compact lie group action with the continuous rokhlin property abstract in this paper we study the continuous rokhlin property of c dynamical systems using techniques of equivariant kk theory and quantum group theory in particular we determine the kk equivalence class and give a classification of kirchberg g algebras when the g is a compact lie group with the hodgkin condition

abelian mathrm c ast subalgebras of mathrm c ast algebras of real rank zero and inductive limit mathrm c ast algebras

classifying c algebras via ordered mod p k theory we introduce an order structure on k 0 9 k0 z p this group may also be thought of as ko 7z z p we exhibit new examples of real rank zero c algebras that are inductive limits of finite dimensional and dimension drop algebras have the same ordered graded k theory with order unit and yet are not isomorphic in fact they are not even stably shape equivalent the order structure on k0 z 3 z p naturally distinguishes these algebras the same invariant is used to give an isomorphism theorem for such realrank zero inductive limits as a corollary we obtain an isomorphism theorem for all real rank zero approximately homogeneous c algebras that arise from systems of bounded dimension growth and torsion free k0 group at the 1980 kingston conference effros posed the problem of finding suitable invariants for use in studying c algebras that are limits of sequences of homogeneous c algebras these are now called almost homogeneous ah c algebras the classification of ah algebras is a rapidly developing field and we will not attempt to summarize all this activity instead we will focus on the growth of the invariants used specifically we consider an ah algebra a that is the direct limit o f a system of the form

higher order single step fully discrete approximations for second order hyperbolic equations with time dependent coefficients error estimates are proved for finite element approximations to the solution of an initial boundary value problem for a second order hyperbolic partial differential equation with time dependent coefficients optimal order rates of convergence in l 2 are shown for single step fully discrete schemes the order nu of the single step schemes is greater than or equal to one and less than or equal to four a class of iterative methods for approximately solving the fully discrete equations is analyzed and optimal order rates of convergence are also obtained these methods avoid the repeated work of new matrix factorizations at each time level

letter to the editor convergence of fem with interpolated coefficients for semilinear hyperbolic equation to solve spatially semidiscrete approximative solution of a class of semilinear hyperbolic equations the finite element method fem with interpolated coefficients is discussed by use of semidiscrete finite element for linear problem as comparative function the error estimate in l norm is derived by the nonlinear argument in chen structure theory of superconvergence of finite elements hunan press of science and technology changsha 2001 in chinese this indicates that convergence of fems with interpolated coefficients for a semilinear equation is similar to that of classical fems

z stability of crossed products by strongly outer actions ii we consider a crossed product of a unital simple separable nuclear stably finite z stable c algebra a by a strongly outer cocycle action of a discrete countable amenable group under the assumption that a has finitely many extremal tracial states and is elementary amenable we show that the twisted crossed product c algebra is z stable as an application we also prove that all strongly outer cocycle actions of the klein bottle group on z are cocycle conjugate to each other this is the first classification result for actions of non abelian infinite groups on stably finite c algebras

inductive limits of interval algebras the tracial state space introduction this is the first in a series of papers where we investigate the structure of the c algebras obtained as inductive limits of interval algebras c 0 1 0m the purpose here is to show that these c algebras comprise a large stock of simple c algebras and that some of them allow endomorphisms with chaotic actions on the tracial state space to be more specific we show that to any dense subgroup g of q containing z and any metrizable choquet simplex s there is a sequence

finite groups acting on higher dimensional noncommutative tori abstract for the canonical action of sl 2 z on 2 dimensional simple rotation algebras a it is known that if f is a finite subgroup of sl 2 z the crossed products a f are all af algebras in this paper we show that this is not the case for higher dimensional noncommutative tori more precisely we show that for each n 3 there exist noncommutative simple n dimensional tori a which admit canonical action of z n and for each odd n 7 with 2 n n 5 their crossed products a z n are not af with nonzero k 1 groups it is also shown that the only possible canonical action by a finite group on a 3 dimensional simple torus is the flip action by z 2 besides we discuss the canonical actions by finite groups z 5 z 8 z 10 and z 12 on the 4 dimensional torus of the form a a

semidiscrete and single step fully discrete approximations for second order hyperbolic equations with time dependent coefficients l2 norm error estimates are proved for finite element approximations to the solutions of initial boundary value problems for second order hyperbolic partial differential equations with time dependent coefficients optimal order rates of convergence are shown for semidiscrete and single step fully discrete schemes using specially constructed initial data the initial data are designed so that the data used for the fully discrete equation is reasonable to compute and so that the optimal order estimates can be proved

non commutative shifts and crossed products abstract when a is a unital simple af c algebra and has a unique tracial state it is shown that the crossed product of the two sided infinite tensor product z a by the shift is a tracially af c algebra a similar result is given to the crossed product of a certain non unital two sided infinite tensor product by the shift applying a far reaching classification result of such c algebras by h lin we obtain an example of a one parameter automorphism group on some af c algebra which is not approximately inner a counter example to the af version of the so called powers sakai conjecture 23

on dualities of actions and inclusions abstract following the results known in the case of a finite abelian group action on c algebras we prove the following two theorems an inclusion p a of watatani index finite type has the rokhlin property is approximately representable if and only if the dual inclusion is approximately representable has the rokhlin property an inclusion p a of watatani index finite type has the tracial rokhlin property is tracially approximately representable if and only if the dual inclusion is tracially approximately representable has the tracial rokhlin property moreover we provide an alternate proof of phillips theorem about the relations between tracial rokhlin action and tracially approximate representable dual action using a new conceptual framework suggested by authors

geotensity combining motion and lighting for 3d surface reconstruction this paper is about automatically reconstructing the full 3d surface of an object observed in motion by a single static camera based on the two paradigms structure from motion and linear intensity subspaces we introduce the geotensity constraint that governs the relationship between four or more images of a moving object we show that it is possible in theory to solve for 3d lambertian surface structure for the case of a single point light source and propose that a solution exists for an arbitrary number point light sources the surface may or may not be textured we then give an example of automatic surface reconstruction of a face under a point light source using arbitrary unknown object motion and a single fixed camera

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

rokhlin dimension and c dynamics we develop the concept of rokhlin dimension for integer and for finite group actions on c algebras our notion generalizes the so called rokhlin property which can be thought of as rokhlin dimension 0 we show that finite rokhlin dimension is prevalent and appears in cases in which the rokhlin property cannot be expected the property of having finite rokhlin dimension is generic for automorphisms of mathcal z stable c algebras where mathcal z denotes the jiang su algebra moreover crossed products by automorphisms with finite rokhlin dimension preserve the property of having finite nuclear dimension and under a mild additional hypothesis also preserve mathcal z stability in topological dynamics our notion may be interpreted as a topological version of the classical rokhlin lemma automorphisms arising from minimal homeomorphisms of finite dimensional compact metrizable spaces always have finite rokhlin dimension the latter result has by now been generalized by szabo to the case of free and aperiodic mathbb z d actions on compact metrizable and finite dimensional spaces

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

almost commuting unitaries and classification of purely infinite simplec algebras we show that for any irrational rotational algebraa a o2 o2 this is proved by combining recently established results forc algebras of real rank zero with the following result for anye 0 there is 0 such that for any pair of unitariesu vin any purely infinite simplec algebraawithk1 a 0 satisfies uv vu and u v 0 there is a pair of commuting unitariesu v awith finite spectrum such that u u eand v v e more general results concerning almost commuting unitaries are also obtained

higher order single step fully discrete approximations for nonlinear second order hyperbolic equations abstract error estimates are proved for finite element approximations to the solution of an initial boundary value problem for nonlinear second order hyperbolic partial differential equations optimal order rates of convergence in l 2 are shown for single step fully discrete schemes which are linearized by extrapolations the order of accuracy in time is 2 3 or 4 a class of iterative methods for approximately solving the fully discrete equations is analyzed and optimal order rates of convergence are also obtained

finite group actions on c algebras with the rohlin property i basic properties of finite group actions with the rohlin property on unital c algebras are investigated a characterization of finite group actions with the rohlin property on the cuntz algebra 02 is given in terms of central sequences which may be considered as an equivariant version of e kirchberg and n c phillips s characterization of 02 a large class of symmetries on 02 are classified in terms of the fixed point algebras for conjugacy and the crossed products for cocycle conjugacy model actions of symmetries of 02 are constructed for given k theoretical invariants

a universal multicoefficient theorem for the kasparov groups that holds in the same generality as the universal coefficient theorem of rosenberg and schochet there are advantages in some circumstances to using hom k a k b in place of kk a b these advantages derive from the fact that k a can be equipped with order and scale structures similar to those on k0 a with this additional structure the module k a becomes a powerful invariant of c algebras we show that it is a complete invariant for the class of real rank zero ad algebras the ad algebras are a certain kind of approximately subhomogeneous c algebras which may have torsion in k1 ell in addition to classifying these algebras we calculate their automorphism groups up to approximately innerautomorphisms

cosine methods for a class of semilinear second order wave equations abstract we analyze fully discrete methods of fourth or second order temporal accuracy for the approximation of the solutions of a class of semilinear second order hyperbolic equations with a nonlinear term that depends on x t u u t u the methods are based on galerkin type discretizations in space and on a class of two step cosine time stepping schemes by suitably extrapolating from previous values in the nonlinear term we compute the approximations by solving linear systems of equations at each time step l 2 optimal error estimates are proved

outer automorphisms and reduced crossed products of simple c algebras every outer automorphism of a separable simplec algebra is shown to have a pure state which is mapped into an inequivalent state under this automorphism the reduced crossed product of a simplec algebra by a discrete group of outer automorphisms is shown to be simple

numerical shape from shading and occluding boundaries an iterative method for computing shape from shading using occluding boundary information is proposed some applications of this method are shown we employ the stereographic plane to express the orientations of surface patches rather than the more commonly used gradient space use of the stereographic plane makes it possible to incorporate occluding boundary information but forces us to employ a smoothness constraint different from the one previously proposed the new constraint follows directly from a particular definition of surface smoothness we solve the set of equations arising from the smoothness constraints and the image irradiance equation iteratively using occluding boundary information to supply boundary conditions good initial values are found at certain points to help reduce the number of iterations required to reach a reasonable solution numerical experiments show that the method is effective and robust finally we analyze scanning electron microscope sem pictures using this method other applications are also proposed

error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations abstract optimal order rates of convergence are proved for fully discrete approximations for nonlinear second order hyperbolic equations which are based on a finite element approximation in the space variables and a single step method in the time variable the r h s of the differential equation can depend on u u 1 or u and the coefficients can depend on u this paper generalizes the work of bales where the r h s and coefficients were allowed to depend on u

photometric motion the author compares the photometric effects of motion which is defined as the variation of a point s imaged intensity as a consequence of motion and the geometric effects of motion which is defined as the variation in projected surface geometry as a consequence of motion it is shown that photometric motion provides a cue to surface shape that is potentially as useful as that provided by geometric motion a simple technique for using this photometric motion information to extract both surface shape and reflectance is developed and a biological implementation is proposed how this photometric motion mechanism can be integrated with and used to enhance existing structure motion algorithms is discussed intensity information is sometimes even more important than geometric distortion when estimating the shape of a single continuous surface that is rotating relative to the observer s frame of reference

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

3d shape recovery of smooth surfaces dropping the fixed viewpoint assumption we present a new method for recovering the 3d shape of a featureless smooth surface from three or more calibrated images illuminated by different light sources three of them are independent this method is unique in its ability to handle images taken from unconstrained perspective viewpoints and unconstrained illumination directions the correspondence between such images is hard to compute and no other known method can handle this problem locally from a small number of images our method combines geometric and photometric information in order to recover dense correspondence between the images and accurately computes the 3d shape only a single pass starting at one point and local computation are used this is in contrast to methods that use the occluding contours recovered from many images to initialize and constrain an optimization process the output of our method can be used to initialize such processes in the special case of fixed viewpoint the proposed method becomes a new perspective photometric stereo algorithm nevertheless the introduction of the multiview setup self occlusions and regions close to the occluding boundaries are better handled and the method is more robust to noise than photometric stereo experimental results are presented for simulated and real images

crossed products by finite group actions with the rokhlin property we prove that a number of classes of separable unital c algebras are closed under crossed products by finite group actions with the rokhlin property including a ai algebras at algebras and related classes characterized by direct limit decompositions using semiprojective building blocks b simple unital ah algebras with slow dimension growth and real rank zero c c algebras with real rank zero or stable rank one d simple c algebras for which the order on projections is determined by traces e c algebras whose quotients all satisfy the universal coefficient theorem f c algebras with a unique tracial state along the way we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective

the small projections property of c algebras abstract we prove a new characterization of rickart c algebras in terms of compact projections we also characterize the small projections property sp for type i c algebras with hausdorff primitive spectrum as an application to group c algebras we identify certain locally compact groups g for which c g has sp finally among other results a characterization of a w algebras is given in terms of sp

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

the tracial rokhlin property for actions of finite groups on c algebras we define tracial analogs of the rokhlin property for actions of finite groups approximate representability of actions of finite abelian groups and approximate innerness we prove the following four analogs of related nontracial results bullet the crossed product of an infinite dimensional simple separable unital c algebra with tracial rank zero by an action of a finite group with the tracial rokhlin property again has tracial rank zero bullet an outer action of a finite abelian group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property if and only if its dual is tracially approximately representable and is tracially approximately representable if and only if its dual has the tracial rokhlin property bullet if a strongly tracially approximately inner action of a finite cyclic group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property then it is tracially approximately representable bullet an automorphism of an infinite dimensional simple separable unital c algebra a with tracial rank zero is tracially approximately inner if and only if it is the identity on k 0 a mod infinitesimals

tracially z absorbing c algebras abstract we study a tracial notion of z absorption for simple unital c algebras we show that if a is a c algebra for which this property holds then a has almost unperforated cuntz semigroup and if in addition a is nuclear and separable we show this property is equivalent to having a a z we furthermore show that this property is preserved under forming certain crossed products by actions satisfying a tracial rokhlin type property

on the classification of nuclear c algebras two of the most influential works on c algebras from the mid seventies brown douglas and fillmore s 6 and elliott s 21 both contain uniqueness and existence results in the now standard sense which we shall outline below these papers served as keystones for two separate theories kk theory and the classification program which for many years parted ways with only moderate interaction but with this common origin in mind it is not surprising that recent years have seen a fruitful interaction which has been one of the main engines behind rapid progress in the classification program in the present paper we take this interaction even further combining a concept of quasidiagonality for representations and a new characterization of equivalence in the cuntz picture of kk theory we achieve a general uniqueness result and from the quasidiagonality notion we derive a corresponding general existence result by comparing well known realizations of the kk groups these results are then employed to obtain new classification results for certain classes of quasidiagonal c algebras introduced by h lin an important novel feature of these classes is that they are defined by a certain local approximation property rather than by an inductive limit construction we emphasize that our fundamental uniqueness result does not depend on the universal coefficient theorem uct nor on nuclearity of the c algebras involved on the other hand when we refine the uniqueness result for use in classification we need to gradually add such conditions on the c algebras it is to be expected that requirements of this type are necessary but we have found that holding them back as long as possible leads to more conceptual proofs while clarifying the role of the uct and nuclearity in classification further since uniqueness results answer fundamental questions about kk and k theory they are of interest in themselves we have pursued this theme in 14 and defer to this paper the proof of the new characterization of kk theory which lies behind our uniqueness results our existence and uniqueness results are in the spirit of the classical ext theory from 6 the main complication overcome in the paper is to control the stabilization which is necessary when one works with finite c algebras in the infinite case where programs of this type have already been successfully carried out stabilization is unnecessary yet our methods are sufficiently versatile to allow us to reprove from a handful of basic results the classification of purely infinite nuclear c algebras of kirchberg and phillips

finite group actions on c algebras with the rohlin property ii abstract we classify finite group actions on some classes of c algebras with the rohlin property in terms of the k groups a group cohomological obstruction is obtained for the k groups of a c algebra allowing such an action for example the tate cohomology groups with the k groups as the coefficient modules must vanish model actions with the rohlin property are constructed for given k theoretical invariants quasi free actions of finite cyclic groups on the cuntz algebras and their dual actions are investigated from the view point of the rohlin property