on schwarz type smoothers for saddle point problems in this paper we consider additive schwarz type iteration methods for saddle point problems as smoothers in a multigrid method each iteration step of the additive schwarz method requires the solutions of several small local saddle point problems this method can be viewed as an additive version of a multiplicative vanka type iteration well known as a smoother for multigrid methods in computational fluid dynamics it is shown that under suitable conditions the iteration can be interpreted as a symmetric inexact uzawa method in the case of symmetric saddle point problems the smoothing property an important part in a multigrid convergence proof is analyzed for symmetric inexact uzawa methods including the special case of the additive schwarz type iterations as an example the theory is applied to the crouzeix raviart mixed finite element for the stokes equations and some numerical experiments are presented

on the general ericksen leslie system parodi s relation well posedness and stability in this paper we investigate the role of parodi s relation in the well posedness and stability of the general ericksen leslie system modeling nematic liquid crystal flows first we give a formal physical derivation of the ericksen leslie system through an appropriate energy variational approach under parodi s relation in which we can distinguish the conservative dissipative parts of the induced elastic stress next we prove global well posedness and long time behavior of the ericksen leslie system under the assumption that the viscosity 4 is sufficiently large finally under parodi s relation we show the global well posedness and lyapunov stability for the ericksen leslie system near local energy minimizers the connection between parodi s relation and linear stability of the ericksen leslie system is also discussed

a mesh refinement method for ax λbx abstact the aim of this paper is to introduce a simple but efficient mesh refinement strategy for use with inverse iteration for finding one or a few solutions of an ordinary or partial differential eigenproblem of the form ax xbx the focus is upon the case where a and b are symmetric and b is positive definite although the approaches have a very broad application a discussion of the combined use of mesh refinement and a correction scheme multigrid technique is also provided the methods are illustrated by numerical results from experiments with two point boundary value problems

a nonmonotone filter trust region method for nonlinear constrained optimization in this paper we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization similar to bryd omojokun class of algorithms each step is composed of a quasi normal step and a tangential step this new method has more flexibility for the acceptance of the trial step compared to the filter methods and requires less computational costs compared with the monotone methods under reasonable conditions we give the globally convergence properties numerical tests are presented that confirm the efficiency of the approach

kumjian pask algebras of locally convex higher rank graphs the kumjian pask algebra of a higher rank graph generalises the leavitt path algebra of a directed graph we extend the definition of kumjian pask algebra to row finite higher rank graphs with sources which satisfy a local convexity condition after proving versions of the graded uniqueness theorem and the cuntz krieger uniqueness theorem we study the kumjian pask algebra of rank 2 bratteli diagrams by studying certain finite subgraphs which are locally convex we show that the desourcification procedure of farthing and webster yields a row finite higher rank graph without sources such that the kumjian pask algebras of and are morita equivalent we then use the morita equivalence to study the ideal structure of the kumjian pask algebra of by pulling the appropriate results across the equivalence

a genetic algorithm approach to the spectral estimation of time series with noise and missed observations this study considers the problem of estimating the autoregressive moving average arma power spectral density when measurements are corrupted by noise and by missed observations the missed observations model is based on a probabilistic structure unlike conventional cases of missed observation in parameter estimation problems the variance of noise is unavailable that is the time points of missed observations are unknown and the probability of missing data needs to be estimated in this situation spectral estimation is more difficult to solve and becomes a highly nonlinear optimization problem with many local minima in this paper we use the genetic algorithm ga method to achieve a global optimal solution with a fast convergence rate for this spectral estimation problem from the simulation results we have determined that the performance is significantly improved if the probability of data loss is considered in the spectral estimation problem

brief papers linear identification of arma processes a new method for estimating the parameters of an arma process is presented the method consists of three linear least squares estimations in the first an autoregressive model is fitted to the observation sequence yielding an estimate of the values of the driving white noise sequence linear least squares is then used to fit an arma model to the observation and estimated white noise sequences this model is used to filter the observation and estimated white noise sequences finally an arma model is fitted to the filtered sequences it is shown that the resultant estimator is p consistent the asymptotic bias tends to zero as the degree p of the autoregressive model tends to infinity and is p efficient the asymptotic efficiency approaches the theoretical maximum as p tends to infinity

category equivalences involving graded modules over path algebras of quivers abstract let q be a finite quiver with vertex set i and arrow set q 1 k a field and k q its path algebra with its standard grading this paper proves some category equivalences involving the quotient category qgr k q gr k q fdim k q of graded k q modules modulo those that are the sum of their finite dimensional submodules namely qgr k q mod s q gr l q mod l q 0 qgr k q n here s q lim end k i k q 1 n is a direct limit of finite dimensional semisimple algebras q is the quiver without sources or sinks that is obtained by repeatedly removing all sinks and sources from q l q is the leavitt path algebra of q l q 0 is its degree zero component and q n is the quiver whose incidence matrix is the n th power of that for q it is also shown that all short exact sequences in qgr k q the full subcategory of finitely presented objects in qgr k q split consequently qgr k q can be given the structure of a triangulated category with suspension functor the serre degree twist 1 this triangulated category is equivalent to the singularity category d b d perf where is the radical square zero algebra k q k q 2 and d b is the bounded derived category of finite dimensional left modules

optimal instrumental variable estimation and approximate implementations the accuracy properties of instrumental variables iv methods are investigated extensions such as prefiltering of data and use of additional instruments are included in the analysis the parameter estimates are shown to be asymptotically gaussian distributed an explicit expression is given for the covariance matrix of their distribution the covariance matrix is then taken as a multivariable measure of accuracy it is shown how it can be optimized by an appropriate selection of instruments and prefilter the so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters a multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty this procedure includes modeling of the disturbance as an arma process using a statistically efficient method such as a prediction error method the statistical properties of the estimates obtained with the multistep procedure are also analyzed those estimates are shown to be asymptotically gaussian distributed as well the covariance matrix of the estimation errors is compared to that corresponding to a prediction error method for some model structures these two approaches give the same asymptotic accuracy the conclusion is that the multistep procedure which is quite easy to implement and also has nice uniqueness properties can be viewed as an interesting alternative to prediction error methods

finite element approximation of nematic liquid crystal flows using a saddle point structure in this work we propose finite element schemes for the numerical approximation of nematic liquid crystal flows based on a saddle point formulation of the director vector sub problem it introduces a lagrange multiplier that allows to enforce the sphere condition in this setting we can consider the limit problem without penalty and the penalized problem using a ginzburg landau penalty function in a unified way further the resulting schemes have a stable behavior with respect to the value of the penalty parameter a key difference with respect to the existing schemes two different methods have been considered for the time integration first we have considered an implicit algorithm that is unconditionally stable and energy preserving the linearization of the problem at every time step value can be performed using a quasi newton method that allows to decouple fluid velocity and director vector computations for every tangent problem then we have designed a linear semi implicit algorithm i e it does not involve nonlinear iterations and proved that it is unconditionally stable verifying a discrete energy inequality finally some numerical simulations are provided

existence and partial regularity of static liquid crystal configurations we establish the existence and partial regularity for solutions of some boundary value problems for the static theory of liquid crystals some related problems involving magnetic or electric fields are also discussed

an energy minimization finite element approach for the frank oseen model of nematic liquid crystals this paper outlines an energy minimization finite element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects the method targets minimization of the system free energy based on the frank oseen free energy model solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions this requires proving continuity coercivity and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite element framework error analysis demonstrates that the method constitutes a convergent scheme numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions the resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research

an energy law preserving c0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics in this paper we use finite element methods to simulate the hydrodynamical systems governing the motions of nematic liquid crystals in a bounded domain w we reformulate the original model in the weak form which is consistent with the continuous dissipative energy law for the flow and director fields in w 1 2 s w s 0 is an arbitrarily small number this enables us to use convenient conformal c 0 finite elements in solving the problem moreover a discrete energy law is derived for a modified midpoint time discretization scheme a fixed iterative method is used to solve the resulted nonlinear system so that a matrix free time evolution may be achieved and velocity and director variables may be solved separately a number of hydrodynamical liquid crystal examples are computed to demonstrate the effects of the parameters and the performance of the method

instrumental variable methods for arma spectral estimation the modified yule walker technique of arma spectral estimation is shown to be a special case of the instrumental variable method of system identification several recursive instrumental variable algorithms are proposed for adaptive spectral estimation including a new algorithm for the overdetermined case an efficient lattice algorithm is presented for solving the modified yule walker equations given the sample correlation coefficients the performance of some of the algorithms is illustrated by simulation results

category equivalences involving graded modules over weighted path algebras and weighted monomial algebras abstract let k be a field q a finite directed graph and kq its path algebra make kq an n graded algebra by assigning each arrow a positive degree let i be an ideal in kq generated by a finite number of paths and write a k q i let qgr a denote the quotient of the category of graded right a modules modulo the serre subcategory consisting of those graded modules that are the sum of their finite dimensional submodules this paper shows there is a finite directed graph q with all its arrows placed in degree 1 and an equivalence of categories qgr a qgr k q a result of smith now implies that qgr a mod s the category of right modules over an ultramatricial hence von neumann regular algebra s

a preconditioned nullspace method for liquid crystal director modeling we present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals the approach effectively deals with pointwise unit vector constraints which are prevalent in such models the indefinite saddle point nature of such problems which can arise from either or both of two sources pointwise unit vector constraints coupled electric fields is illustrated both analytical and numerical results are given for a model problem

least squares arma modeling of linear time varying systems lattice filter structures and fast rls algorithms the problem of modeling linear time varying systems is one of considerable importance in many varied and diverse applications this paper looks at ar ma and arma modeling of linear time varying systems with lattice filters there are two parts to this paper the first part develops the lattice filter structures in particular a new arma n m lattice filter structure is presented n ar order m ma order which is fully consistent with the geometric characteristics of the ar and ma lattice filter structures in that it evaluates all optimal arma i j filters of order lower than n m and each such filter is realized in terms of a fully orthogonal set of realization vectors for uncorrelated input this arma lattice filter simplifies greatly resulting in the white input arma lattice filter the second part of the paper develops new fast rls algorithms for the evaluation of the lattice filter coefficients there are two classes of algorithms presented one class is based on projection error sample averaging while the other uses input output sample averaging and some orthogonality relations this latter approach is equivalent to the exact rls formulation the algorithms of the former class are the most efficient modeling algorithms known to the authors and the algorithms of the latter class are of comparable or better efficiency than other algorithms in the same class

an optimal instrumental variable method for arma spectral estimation a multistep iterative and fast recursive algorithm for autoregressive moving average arma spectral estimation is presented the ar parameters of an arma process are estimated using the extended instrumental variable eiv method the optimal choice of instruments prefilter and weighting matrix is investigated a bootstrapping procedure that has computational convenience is proposed for the algorithm the statistical analysis and experiments show that the optimal iv estimate is unbiased consistent efficient asymptotically normal and equivalent to the maximum likelihood ml estimate and the prediction error pe estimate and the proposed algorithm has the advantages of sharper resolution less frequency bias and better efficiency of convergence

optimal instrumental variable estimates of the ar parameters of an arma process the modified yule walker myw equations for estimating the ar parameters of an arma process are presented as a special case of an instrumental variable iv method the consistency and accuracy of the ar parameter estimates are studied it is shown that estimation accuracy increases monotonically with the number of myw equations for an optimal choice of the weighting matrix used in the least squares solution of these equations the asymptotic error covariance of the optimal iv method equals that of the prediction error method the results of this paper verify experimental results reported in the literature regarding the performance of the myw method and provide the necessary accuracy analysis furthermore they suggest several simple asymptotically efficient multistep algorithms for estimating the ar parameters which are presented in a companion paper

fractional skew monoid rings abstract given an action of a monoid t on a ring a by ring endomorphisms and an ore subset s of t a general construction of a fractional skew monoid ring s op a t is given extending the usual constructions of skew group rings and of skew semigroup rings in case s is a subsemigroup of a group g such that g s 1s we obtain a g graded ring s op a s with the property that for each s s the s component contains a left invertible element and the s 1 component contains a right invertible element in the most basic case where g z and s t z the construction is fully determined by a single ring endomorphism of a if is an isomorphism onto a proper corner pap we obtain an analogue of the usual skew laurent polynomial ring denoted by a t t examples of this construction are given and it is proven that several classes of known algebras including the leavitt algebras of type 1 n can be presented in the form a t t finally mild and reasonably natural conditions are obtained under which s op a s is a purely infinite simple ring

newton s method with a model trust region modification a modified newton method for unconstrained minimization is presented and analyzed the modification is based upon the model trust region approach this report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified newton iteration several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis very strong convergence results are presented concerning the minimization algorithm in particular the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization with the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives

isomorphism and morita equivalence of graph algebras for any countable graph e we investigate the relationship between the leavitt path algebra l e and the graph c algebra c e for graphs e and f we examine ring homomorphisms ring homomorphisms algebra homomorphisms and algebra homomorphisms between l e and l f we prove that in certain situations isomorphisms between l e and l f yield isomorphisms between the corresponding c algebras c e and c f conversely we show that isomorphisms between c e and c f produce isomorphisms between l e and l f in specific cases the relationship between leavitt path algebras and graph c algebras is also explored in the context of morita equivalence

strongly graded groupoids and strongly graded steinberg algebras abstract we study strongly graded groupoids which are topological groupoids g equipped with a continuous surjective functor g to a discrete group such that 1 1 1 for all we introduce the category of graded g sheaves and prove an analogue of dade s theorem g is strongly graded if and only if every graded g sheaf is induced by a g e sheaf the steinberg algebra of a graded ample groupoid is graded and we prove that the algebra is strongly graded if and only if the groupoid is applying this result we obtain a complete graphical characterisation of strongly graded leavitt path and kumjian pask algebras

efficient solution of a toeplitz plus hankel coefficient matrix system of equations there are well known fast algorithms such as the levinson recursion for solving linear equations with a toeplitz or hankel coefficient matrix this paper extends the saving obtained by the levinson recursion for inversion of a toeplitz matrix to problems involving the inversion of matrices which are the sum of toeplitz and hankel matrices

a note on the isomorphism conjectures for leavitt path algebras abstract we relate two conjectures which have been raised for classification of leavitt path algebras for purely infinite simple unital leavitt path algebras it is conjectured that k 0 classifies them completely abrams et al 2008 2011 3 4 for arbitrary unital leavitt path algebras it is conjectured that k 0 gr classifies them completely hazrat in press 12 we show that for two finite graphs with no sinks which their associated leavitt path algebras include the purely infinite simple ones if their k 0 gr groups of their leavitt path algebras are isomorphic then their k 0 groups are isomorphic as well we also provide a short proof of the fact that for a finite graph its associated leavitt path algebra is strongly graded if and only if the graph has no sinks

the ericksen model of liquid crystals with colloidal and electric effects we present a robust discretization of the ericksen model of liquid crystals with variable degree of orientation coupled with colloidal effects and electric fields the total energy consists of the ericksen energy a weak anchoring or penalized dirichlet energy to model colloids and an electrical energy for a given electric field we describe our special discretization of the total energy along with a method to compute minimizers via a discrete quasi gradient flow algorithm which has a strictly monotone energy decreasing property numerical experiments are given in two and three dimensions to illustrate that the method is able to capture non trivial defect patterns such as the saturn ring defect we conclude with a rigorous proof of the convergence of our discrete energy to the continuous energy

local fourier analysis for mixed finite element methods for the stokes equations abstract in this paper we develop a local fourier analysis of multigrid methods based on block structured relaxation schemes for stable and stabilized mixed finite element discretizations of the stokes equations to analyse their convergence behaviour three relaxation schemes are considered distributive braess sarazin and uzawa relaxation from this analysis parameters that minimize the local fourier analysis smoothing factor are proposed for the stabilized methods with distributive and braess sarazin relaxation considering the failure of the local fourier analysis smoothing factor in predicting the true two grid convergence factor for the stable discretization we numerically optimize the two grid convergence predicted by local fourier analysis in this case we also compare the efficiency of the presented algorithms with variants using inexact solvers finally some numerical experiments are presented to validate the two grid and multigrid convergence factors

degenerate 3 dimensional sklyanin algebras are monomial algebras abstract the 3 dimensional sklyanin algebras s a b c form a flat family parametrized by points a b c p 2 d where d is a set of 12 points when a b c d the algebras having the same defining relations as the 3 dimensional sklyanin algebras are called degenerate sklyanin algebras c walton showed they do not have the same properties as the non degenerate ones here we prove that a degenerate sklyanin algebra is isomorphic to the free algebra on u v and w modulo either the relations u 2 v 2 w 2 0 or the relations u v v w w u 0 these monomial algebras are zhang twists of each other therefore all degenerate sklyanin algebras have the same category of graded modules a number of properties of the degenerate sklyanin algebras follow from this observation we exhibit a quiver q and an ultramatricial algebra r such that if s is a degenerate sklyanin algebra then the categories qgr s qgr k q and mod r are equivalent here qgr denotes the category of graded right modules modulo the full subcategory of graded modules that are the sum of their finite dimensional submodules the group of cube roots of unity 3 acts as automorphisms of the free algebra on two variables f in such a way that qgr s is equivalent to qgr f 3

constrained optimization for liquid crystal equilibria this paper compares the performance of penalty and lagrange multiplier approaches for the necessary unit length constraint in the computation of liquid crystal equilibrium configurations building on previous work in siam j sci comput 37 2015 pp s157 s176 siam j numer anal 53 2015 pp 2226 2254 the penalty method is derived and well posedness of the linearizations within the nonlinear iteration is discussed in addition the paper considers the effects of tailored trust region methods in the context of finite element discretizations and nested iteration for both formulations such methods are aimed at increasing the efficiency and robustness of each algorithm s nonlinear iterations three representative elastic equilibrium problems are considered to examine each method s performance the first two configurations have analytical expressions for their exact solutions and therefore convergence to the true solution is considered the third problem considers complicated boundary conditio

time series analysis in the frequency domain this correspondence presents a parametric frequency domain identification algorithm for autoregressive moving average arma processes that does not suffer from spectral leakage errors it is based on an extended transfer function model that takes into account the begin and end effect of the finite data record the relationship with the one step ahead prediction error method is established the advantages of the proposed method are easy prefiltering and leakage free spectral representation of the raw data

perpendicular categories with applications to representations and sheaves this paper is concerned with the omnipresence of the formation of the subcategories right left perpendicular to a subcategory of objects in an abelian category we encounter these subcategories in various contexts the formation of quotient categories with respect to localizing subcategories cf section 2 the deletion of vertices and shrinking of arrows see 37 in the representation theory of finite dimensional algebras cf section 5 the comparison of the representation theories of different extended dynkin quivers cf section 10 the theory of tilting cf sections 4 and 6 the study of homological epimorphisms of rings cf section 4 the passage from graded modules to coherent sheaves on a possibly weighted projective variety or scheme cf section 7 and 21 the study of maximal cohen macaulay modules over surface singularities cf sections the comparison of weighted projective lines for different weight sequences cf section 9 the formation of affine and local algebras attached to path algebras of extended dynkin quivers canonical algebras and weighted projective lines cf section 11 and 21 and the concept of universal localization in 40 formation of the perpendicular category has many aspects in common with localization and allows one to dispose of localization techniques in situations not accessible to any of the classical concepts of localization this applies in particular to applications in the domain of finite dimensional algebras and their representations several applications of the methods presented in this paper are already in existence partly published or appearing in print in the near future see for instance 40 39 4 45 26 49 46 and have show the versatility of the notion of a perpendicular category it seems that right perpendicular categories first appeared as the subcategories of so called closed objects in the process of the formation of the quotient cateogory of an abelian category with respect to a localizing serre subcategory see 18 47 34 another natural occurrence is encountered in commutative algebra forming the possibly infinitely generated modules of depth 2 cf section 7 the concept and some of the central applications were first presented in a talk given by the first author at the honnef meeting in january 1985 we also note that the perfectly matching nomination perpendicular category was coined by a schofield who discovered independently the usefulness of this concept in dealing with hereditary algebras see 39 cf also section 7 the authors further acknowledge the support of the deutsche forschungsgemeinschaft spp darstellungstheorie von endlichen gruppen und endlichdimensionalen algebren throughout this paper rings are associative with unit and modules are unitary right modules mod r respectively mod r denotes the category of all respectively all finitely presented right r modules

energy minimization for liquid crystal equilibrium with electric and flexoelectric effects this paper outlines an energy minimization finite element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields the method targets minimization of free energy based on the electrically and flexoelectrically augmented frank oseen free energy models the hessian resulting from the linearization of the first order optimality conditions is shown to be invertible for both models when discretized by a mixed finite element method under certain assumptions this implies that the intermediate discrete linearizations are well posed a coupled multigrid solver with vanka type relaxation is proposed and numerically vetted for approximation of the solution to the linear systems arising in the linearizations two electric model numerical experiments are performed with the proposed multigrid solver the first compares the algorithm s solution of a classical freedericksz transition problem to the known analytical solution and demons

finitely presented simple modules over leavitt path algebras abstract let e be an arbitrary graph and k be any field we construct various classes of non isomorphic simple modules over the leavitt path algebra l k e induced by vertices which are infinite emitters closed paths which are exclusive cycles and paths which are infinite and call these simple modules chen modules it is shown that every primitive ideal of l k e can be realized as the annihilator ideal of some chen module our main result establishes the equivalence between a graph theoretic condition and various conditions concerning the structure of simple modules over l k e

a renormalized newton method for liquid crystal director modeling we consider the nonlinear systems of equations that result from discretizations of a prototype variational model for the equilibrium director field characterizing the orientational properties of a liquid crystal material in the presence of pointwise unit vector constraints and coupled electric fields the numerical solution of such equations by lagrange newton methods leads to linear systems with a double saddle point form for which we have previously proposed a preconditioned nullspace method as an effective solver a ramage and e c gartland jr siam j sci comput 35 2013 pp b226 b247 here we propose and analyze a modified outer iteration renormalized newton method in which the orientation variables are normalized onto the constraint manifold at each iterative step this scheme takes advantage of the special structure of these problems and we prove that it is locally quadratically convergent the renormalized newton method bears some resemblance to the truncated newton method of

approximate solution of the trust region problem by minimization over two dimensional subspaces the trust region problem minimization of a quadratic function subject to a spherical trust region constraint occurs in many optimization algorithms in a previous paper the authors introduced an inexpensive approximate solution technique for this problem that involves the solution of a two dimensional trust region problem they showed that using this approximation in an unconstrained optimization algorithm leads to the same theoretical global and local convergence properties as are obtained using the exact solution to the trust region problem this paper reports computational results showing that the two dimensional minimization approach gives nearly optimal reductions in then dimension quadratic model over a wide range of test cases we also show that there is very little difference in efficiency and reliability between using the approximate or exact trust region step in solving standard test problems for unconstrained optimization these results may encourage the application of similar approximate trust region techniques in other contexts

finite element analysis of the landau de gennes minimization problem for liquid crystals this paper describes the landau de gennes free energy minimization problem for computing equilibrium configurations of the tensor order parameter field that characterizes the molecular orientational properties of liquid crystal materials analytical and numerical issues are addressed conditions guaranteeing well posedness existence regularity of the problem are given as is a nonlinear finite element convergence analysis

the dynamics of leavitt path algebras abstract recently it was shown that the notion of flow equivalence of shifts of finite type in symbolic dynamics is related to the morita theory and the grothendieck group in the theory of leavitt path algebras abrams et al 2011 4 in this paper we show that the notion of the conjugacy of shifts of finite type is closely related to the graded morita theory and consequently the graded grothendieck group this fits into the general framework we have in these two theories conjugacy yields the flow equivalence and the graded morita equivalence can be lifted to the morita equivalence starting from a finite directed graph the observation that the graded grothendieck group of the leavitt path algebra associated to e coincides with the krieger dimension group of the shift of finite type associated to e provides a link between the theory of leavitt path algebras and symbolic dynamics it has been conjectured that the ordered graded grothendieck group as z x x 1 module we call this the graded dimension group classifies the unital leavitt path algebras completely hazrat 2013 20 via the above correspondence utilising the results from symbolic dynamics we prove that for two purely infinite simple unital leavitt path algebras if their graded dimension groups are isomorphic then the algebras are isomorphic

quantum spheres and projective spaces as graph algebras the c algebras of continuous functions on quantum spheres quantum real projective spaces and quantum complex projective spaces are realized as cuntz krieger algebras corresponding to suitable directed graphs structural results about these quantum spaces especially about their ideals and k theory are then derived from the general theory of graph algebras it is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle respectively

on simple modules over leavitt path algebras abstract given an arbitrary graph e and any field k a new class of simple modules over the leavitt path algebra l k e is constructed by using vertices that emit infinitely many edges in e the corresponding annihilating primitive ideals are also described given a fixed simple l k e module s we compute the cardinality of the set of all simple l k e modules isomorphic to s using a boolean subring of idempotents induced by paths in e bounds for the cardinality of the set of distinct isomorphism classes of simple l k e modules are given we also obtain a complete structure theorem about the leavitt path algebra l k e of a finite graph e over which every simple module is finitely presented

a saddle point approach to the computation of harmonic maps in this paper we consider numerical approximations of a constraint minimization problem where the object function is a quadratic dirichlet functional for vector fields and the interior constraint is given by a convex function the solutions of this problem are usually referred to as harmonic maps the solution is characterized by a nonlinear saddle point problem and the corresponding linearized problem is well posed near strict local minima the main contribution of the present paper is to establish a corresponding result for a proper finite element discretization in the case of two space dimensions iterative schemes of newton type for the discrete nonlinear saddle point problems are investigated and mesh independent preconditioners for the iterative methods are proposed

recursive estimation of mixed autoregressive moving average order summary the order p q of an autoregressive moving average sequence y t may be estimated by minimizing a criterion log 2 p q log t t with respect to p and q where 2 is the maximum likelihood estimate of the variance of the innovations t it is suggested that instead a2 be estimated from a series of regressions of y t on y t 1 y t 2 y t p 5 t 1 t q where the t are obtained by fitting a long autoregression to the data it is shown how the sequence of regressions may for p q be economically recursively calculated by embedding them in a sequence of bivariate autoregressions asymptotic properties of the procedure are established under very general conditions

numerical analysis of vanka type solvers for steady stokes and navier stokes flows we consider vanka type smoothers for solving stokes and navier stokes problems in each iteration step this smoother requires the solution of several small local subproblems over finite element blocks it is shown that for particular choices for the blocks the algorithm always converges to the solution of the stokes problem and under suitable conditions to the solution of the navier stokes problem the convergence properties are analyzed and numerical examples are presented