mean and variance of implicitly defined biased estimators such as penalized maximum likelihood applications to tomography many estimators in signal processing problems are defined implicitly as the maximum of some objective function examples of implicitly defined estimators include maximum likelihood penalized likelihood maximum a posteriori and nonlinear least squares estimation for such estimators exact analytical expressions for the mean and variance are usually unavailable therefore investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators this paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters we derive the approximations using the implicit function theorem the taylor expansion and the chain rule the expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation as illustrations we demonstrate that the approximations work well in two tomographic imaging applications with poisson statistics we also describe a plug in approximation that provides a remarkably accurate estimate of variability even from a single noisy poisson sinogram measurement the approximations should be useful in a wide range of estimation problems

vertex operators of uq gl n n and highest weight representations of uq gl 2 2 we determine the exchange relations of the level one q vertex operators of the quantum affine superalgebra uq gl n n we study in detail the level one irreducible highest weight representations of uq gl 2 2 and compute the characters and supercharacters associated with these irreducible modules

a q deformation of wakimoto modules primary fields and screening operators theq vertex operators of frenkel and reshetikhin are studied by means of aq deformation of the wakimoto module for the quantum affine algebrau q widehat mathfrak s mathfrak l 2 at an arbitrary levelk 0 2 a fock module version of theq deformed primary field of spinj is introduced as well as the screening operators which anti commute with the action ofu q widehat mathfrak s mathfrak l 2 up to a total difference of a field a proof of the intertwining property is given for theq vertex operators corresponding to the primary fields of spinj 1 2z 0 a sample calculation of the correlation function is also given

a quantum analog of the z algebra we define a natural quantum analog for the z algebra and which we refer to as the zq algebra by modding out the heisenberg algebra from the quantum affine algebra uq sl 2 with level k we discuss the representation theory of this zq algebra in particular we exhibit its reduction to a group algebra and to a tensor product of a group algebra with a quantum clifford algebra when k 1 and k 2 and thus we recover the explicit constructions of uq sl 2 standard modules as achieved by frenkel jing and bernard respectively moreover for arbitrary nonzero level k we show that the explicit basis for the simplest z generalized verma module as constructed by lepowsky and primc is also a basis for its corresponding zq module i e it is invariant under the q deformation for generic q we expect this zq algebra associated with uq sl 2 at level k to play the role of a dynamical symmetry in the off critical zk statistical models

generalized taylor operators and polynomial chains for hermite subdivision schemes hermite subdivision schemes act on vector valued data that is not only considered as functions values of a vector valued function from mathbb r to mathbb r r but as evaluations of r consecutive derivatives of a function this intuition leads to a mild form of level dependence of the scheme previously we have proved that a property called spectral condition or sum rule implies a factorization in terms of a generalized difference operator that gives rise to a difference scheme whose contractivity governs the convergence of the scheme but many convergent hermite schemes for example those based on cardinal splines do not satisfy the spectral condition in this paper we generalize the property in a way that preserves all the above advantages the associated factorizations and convergence theory based on these results we can include the case of cardinal splines in a systematic way and are also able to construct new types of convergent hermite subdivision schemes

twisted quantum affinizations and their vertex representations in this paper we generalize drinfeld s twisted quantum affine algebras to construct twisted quantum algebras for all simply laced generalized cartan matrices and present their vertex representation realizations

resolution and noise properties of map reconstruction for fully 3 d pet derives approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three dimensional 3 d positron emission tomography pet data using maximum a posteriori map estimation these expressions explicitly account for the spatially variant detector response and sensitivity of a 3 d tomograph the resulting spatially variant impulse response and covariance are computed using 3 d fourier transforms a truncated gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in map reconstruction using monte carlo simulations and phantom data from the micropet small animal scanner the authors show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of map reconstruction for priors with quadratic energy functions they also describe how these analytical results can be used to achieve near uniform contrast recovery throughout the reconstructed volume

vertex operator representation of some quantum tori lie algebras we are defining the trigonometric lie subalgebras in bar x infty bar a infty bar b infty bar c infty bar d infty which are the natural generalization of the well known sin lie algebra the embedding formulas into bar x infty are introduced these algebras can be considered as some lie algebras of quantum tori an irreducible representation ofa b series of trigonometric lie algebras is constructed special cases of the trigonometric lie factor algebras which can be considered as a quantum preserving lie algebra structure deformation of the kac moody algebras are considered

quantum vertex f t algebras and their modules this is a paper in a series to study vertex algebra like structures arising from various algebras including quantum affine algebras and yangians in this paper we develop a theory of what we call weak quantum vertex f t algebras with f a field of characteristic zero and t a formal variable and we give a conceptual construction of weak quantum vertex f t algebras and their modules as an application we associate weak quantum vertex f t algebras to quantum affine algebras providing a solution to a problem posed by frenkel and jing we also explicitly construct an example of quantum vertex f t algebras from a certain quantum system

regularization for uniform spatial resolution properties in penalized likelihood image reconstruction traditional space invariant regularization methods in tomographic image reconstruction using penalized likelihood estimators produce images with nonuniform spatial resolution properties the local point spread functions that quantify the smoothing properties of such estimators are space variant asymmetric and object dependent even for space invariant imaging systems the authors propose a new quadratic regularization scheme for tomographic imaging systems that yields increased spatial uniformity and is motivated by the least squares fitting of a parameterized local impulse response to a desired global response the authors have developed computationally efficient methods for pet systems with shift invariant geometric responses they demonstrate the increased spatial uniformity of this new method versus conventional quadratic regularization schemes in simulated pet thorax scans

difference equations for correlation functions of belavin s ℤn symmetric model with boundary reflection belavin s n symmetric elliptic model with boundary reflection is considered on the basis of the boundary ctm bootstrap we find non diagonal k matrices for n 2 that satisfy the reflection equation boundary yang baxter equation and also find non diagonal boltzmann weights for the a 1 n 1 face model even for n 2 we derive difference equations of the quantum knizhnik zamolodchikov type for correlation functions of the boundary model the boundary spontaneous polarization is obtained by solving the simplest difference equations in the case of the free boundary condition the resulting quantity is the square of the spontaneous polarization for the bulk n symmetric model up to a phase factor

vertex operators and symmetric functions an algorithm for the calculation of q dependent spin characters of the symmetric group is given with an explicit example of s4 a method for constructing the q analogue of the vertex operators is developed a 1 1 correspondence between the space v of twisted q vertex operators and the ring of q deformed symmetric functions lambda x zq q t is established and a mapping from v to lambda x zq q t is defined a number of relevant theorems are given

full rank interpolatory subdivision schemes kronecker filters and multiresolution in this extension of earlier work we point out several ways how a multiresolution analysis can be derived from a finitely supported interpolatory matrix mask which has a positive definite symbol on the unit circle except at 1 a major tool in this investigation will be subdivision schemes that are obtained by using convolution or correlation operations based on replacing the usual matrix multiplications by kronecker products

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

multivariate refinable functions differences and ideals a simple tutorial this paper summarizes the algebraic quotient ideal approach to polynomial generation by refinable functions and connects it to strang fix conditions and factorization with respect to difference operators motivated by the latter one we also consider vector subdivision schemes with matrix valued coefficients and review some of their properties

noise characterization of block iterative reconstruction algorithms i theory researchers have shown increasing interest in block iterative image reconstruction algorithms due to the computational and modeling advantages they provide although their convergence properties have been well documented little is known about how they behave in the presence of noise in this work the authors fully characterize the ensemble statistical properties of the rescaled block iterative expectation maximization rbi em reconstruction algorithm and the rescaled block iterative simultaneous multiplicative algebraic reconstruction technique rbi smart also included in the analysis are the special cases of rbi em maximum likelihood em ml em and ordered subset em os em and the special case of rbi smart smart a theoretical formulation strategy similar to that previously outlined for ml em is followed for the rbi methods the theoretical formulations in this paper rely on one approximation namely that the noise in the reconstructed image is small compared to the mean image in a second paper the approximation will be justified through monte carlo simulations covering a range of noise levels iteration points and subset orderings the ensemble statistical parameters could then be used to evaluate objective measures of image quality

plethysms replicated schur functions and series with applications to vertex operators specializations of schur functions are exploited to define and evaluate the schur functions s x and plethysms s s x for any integer real or complex plethysms are then used to define pairs of mutually inverse infinite series of schur functions m and l specified by arbitrary partitions these are used in turn to define and provide generating functions for formal characters s of certain groups h thereby extending known results for orthogonal and symplectic group characters each of these formal characters is then given a vertex operator realization first in terms of the seriesm m 0 and various l dual to l and then more explicitly in the exponential form finally the replicated form of such vertex operators are written down the characters of the orthogonal and symplectic groups have been found by schur 34 and weyl 35 respectively the method used is transcendental and depends on integration over the group manifold these characters however may be obtained by purely algebraic methods this algebraic method would seem to offer a better prospect of successful application to other restricted groups than the method of group integration littlewood d e 1944 phil trans r soc london ser a 239 809 392 pacs numbers 02 10 v 02 10 de 02 20 a 02 20 hj mathematics subject classification 05e05 17b69 11e57 16w30 20e22 33d52 43a40 1751 8113

γ conformal algebras conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points we classify these algebras and their representations in terms of lie algebras and their representations with an action of the group to every conformal algebra and a character of we associate a lie algebra generated by fields with the ope with simple poles examples include twisted affine kac moody algebras the sin algebra which is a conformal analogue of the general linear algebra and its analogues the algebra of pseudodifferential operators on the circle etc

triangular 3 subdivision schemes the regular case the paper deals with the investigation of triangular 3 subdivision schemes in the stationary shift invariant setting in section 2 we collect the available theory on refinable functions subdivision surfaces with emphasis on their sobolev and holder smoothness families of interpolatory and approximating 3 subdivision schemes are investigated in section 3 some dual 3 subdivision schemes which are related to vector valued refinable functions are also analyzed for this purpose we have developed matlab routines for numerically investigating properties of vector subdivision schemes

evaluation of fisher information matrix based methods for fast assessment of image quality in pinhole spect the accurate determination of the local impulse response and the covariance in voxels from penalized maximum likelihood reconstructed images requires performing reconstructions from many noise realizations of the projection data as this is usually a very time consuming process efficient analytical approximations based on the fisher information matrix fim have been extensively used in pet and spect to estimate these quantities for 3d imaging however additional approximations need to be made to the fim in order to speed up the calculations the most common approach is to use the local shift invariant lsi approximation of the fim but this assumes specific conditions which are not always necessarily valid in this paper we take a single pinhole spect system and compare the accuracy of the lsi approximation against two other methods that have been more recently put forward the non uniform object space pixelation nuop and the subsampled fim these methods do not assume such restrictive conditions while still increasing the speed of the calculations considerably our results indicate that in pinhole spect the nuop and subsampled fim approaches could be more reliable than the lsi approximation especially when a high accuracy is required

free field representation for massive integrable models a new approach to massive integrable models is considered it allows one to find symmetry algebras which define the spaces of local operators and to get general integral representations for form factors in thesu 2 thirring and sine gordon models

a theoretical study of the contrast recovery and variance of map reconstructions from pet data the authors examine the spatial resolution and variance properties of pet images reconstructed using maximum a posteriori map or penalized likelihood methods resolution is characterized by the contrast recovery coefficient crc of the local impulse response simplified approximate expressions are derived for the local impulse response crcs and variances for each voxel using these results the authors propose a practical scheme for selecting spatially variant smoothing parameters to optimize lesion detectability through maximization of the local crc to noise ratio in the reconstructed image

extended hermite subdivision schemes subdivision schemes are efficient tools for building curves and surfaces for vector subdivision schemes it is not so straightforward to prove more than the hlder regularity of the limit function on the other hand hermite subdivision schemes produce function vectors that consist of derivatives of a certain function so that the notion of convergence automatically includes regularity of the limit in this paper we establish an equivalence between a spectral condition and operator factorizations then we study how such schemes with smooth limit functions can be extended into ones with higher regularity we conclude by pointing out how this new approach applies to cardinal splines

vertex operator realization of symplectic and orthogonal s functions it is shown that symplectic and orthogonal schur functions can be realized by the action of the modes of certain vertex operators on the function the properties of these vertex operators allow one to reproduce the basic propreties of these types of symmetric functions the vertex operator modes are shown to obey free fermionic relations which provide applications such as calculating products and plethysms as well as generating hirota type partial differential equations pdes which have symplectic s functions as functions

theoretical study of lesion detectability of map reconstruction using computer observers the low signal to noise ratio snr in emission data has stimulated the development of statistical image reconstruction methods based on the maximum a posteriori map principle experimental examples have shown that statistical methods improve image quality compared to the conventional filtered backprojection fbp method however these results depend on isolated data sets here the authors study the lesion detectability of map reconstruction theoretically using computer observers these theoretical results can be applied to different object structures they show that for a quadratic smoothing prior the lesion detectability using the prewhitening observer is independent of the smoothing parameter and the neighborhood of the prior while the nonprewhitening observer exhibits an optimum smoothing point the authors also compare the results to those of fbp reconstruction the comparison shows that for ideal positron emission tomography pet systems where data are true line integrals of the tracer distribution the map reconstruction has a higher snr for lesion detection than fbp reconstruction due to the modeling of the poisson noise for realistic systems map reconstruction further benefits from accurately modeling the physical photon detection process in pet

on vector subdivision in this paper we give a complete characterization of the convergence of stationary vector subdivision schemes and the regularity of the associated limit function these results extend and complete our earlier work on vector subdivision and its use in the construction of multiwavelets

quantum knizhnik zamolodchikov equation for uq sln and integral formula an integral formula for solutions to the level zero quantum knizhnik zamolodchikov equation associated with the vector representation of uq sln is presented this formula gives a generalization of both our previous work for uq sln and smirnov s formula for form factors of the su n chiral gross neveu model

quantum algebra structure of certain jackson integrals theq difference system satisfied by jackson integrals with a configuration ofa type root system is studied we explicitly construct some linear combination of jackson integrals which satisfies the quantum knizhnik zamolodchikov equation for the 2 point correlation function ofq vertex operators introduced by frenkel and reshetikhin for the quantum affine algebra u q widehat mathfrak s mathfrak l 2 the expression of integrands for then point case is conjectured and a set of linear relations for the corresponding jackson integrals is proved

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

monotonic algorithms for transmission tomography we present a framework for designing fast and monotonic algorithms for transmission tomography penalized likelihood image reconstruction the new algorithms are based on paraboloidal surrogate functions for the log likelihood due to the form of the log likelihood function it is possible to find low curvature surrogate functions that guarantee monotonicity unlike previous methods the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log likelihood that arises due to background events such as scatter and random coincidences the gradient and the curvature of the likelihood terms are evaluated only once per iteration since the problem is simplified at each iteration the cpu time is less than that of current algorithms which directly minimize the objective yet the convergence rate is comparable the simplicity monotonicity and speed of the new algorithms are quite attractive the convergence rates of the algorithms are demonstrated using real and simulated pet transmission scans

filters for anisotropic wavelet decompositions abstract like the continuous shearlet transform and their relatives discrete transformations based on the interplay between several filterbanks with anisotropic dilations provide a high potential to recover directed features in two and more dimensions due to simplicity most of the directional systems constructed so far were using prediction correction methods based on interpolatory subdivision schemes in this paper we give a simple but effective construction for qmf quadrature mirror filter filterbanks which are the usual discrete tools in orthogonal wavelet analysis we characterize when the filterbank gives rise to the existence of refinable functions and hence wavelets and give a generalized shearlet construction for arbitrary dimensions and arbitrary scalings for which the filterbank construction ensures the existence of an orthogonal wavelet analysis we also show that under some restriction on the dilation factors this multiple filterbank system satisfies the slope resolution property which is a key feature in all types of directional transforms

analysis of resolution and noise properties of nonquadratically regularized image reconstruction methods for pet we present accurate and efficient methods for estimating the spatial resolution and noise properties of nonquadratically regularized image reconstruction for positron emission tomography pet it is well known that quadratic regularization tends to over smooth sharp edges many types of edge preserving nonquadratic penalties have been proposed to overcome this problem however there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity in contrast quadratically regularized estimators are approximately linear and are well understood in terms of resolution and variance properties we derive new approximate expressions for the linearized local perturbation response llpr and variance using the taylor expansion with the remainder term although the expressions are implicit we can use them to accurately predict resolution and variance for nonquadratic regularization where the conventional expressions based on the first order taylor truncation fail they also motivate us to extend the use of a certainty based modified penalty to nonquadratic regularization cases in order to achieve spatially uniform perturbation responses analogous to uniform spatial resolution in quadratic regularization finally we develop computationally efficient methods for predicting resolution and variance of nonquadratically regularized reconstruction and present simulations that illustrate the validity of these methods

level one highest weight representation of uq sl n 1 and bosonization of the multicomponent super t j model we study the level one irreducible highest weight representations of the quantum affine superalgebra uq sl n 1 and calculate their characters and supercharacters we obtain bosonized q vertex operators acting on the irreducible uq sl n 1 modules and derive the exchange relations satisfied by the vertex operators we give the bosonization of the multicomponent super t j model by using the bosonized vertex operators

a generalized taylor factorization for hermite subdivision schemes in a recent paper we investigated factorization properties of hermite subdivision schemes by means of the so called taylor factorization this decomposition is based on a spectral condition which is satisfied for example by all interpolatory hermite schemes nevertheless there exist examples of hermite schemes especially some based on cardinal splines which fail the spectral condition for these schemes and others we provide the concept of a generalized taylor factorization and show how it can be used to obtain convergence criteria for the hermite scheme by means of factorization and contractivity

smirnov s integrals and the quantum knizhnik zamolodchikov equation of level 0 we study the quantum knizhnik zamolodchikov equation 1984 of level 0 associated with the spin 1 2 representation of uq sl2 we find an integral formula for solutions in the case of an arbitrary total spin and mod q mod 1 in the formula different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed

stability implies convergence of cascade algorithms in sobolev space this article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in sobolev space to which the refinable function vector belongs an example of hermite interpolants is presented to illustrate the result

annihilation poles of a smirnov type integral formula for solutions to the quantum knizhnik zamolodchikov equation we consider the recently obtained integral representation of the quantum knizhnik zamolodchikov equation of level 0 we obtain the condition for the integral kernel such that these solutions satisfy three axioms for the form factor in the manner of smirnov we discuss the relation between this integral representation and the form factor of the xxz spin chain

analysis of non stationary hermite subdivision schemes reproducing exponential polynomials abstract the aim of this paper is to study the convergence and smoothness of non stationary hermite subdivision schemes of order 2 in conti et al 2017 provided sufficient conditions for the convergence of a non stationary hermite subdivision scheme that reproduces a set of functions including exponential polynomials the analysis has been focused on the non stationary hermite scheme with the order 3 but the case of 2 which is practically most useful is yet to be investigated in this regard the first goal of this paper is to fill the gap we analyze the convergence of non stationary hermite subdivision schemes of order 2 next we provide a tool which allows us to estimate the smoothness of a non stationary hermite scheme by developing a novel factorization framework of non stationary vector subdivision operators using the proposed non stationary factorization framework we estimate the smoothness of the non stationary hermite subdivision schemes the non stationary interpolatory hermite scheme proposed by conti et al 2015 and a new class of non stationary dual hermite subdivision schemes of de rham type

form factors of the xxz model and the affine quantum group symmetry we present new expressions of form factors of the xxz model which satisfy smirnov s three axioms these new form factors are obtained by applying the affine quantum group to the known ones obtained in our previous works we also find the relations among all the new and known form factors i e all other form factors are obtained by applying to a singlet form factor

fast predictions of variance images for fan beam transmission tomography with quadratic regularization accurate predictions of image variances can be useful for reconstruction algorithm analysis and for the design of regularization methods computing the predicted variance at every pixel using matrix based approximations is impractical even most recently adopted methods that are based on local discrete fourier approximations are impractical since they would require a forward and backprojection and two fast fourier transform fft calculations for every pixel particularly for shift variant systems like fan beam tomography this paper describes new analytical approaches to predicting the approximate variance maps of 2 d images that are reconstructed by penalized likelihood estimation with quadratic regularization in fan beam geometries the simplest of the proposed analytical approaches requires computation equivalent to one backprojection and some summations so it is computationally practical even for the data sizes in x ray computed tomography ct simulation results show that it gives accurate predictions of the variance maps the parallel beam geometry is a simple special case of the fan beam analysis the analysis is also applicable to 2 d positron emission tomography pet

choquet integrals as projection operators for quantified tomographic reconstruction in this paper we propose to investigate and analyze a new method for performing quantified projection and back projection in emission tomography this method is based on using non summative kernels capacities and asymmetric choquet integral to obtain imprecise projected values i e intervals instead of usual reconstructed pixel values validation studies using numerical and physical single photon computed emission tomography spect phantoms were used to demonstrate links between the length of these reconstructed intervals and the stochastic noise level in reconstructed slices

convergence of subdivision schemes and smoothness of limit functions abstract starting with vector k k z l p z the subdivision scheme generates a sequence s a n n 1 of vectors by the subdivision operator s a k j z j a k 2 j k z subdivision schemes play an important role in computer graphics and wavelet analysis it is very interesting to understand under what conditions the sequence s a n n 1 converges to a l p function in an appropriate sense this problem has been studied extensively in this paper we consider the convergence of subdivision scheme in sobolev spaces with the tool of joint spectral radius firstly the conditions under which the sequence s a n n 1 converges to a w p k function in an appropriate sense are given then we show that the subdivision scheme converges for any initial vector in w p k r provided that it does for one nonzero vector in that space moreover if the shifts of the refinable function are stable the smoothness of the limit function corresponding to the vector is also independent of where the smoothness of a given function is measured by the generalized lipschitz space

vertex operators arising from the homogeneous realization for we use the underlying fock space for the homogeneous vertex operator representation of the affine lie algebra to construct a family of vertex operators as an application an irreducible module for an extended affine lie algebra of type a n 1 coordinatized by a quantum torus q of 2 variables or 3 variables is obtained moreover this module turns out to be a highest weight module which is an analog of the basic module for affine lie algebras

efficient calculation of resolution and covariance for penalized likelihood reconstruction in fully 3 d spect resolution and covariance predictors have been derived previously for penalized likelihood estimators these predictors can provide accurate approximations to the local resolution properties and covariance functions for tomographic systems given a good estimate of the mean measurements although these predictors may be evaluated iteratively circulant approximations are often made for practical computation times however when numerous evaluations are made repeatedly as in penalty design or calculation of variance images these predictors still require large amounts of computing time in stayman and fessler 2000 we discussed methods for precomputing a large portion of the predictor for shift invariant system geometries in this paper we generalize the efficient procedure discussed in stayman and fessler 2000 to shift variant single photon emission computed tomography spect systems this generalization relies on a new attenuation approximation and several observations on the symmetries in spect systems these new general procedures apply to both two dimensional and fully three dimensional 3 d spect models that may be either precomputed and stored or written in procedural form we demonstrate the high accuracy of the predictions based on these methods using a simulated anthropomorphic phantom and fully 3 d spect system the evaluation of these predictors requires significantly less computation time than traditional prediction techniques once the system geometry specific precomputations have been made

yangian doubles of classical types and their vertex representations the yangian double dy gn is introduced for the classical types of gn o2n 1 sp2n and o2n via the gauss decomposition of the generator matrix the yangian double is given the drinfeld presentation in addition bosonization of level 1 realizations for the yangian double dy gn of non simply laced types are explicitly constructed

spatial resolution properties of penalized likelihood image reconstruction space invariant tomographs this paper examines the spatial resolution properties of penalized likelihood image reconstruction methods by analyzing the local impulse response the analysis shows that standard regularization penalties induce space variant local impulse response functions even for space invariant tomographic systems paradoxically for emission image reconstruction the local resolution is generally poorest in high count regions we show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections this analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution the modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized likelihood methods

particle field duality and form factors from vertex operators using a duality between the space of particles and the space of fields we show how one can compute form factors directly in the space of fields this introduces the notion of vertex operators and form factors are vacuum expectation values of such vertex operators in the space of fields the vertex operators can be constructed explicitly in radial quantization furthermore these vertex operators can be exactly bosonized in momentum space we develop these ideas by studying the free fermion point of the sine gordon theory and use this scheme to compute some form factors of some non free fields in the sine gordon theory this work further clarifies earlier work of one of the authors and extends it to include the periodic sector

vertex representations of quantum affine algebras we construct vertex representations of quantum affine algebras of ade type which were first introduced in greater generality by drinfeld and jimbo the limiting special case of our construction is the untwisted vertex representation of affine lie algebras of frenkel kac and segal our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisfying the defining relations in the case of the quantum affine algebra of type a we introduce vertex operators corresponding to all the roots and determine their commutation relations this provides an analogue of a chevalley basis of the affine lie algebra unk n in the basic representation

vertex operator of for level one in this paper we give the explicit formulae of vertex operators of u q b l 1 for level one as operators on the fock space meanwhile we point out that the free field realization by one fermionic field and l bosonic fields of highest weight module with highest weight lambda l has two irreducible modules