of high quality and ensures high detection rates under several non geometric attacks by using less prior knowledge at the detector s side extensive experiments have shown that by handling the watermarking process as an optimization problem more robust and accurate watermarking schemes can be derived

homotopical localizations of spaces for a map f of spaces dror farjoun and the author have constructed an f localization functor where a space y is called f local when map f y is an equivalence this very general construction gives all known idempotent homotopy functors of spaces the main theorem of this paper shows that f localization functors always preserve fiber sequences of connected h spaces up to small error terms for instance the localization with respect to the n th morava k theory preserves such fiber sequences up to error terms with at most three nontrivial homotopy groups this implies for example that a k 1 homology equivalence of h spaces must induce an isomorphism of v 1 periodic homotopy groups results are also obtained on the a nullification or a periodization functors which are just the f localization functors for the maps f from spaces a to points two spaces are said to have the same nullity when they give the same nullification functors and it is shown that arbitrary sets of nullity classes have both least upper bounds and greatest lower bounds the a nullifications of nilpotent postnikov spaces are completely determined

a comparative analysis of algorithms for fast computation of zernike moments abstract this paper details a comparative analysis on time taken by the present and proposed methods to compute the zernike moments z pq the present method comprises of direct belkasim s prata s kintner s and coefficient methods we propose a new technique denoted as q recursive method specifically for fast computation of zernike moments it uses radial polynomials of fixed order p with a varying index q to compute zernike moments fast computation is achieved because it uses polynomials of higher index q to derive the polynomials of lower index q and it does not use any factorial terms individual order of moments can be calculated independently without employing lower or higher order moments this is especially useful in cases where only selected orders of zernike moments are needed as pattern features the performance of the present and proposed methods are experimentally analyzed by calculating zernike moments of orders 0 to p and specific order p using binary and grayscale images in both the cases the q recursive method takes the shortest time to compute zernike moments

an efficient illumination invariant face recognition framework via illumination enhancement and dd dtcwt filtering in this paper it is shown that multiscale analysis of facial structure and features of face images leads to superior recognition rates for images under varying illumination the proposed method which is computationally cost effective significantly suppresses illumination effects the problem is defined as how better to extract the reflectance portion from a given image this can be used directly as an input to a dimensionality reduction unit followed by a classifier for recognition purposes we first assume that an image i x y is a black box consisting of a combination of illumination and reflectance a new approximation is proposed to enhance the illumination removal phase as illumination resides in the low frequency part of image it is reasonable to consider the use of a high performance multiresolution transformation to first accurately separate the frequency components of an image the double density dual tree complex wavelet transform dd dtcwt possesses three core advantages i e the transformation is i shift invariant ii directionally selective with no checkerboard effect iii enriched by extra wavelets interpreted as double density the output of the first phase is sent to a dd dtcwt unit to be decomposed into frequency subbands high frequency subbands are thresholded and an inverse dd dtcwt is then applied to subbands to construct a low frequency raw image which is followed by a fine tuning process finally after extracting a mask feature vector is formed and the principal component analysis pca is used for dimensionality reduction which is then proceeded by the extreme learning machine elm as a classifier to evaluate the performance of the proposed algorithm for face recognition under varying illumination unlike similar works the proposed method is free of any prior information about the face shape it is systematic and easy to implement and it can be applied separately on each image furthermore the proposed method which is significantly faster than similar techniques presents a robust behavior against the reduction in the number of images required for the training cycle several experiments are performed employing the available well known databases such as the yale b extended yale b cmu pie feret at t and the labeled faces in the wild lfw illustrative examples are given and the results compare favorably to the current results in the literature

robust multivariable pi controller for infinite dimensional systems a robust multivariable controller is introduced for a class of distributed parameter systems the system to be controlled is given as dot x ax bu y cx in a banach space the purpose of the control which is based on the measurement y is to stabilize and regulate the system so that y t rightarrow y r as t rightarrow infty where y r is a constant reference vector under the assumptions that operator a generates a holomorphic stable semigroup b is linear and bounded c is linear and a bounded and the input and output spaces are of the same dimension a necessary and sufficient condition is found for the existence of a robust multivariable controller this controller appears to be a multivariable pi controller also a simple necessary criterion for the existence of a decentralized controller is derived the tuning of the controller is discussed and it is shown that the i part of the controller can be tuned on the basis of step responses without exact knowledge of the system s parameters the presented theory is then used as an example to control the temperature profile of a bar with the dirichlet boundary conditions

stable fast computation of high order zernike moments using a recursive method zernike moments and zernike polynomials have been widely applied in the fields of image processing and pattern recognition when high order zernike moments are computed both computing speed and numerical accuracy become inferior the main purpose of this study is to propose a stable fast method for computing high order zernike moments based on the recursive formulas for computing zernike radial polynomials this study develops stable fast algorithms to compute zernike moments symmetry under group action and farey sequence are both applied to shorten the computing time the experimental results show that the proposed method took 5 292 seconds to compute the top 500 order zernike moments of an image with 512 512 pixels the normalized mean square error is 0 00124846 if 450 order moments are used to reconstruct the image when computing the high order zernike moments the proposed method outperformed other compared methods in terms of speed and accuracy this study has proposed a recursive method for fast computation of zernike moments the idea of pascal s triangle is introduced to pre calculate the binomial coefficients symmetry property and farey sequence are applied to speed up the computation the proposed method can yield accurate values of the high order zernike moments the proposed took 5 398 seconds to compute the top 500 order zernike moments

james maps and en ring spaces we parametrize by operad actions the multiplicative analysis of the total james map given by caruso and ourselves the target of the total james map q c r n x it qdq r n x q o is an en ring space and is a en map where en is the little n cubes operad this implies that has an n fold delooping with domain n x it also implies an algorithm for the calculation of and thus of each q on mod p homology when n 00 and p 2 this algorithm is the essential starting point for kuhn s proof of the whitehead conjecture in 2 4 we analyzed the behavior with respect to pairings of the lames maps iq ex qdq e x used in 4 to obtain the stable splittings of spaces ex in particular we proved that if the given coefficient system e has a sum then the product of the targets is a ring space and the product of the iq s is an exponential h map in fact this is only a fragment of the full structure present in the most interesting examples in the first two sections we give a parametrized elaboration of this analysis we assume the given coefficient system e is a module over an operad and we deduce essentially that

generalized group characters and complex oriented cohomology theories let bg be the classifying space of a finite group g given a multiplicative cohomology theory e the assignment g 7i e bg is a functor from groups to rings endowed with induction transfer maps in this paper we investigate these functors for complex oriented cohomology theories e using the theory of complex representations of finite groups as a model for what one would like to know an analogue of artin s theorem is proved for all complex oriented e the abelian subgroups of g serve as a detecting family for e bg modulo torsion dividing the order of g when e is a complete local ring with residue field of characteristic p and associated formal group of height n we construct a character ring of class functions that computes 1 e bg the domain of the characters is gn p the set of n tuples of elements in g each of which has order a power of p a formula for induction is also found the ideas we use are related to the lubin tate theory of formal groups the construction applies to many cohomology theories of current interest completed versions of elliptic cohomology e n theory etc the nth morava k theory euler characteristic for bg is computed to be the number of g orbits in gn p for various groups g including all symmetric groups we prove that k n bg concentrated in even degrees our results about e bg extend to theorems about e eg gx where x is a finite g cw complex

a unified methodology for computing accurate quaternion color moments and moment invariants in this paper a general framework for computing accurate quaternion color moments and their corresponding invariants is proposed the proposed unified scheme arose by studying the characteristics of different orthogonal polynomials these polynomials are used as kernels in order to form moments the invariants of which can easily be derived the resulted scheme permits the usage of any polynomial like kernel in a unified and consistent way the resulted moments and moment invariants demonstrate robustness to noisy conditions and high discriminative power additionally in the case of continuous moments accurate computations take place to avoid approximation errors based on this general methodology the quaternion tchebichef krawtchouk dual hahn legendre orthogonal fourier mellin pseudo zernike and zernike color moments and their corresponding invariants are introduced a selected paradigm presents the reconstruction capability of each moment family whereas proper classification scenarios evaluate the performance of color moment invariants

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

on the telescopic homotopy theory of spaces in telescopic homotopy theory a space or spectrum x is approximated by a tower of localizations lnx n 0 taking account of vn periodic homotopy groups for progressively higher n for each n 1 we construct a telescopic kuhn functor n carrying a space to a spectrum with the same vn periodic homotopy groups and we construct a new functor n left adjoint to n using these functors we show that the nth stable monocular homotopy category comprising the nth fibers of stable telescopic towers embeds as a retract of the nth unstable monocular homotopy category in two ways one giving infinite loop spaces and the other giving infinite ln suspension spaces we deduce that ravenel s stable telescope conjectures are equivalent to unstable telescope conjectures in particular we show that the failure of ravenel s nth stable telescope conjecture implies the existence of highly connected infinite loop spaces with trivial johnson wilson e n homology but nontrivial vn periodic homotopy groups showing a fundamental difference between the unstable chromatic and telescopic theories as a stable chromatic application we show that each spectrum is k n equivalent to a suspension spectrum as an unstable chromatic application we determine the e n localizations and k n localizations of infinite loop spaces in terms of e n localizations of spectra under suitable conditions we also determine the e n localizations and k n localizations of arbitrary postnikov h spaces

novel moment invariants for improved classification performance in computer vision applications a novel set of moment invariants based on the krawtchouk moments are introduced in this paper these moment invariants are computed over a finite number of image intensity slices extracted by applying an innovative image representation scheme the image slice representation isr method based on this technique an image is decomposed to a several non overlapped intensity slices which can be considered as binary slices of certain intensity this image representation gives the advantage to accelerate the computation of image s moments since the image can be described in a number of homogenous rectangular blocks which permits the simplification of the computation formulas the moments computed over the extracted slices seem to be more efficient than the corresponding moments of the same order that describe the whole image in recognizing the pattern under processing the proposed moment invariants are exhaustively tested in several well known computer vision datasets regarding their rotation scaling and translation rst invariant recognition performance by resulting to remarkable outcomes

the balmer spectrum of the equivariant homotopy category of a finite abelian group for a finite abelian group a we determine the balmer spectrum of mathrm sp a omega the compact objects in genuine a spectra this generalizes the case a mathbb z p mathbb z due to balmer and sanders invent math 208 1 283 326 2017 by establishing a corrected version of their hbox log p conjecture for abelian groups we also work out the consequences for the chromatic type of fixed points and establish a generalization of kuhn s blue shift theorem for tate constructions kuhn in invent math 157 2 345 370 2004

the morava k theories of some classifying spaces let p be a finite abelian p group with classifying space bp we compute in representation theoretic terms the morava k theories of the stable wedge summands of bp in particular we obtain a simple and purely group theoretic description of the rank of k s bg for any finite group g with an abelian p sylow subgroup a minimal amount of topology quickly reduces the problem to an algebraic one of analyzing truncated polynomial algebras as modular representations of the semigroup m 1 z p 1 main results for a fixed prime p there exists a sequence of cohomology theories k 1 k 2 with k s periodic with period 2 ps 1 these are the morava k theories 13 and generalize ordinary complex k theory in the sense that k 1 is one of the p 1 isomorphic summands of k z p recently it has been becoming clear that they play a central role in homotopy theory see for example the work of m hopkins and j smith 6 k s has further computational virtues k s x is always a free module over the coefficient ring k s and there is a kunneth isomorphism a major outstanding problem is to find good models for the spaces representing these theories related to this is the question of finding for finite groups g a group theoretic description for the rings k s bg analogous to atiyah s isomorphism 2 r g k bg the author together with j harris recently analyzed stable wedge decompositions of classifying spaces of abelian p groups 5 in this paper we compute in representation theoretic terms the morava k theories of the resulting wedge summands as a consequence we obtain a very simple and purely group theoretic description of the rank of k s bg for any finite group g with an abelian p sylow subgroup to state our results we establish some notation it is convenient to let k o be rational cohomology we let k s x always denote the reduced sth morava k theory of x if x is a space or spectrum we let k5 x equal the rank of k s x as a k s module and by abuse of notation we let ks g ks bg for a finite group g bg is the union of bg with a disjoint basepoint received bv the editors may 27 1986 1980 marhemat7es subject cl lssific ltion primary 55n22 secondary 20g05 research partially supported by the sloan foundation and the nsf t1987 american mathematical society 0002 9947 87 1 00 25 per page

strictly commutative complex orientation theory for a multiplicative cohomology theory e complex orientations are in bijective correspondence with multiplicative natural transformations to e from complex bordism cohomology mu if e is represented by a spectrum with a highly structured multiplication we give an iterative process for lifting an orientation mu rightarrow e to a map respecting this extra structure based on work of arone lesh the space of strictly commutative orientations is the limit of an inverse tower of spaces parametrizing partial lifts stage 1 corresponds to ordinary complex orientations and lifting from stage m 1 to stage m is governed by the existence of an orientation for a family of e modules over a fixed base space f m when e is p local we can say more we find that this tower only changes when m is a power of p and if e is e n local the tower is constant after stage p n moreover if the coefficient ring e is p torsion free the ability to lift from stage 1 to stage p is equivalent to a condition on the associated formal group law that was shown necessary by ando

realization theory and the infinite dimensional root locus the theory of realization of linear input output maps is applied to the study of root loci of distributed systems with bounded defining operators

fast computation of legendre and zernike moments this paper presents recursive algorithms for fast computation of legendre and zernike moments of a grey level image intensity distribution for a binary image a contour integration method is developed for the evaluation of legendre moments using only the boundary information a method for recursive calculation of zernike polynomial coefficients is also given a square to circular image transformation scheme is introduced to minimize the computation involved in zernike moment functions the recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments the mathematical framework of the algorithms is given in detail and illustrated with binary and grey level images

new computational methods for full and subset zernike moments the computation of zernike radial polynomials contributes most of the computation time in computing the zernike moments due to the involvement of factorial terms the common approaches used in fast computation of zernike moments are kintner s prata s coefficient and q recursive methods in this paper we propose faster methods to derive the full set of zernike moments as well as a subset of zernike moments a hybrid algorithm that uses prata s simplified kintner s and coefficient methods is used to derive the full set of zernike moments in the computation of a subset of zernike moments we propose using the combination of prata s simplified kintner s coefficient and q recursive methods fast computation is achieved by using the recurrence relations between the zernike radial polynomials of successive order without any involvement of factorial terms in the first and second experiments we show both the hybrid algorithms take lesser computation time than the existing methods in computing the full set of zernike moments and a selected subset of zernike moments which are not in successive sequence both hybrid algorithms have been applied in real world application in the classification of rice grains using full set and subset of zernike moments the classification performance using optimal subset of zernike moments is better than using full set of zernike moments

global adaptive stabilization of infinite dimensional systems abstract the purpose of this paper is to show that a first order adaptive regulator globally stabilizes a class of infinite dimensional systems having no right half plane zeros knowledge of the spectrum of the model s high frequency gain is not required

fast computation of exact zernike moments using cascaded digital filters zernike moments have been extensively used and have received much research attention in a number of fields object recognition image reconstruction image segmentation edge detection and biomedical imaging however computation of these moments is time consuming thus we present a fast computation technique to calculate exact zernike moments by using cascaded digital filters the novelty of the method proposed in this paper lies in the computation of exact geometric moments directly from digital filter outputs without the need to first compute geometric moments the mathematical relationship between digital filter outputs and exact geometric moments is derived and then they are used in the formulation of exact zernike moments a comparison of the speed of performance of the proposed algorithm with other state of the art alternatives shows that the proposed algorithm betters current computation time and uses less memory

a novel algorithm for fast computation of zernike moments abstract zernike moments zms have been successfully used in pattern recognition and image analysis due to their good properties of orthogonality and rotation invariance however their computation by a direct method is too expensive which limits the application of zms in this paper we present a novel algorithm for fast computation of zernike moments by using the recursive property of zernike polynomials the inter relationship of the zernike moments can be established as a result the zernike moment of order n with repetition m znm can be expressed as a combination of zn 2 m and zn 4 m based on this relationship the zernike moment znm for n m can be deduced from zmm to reduce the computational complexity we adopt an algorithm known as systolic array for computing these latter moments using such a strategy the multiplication number required in the moment calculation of zmm can be decreased significantly comparison with known methods shows that our algorithm is as accurate as the existing methods but is more efficient

the bousfield kuhn functor and topological andre quillen cohomology we construct a natural transformation from the bousfield kuhn functor evaluated on a space to the topological andre quillen cohomology of the k n local spanier whitehead dual of the space and show that the map is an equivalence in the case where the space is a sphere this results in a method for computing unstable v n periodic homotopy groups of spheres from their morava e cohomology as modules over the dyer lashof algebra of morava e theory we relate the resulting algebraic computations to the algebraic geometry of isogenies between lubin tate formal groups

fast and numerically stable methods for the computation of zernike moments zernike moments zms are used in many image processing applications due to their superior performance over other moments however they suffer from high computation cost and numerical instability at high order of moments in the past many recursive methods have been developed to improve their speed performance and considerable success has been achieved the analysis of numerical stability has also gained momentum as it affects the accuracy of moments and their invariance property there are three recursive methods which are normally used in zms calculation prata s kintner s and q recursive methods the earlier studies have found the q recursive method outperforming the two other methods in this paper we modify prata s method and present a recursive relation which is proved to be faster than the q recursive method numerical instability is observed at high orders of moments with the q recursive method suffering from the underflow problem while the modified prata s method suffering from finite precision error the modified kintner s method is the least susceptible to these errors keeping in view the better numerical stability we further make the modified kintner s method marginally faster than the q recursive method we recommend the modified prata s method for low orders 90 and kintner s fast method for high orders 90 of zms

a unified methodology for the efficient computation of discrete orthogonal image moments a novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments the computation scheme is mainly based on a new image representation method the image slice representation isr method according to which an image can be expressed as the outcome of an appropriate combination of several non overlapped intensity slices this image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities black or any other gray level value therefore the image block representation can be effectively applied to describe the image in a more compact way once the image is partitioned into intensity blocks the computation of the image moments can be accelerated as the moments can be computed by using decoupled computation forms the proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results as has been concluded through a detailed experimental investigation

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

a systematic method for efficient computation of full and subsets zernike moments a new method is proposed for fast and accurate computation of zernike moments this method presents a novel formula for computing exact zernike moments by using exact complex moments where the exact values of complex moments are computed by mathematical integration of the monomials over digital image pixels the proposed method is applicable to compute the full set of zernike moments as well as the subsets of individual order repetition and an individual moment a comparison with other conventional methods is performed the results show the superiority of the proposed method

a new class of zernike moments for computer vision applications a modified direct method for the computation of the zernike moments is presented in this paper the presence of many factorial terms in the direct method for computing the zernike moments makes their computation process a very time consuming task although the computational power of the modern computers is impressively increasing the calculation of the factorial of a big number is still an inaccurate numerical procedure the main concept of the present paper is that by using stirling s approximation formula for the factorial and by applying some suitable mathematical properties a novel factorial free direct method can be developed the resulted moments are not equal to those computed by the original direct method but they are a sufficiently accurate approximation of them besides their variability does not affect their ability to describe uniquely and distinguish the objects they represent this is verified by pattern recognition simulation examples

orbifold genera product formulas and power operations we generalize the definition of orbifold elliptic genus and introduce orbifold genera of chromatic level h using h tuples rather than pairs of commuting elements we show that our genera are in fact orbifold invariants and we prove integrality results for them if the genus arises from an h8 map into the morava lubin tate theory eh then we give a formula expressing the orbifold genus of the symmetric powers of a stably almost complex manifold m in terms of the genus of m itself our formula is the p typical analogue of the dijkgraaf moore verlinde verlinde formula for the orbifold elliptic genus r dijkgraaf et al elliptic genera of symmetric products and second quantized strings comm math phys 185 1 1997 197 209 it depends only on h and not on the genus

localization of andre quillen goodwillie towers and the periodic homology of infinite loopspaces abstract let k n be the n th morava k theory at a prime p and let t n be the telescope of a v n self map of a finite complex of type n in this paper we study the k n homology of x the 0th space of a spectrum x and many related matters we give a sampling of our results let p x be the free commutative s algebra generated by x it is weakly equivalent to the wedge of all the extended powers of x we construct a natural map s n x l t n p x l t n x of commutative algebras over the localized sphere spectrum l t n s the induced map of commutative cocommutative k n hopf algebras s n x k n p x k n x satisfies the following properties it is always monic it is an isomorphism if x is n connected n 1 x is torsion and t i x 0 for 1 i n 1 it is an isomorphism only if k i x 0 for 1 i n 1 it is universal the domain of s n x preserves k n isomorphisms and if f is any functor preserving k n isomorphisms then any natural transformation f x k n x factors uniquely through s n x the construction of our natural transformation uses the telescopic functors constructed and studied previously by bousfield and the author and thus depends heavily on the nilpotence theorem of devanitz hopkins and smith our proof that s n x is always monic uses topological andre quillen homology and goodwillie calculus in nonconnective settings

equivariant k theory generalized symmetric products and twisted heisenberg algebra for a space x acted on by a finite group the product space xn affords a natural action of the wreath product n n sn the direct sum of equivariant k groups were shown earlier by the author to carry several interesting algebraic structures in this paper we study the k groups of n equivariant clifford supermodules on xn we show that is a hopf algebra and it is isomorphic to the fock space of a twisted heisenberg algebra twisted vertex operators make a natural appearance the algebraic structures on x when is trivial and x is a point specialize to those on a ring of symmetric functions with the schur q functions as a linear basis as a by product we present a novel construction of k theory operations using the spin representations of the hyperoctahedral groups

the sigma orientation is an h map in an earlier paper the authors constructed a natural map called the sigma orientation from the thom spectrum mu 6 to any elliptic spectrum mu 6 is an h ring spectrum and in this paper we show that if e c t is the elliptic spectrum associated to the universal deformation of a supersingular elliptic curve over a perfect field of characteristic p 0 then the sigma orientation is a map of h ring spectra

power operations in elliptic cohomology and representations of loop groups the first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve the second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups the third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part

research on system zeros a survey this report provides a review of notable publications regarding the topic of zeros of multivariable systems in the period from 1970 into 1989 particular attention is paid to relationships between definitions of such zeros and their theoretical development transmission invariant system module infinite and finite zeros are addressed the latter subdivided into a hierarchical structure with respect to information considered in the definition process

generalized moonshine ii borcherds products the goal of this paper is to construct infinite dimensional lie algebras by using infinite product identities and to use these lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and lie algebras we expect the lie algebras that we construct to manifest as algebras of physical states in an orbifold conformal field theory yet to be fully constructed with symmetries given by the monster simple group we introduce vector valued modular functions attached to families of modular functions of different levels and we prove infinite product identities for a distinguished class of automorphic functions on a product of two half planes we recast this result using the borcherds harvey moore singular theta lift and show that the vector valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps for each element of the monster simple group we construct an infinite dimensional lie algebra such that its denominator formula is an infinite product expansion of the automorphic function arising from that element s mckay thompson series these lie algebras have the unusual property that their simple roots and all root multiplicities are known we show that under certain hypotheses characters of groups acting on these lie algebras form functions on the upper half plane that are either constant or invariant under a genus zero congruence group