the novikov conjecture for algebraic k theory of the group algebra over the ring of schatten class operators abstract in this paper we prove the algebraic k theory novikov conjecture for group algebras over the ring of schatten class operators the main technical tool in the proof is an explicit construction of the connes chern character

banach strong novikov conjecture for polynomially contractible groups abstract we prove the banach strong novikov conjecture for groups having polynomially bounded higher order combinatorial functions this includes all automatic groups

space time continuous analysis of waveform relaxation for the heat equation waveform relaxation algorithms for partial differential equations pdes are traditionally obtained by discretizing the pde in space and then splitting the discrete operator using matrix splittings for the semidiscrete heat equation one can show linear convergence on unbounded time intervals and superlinear convergence on bounded time intervals by this approach however the bounds depend in general on the mesh parameter and convergence rates deteriorate as one refines the mesh motivated by the original development of waveform relaxation in circuit simulation where the circuits are split in the physical domain into subcircuits we split the pde by using overlapping domain decomposition we prove linear convergence of the algorithm in the continuous case on an infinite time interval at a rate depending on the size of the overlap this result remains valid after discretization in space and the convergence rates are robust with respect to mesh refinement the algorithm is in the class of waveform relaxation algorithms based on overlapping multisplittings our analysis quantifies the empirical observation by jeltsch and pohl siam j sci comput 16 1995 pp 40 49 that the convergence rate of a multisplitting algorithm depends on the overlap numerical results are presented which support the convergence theory

waveform relaxation for reaction diffusion equations abstract we report a new waveform relaxation wr algorithm for general semi linear reaction diffusion equations the superlinear rate of convergence of the new wr algorithm is proved and we also show the advantages of the new approach superior to the classical wr algorithms by the estimation on iteration errors the corresponding discrete wr algorithm for reaction diffusion equations is presented and further the parallelism of the discrete wr algorithm is analyzed moreover the new approach is extended to handle the coupled reaction diffusion equations numerical experiments are carried out to verify the effectiveness of the theoretic work

the domino problem of the hyperbolic plane is undecidable in this paper we prove that the general tiling problem of the hyperbolic plane is undecidable by proving a slightly stronger version using only a regular polygon as the basic shape of the tiles the problem was raised by a paper of raphael robinson in 1971 in his famous simplified proof that the general tiling problem is undecidable for the euclidean plane initially proved by robert berger in 1966

self affine delone sets and deviation phenomena we study the growth of norms of ergodic integrals for the translation action on spaces coming from expansive self affine delone sets the linear map giving the self affinity induces a renormalization map on the pattern space and we show that the rate of growth of ergodic integrals is controlled by the induced action of the renormalizing map on the cohomology of the pattern space up to boundary errors we explore the consequences for the diffraction of such delone sets and explore in detail what the picture is for substitution tilings as well as for cut and project sets which are self affine we also explicitly compute some examples

higher index theory for certain expanders and gromov monster groups ii abstract in this paper the first of a series of two we continue the study of higher index theory for expanders we prove that if a sequence of graphs is an expander and the girth of the graphs tends to infinity then the coarse baum connes assembly map is injective but not surjective for the associated metric space x expanders with this girth property are a necessary ingredient in the construction of the so called gromov monster groups that coarsely contain expanders in their cayley graphs we use this connection to show that the baum connes assembly map with certain coefficients is injective but not surjective for these groups using the results of the second paper in this series we also show that the maximal baum connes assembly map with these coefficients is an isomorphism

quasiperiodic tilings with tenfold symmetry and equivalence with respect to local derivability two 2d quasiperiodic tilings with generalized tenfold symmetry are derived from the lattice a4r the reciprocal of the root lattice a4 both tilings are built from four tiles triangles in one case rhombi and hexagons in the other after a brief description of the tilings and their structures the authors introduce the equivalence concept of mutual local derivability they present its key properties and its application to several tenfold tilings and discuss some implications on a future classification of tilings in position space

schwarz waveform relaxation methods for parabolic equations in space frequency domain some schwarz waveform relaxation algorithms based on frequency domain analysis for parabolic equations are proposed and analyzed in this paper we mainly study an overlapping process with dirichlet transmission conditions and a non overlapping process with robin transmission conditions the convergence conditions for these algorithms are also obtained by our frequency domain analysis numerical experiments are given to illustrate effectiveness of the algorithms

convergence of waveform relaxation methods for differential algebraic systems this paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of picard iterations and more general waveform relaxation methods for differential algebraic systems of neutral type the results are obtained by the contraction mapping principle on banach spaces with weighted norms and by the use of the perron frobenius theory of nonnegative and nonreducible matrices it is demonstrated that waveform relaxation methods are convergent faster than the classical picard iterations

alternating splitting waveform relaxation method and its successive overrelaxation acceleration for the large sparse implicit linear initial value problem we present a block successive overrelaxation scheme for the alternating direction implicit waveform relaxation method to further accelerate its convergence speed and discuss the convergence property of the resulting iteration method in detail numerical implementations about several non hermitian implicit linear initial value problems show that the alternating direction implicit waveform relaxation method is very effective and the block successive overrelaxation technique really accelerates its convergence speed

multigrid methods for implicit runge kutta and boundary value method discretizations of parabolic pdes advanced time discretization schemes for stiff systems of ordinary differential equations odes such as implicit runge kutta and boundary value methods have many appealing properties however the resulting systems of equations can be quite large and expensive to solve many techniques exploiting the structure of these systems have been developed for general odes for spatial discretizations of time dependent partial differential equations pdes these techniques are in general not sufficient and also the structure arising from spatial discretization has to be taken into consideration we show here that for time dependent parabolic problems this can be done by multigrid methods as in the stationary elliptic case the key to this approach is the use of a smoother that updates several unknowns at a spatial grid point simultaneously the overall cost is essentially proportional to the cost of integrating a scalar ode for each grid point combination of the multigrid principle with both time stepping and waveform relaxation techniques is described together with a convergence analysis numerical results are presented for the isotropic heat equation and a general diffusion equation with variable coefficients

regular production systems and triangle tilings we discuss regular production systems as a tool for analyzing tilings in general as an application we give necessary and sufficient conditions for a generic triangle to admit a tiling of and show that almost every triangle that admits a tiling is weakly aperiodic we pause for informal discussion of a variety of other applications such as non quasi isometric maps between regular tilings non periodic archimedean tilings growth and decidability most generally regular production systems provide a model for the organized growth of surfaces along a front subject to local rules

electrons in deterministic quasicrystalline potentials and hidden conserved quantities we propose an ansatz for the wave function of a non interacting quantum particle in a deterministic quasicrystalline potential it is applicable to both continuous and discrete models and includes sutherland s hierarchical wave function as a special case the ansatz is parameterized by a first cohomology class of the hull of the structure the structure of the ansatz and the values of its parameters are preserved by the time evolution numerical results suggest that the ground states of the standard vertex models on ammann beenker and penrose tilings belong to this class of functions this property remains valid for the models perturbed within their mutual local derivability class e g by adding links along diagonals of rhombi the convergence of the numerical simulations in a finite patch of the tiling critically depends on the boundary conditions and can be significantly improved when the choice of the latter respects the structure of the ansatz

fibrations of classifying spaces we investigate fibrations of the form z y x where two of the three spaces are classifying spaces of compact connected lie groups we obtain certain finiteness conditions on the third space which make it also a classifying space our results allow to express some of the basic notions in group theory in terms of homotopy theory i e in terms of classifying spaces as an application we prove that every retract of the classifying space of a compact connected lie group is again a classifying space

a schwarz waveform moving mesh method an r refinement moving mesh method is considered for solving time dependent partial differential equations pdes the resulting coupled system consisting of the physical pde and a moving mesh pde is solved by a schwarz waveform relaxation method in particular the computational space time domain is decomposed into overlapping subdomains and the solution obtained by iteratively solving the system of pdes on each subdomain dirichlet boundary conditions are used to pass solution information between neighboring regions the efficacy of this approach is demonstrated for some model problems for problems where the solutions evolve on disparate time scales in different regions of the spatial domain this approach demonstrates the significant savings in computational time and effort which are possible

optimized schwarz waveform relaxation for advection reaction diffusion equations in two dimensions optimized schwarz waveform relaxation methods have been developed over the last decade for the parallel solution of evolution problems they are based on a decomposition in space and an iteration where only subproblems in space time need to be solved each subproblem can be simulated using an adapted numerical method for example with local time stepping or one can even use a different model in different subdomains which makes these methods very suitable also from a modeling point of view for rapid convergence however it is important to use effective transmission conditions between the space time subdomains and for best performance these transmission conditions need to take the physics of the underlying evolution problem into account the optimization of these transmission conditions leads to mathematically hard best approximation problems of homographic functions we study in this paper in detail the best approximation problem for the case of linear advection reaction diffusion equations in two spatial dimensions we prove comprehensively best approximation results for transmission conditions of robin and ventcel higher order type which can also be used in the various limits for example for the heat equation since we include in our analysis a positive low frequency limiter both in space and time we give for each case closed form asymptotic values for the parameters which can directly be used in implementations of these algorithms and which guarantee asymptotically best performance of the iterative methods we finally show extensive numerical experiments including cases not covered by our analysis for example decompositions with cross points we use q1 finite element discretizations in space and forward and backward euler discretizations in time other discretization could also have been considered since all our analysis is at the continuous level and in all cases we measure performance corresponding to our analysis

uniform k theory and poincare duality for uniform k homology abstract we revisit spakula s uniform k homology construct the external product for it and use this to deduce homotopy invariance of uniform k homology we define uniform k theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry we further construct a cap product with uniform k homology and prove poincare duality between uniform k theory and uniform k homology on spinc manifolds of bounded geometry

a hierarchical strongly aperiodic set of tiles in the hyperbolic plane we give a new construction of strongly aperiodic set of tiles in h 2 exhibiting a kind of hierarchical structure simplifying the central framework of margenstern s proof that the domino problem is undecidable in the hyperbolic plane margenstern 2008 16

convergence analysis of a periodic like waveform relaxation method for initial value problems via the diagonalization technique we present in this paper a time parallel algorithm for dot u f t u with initial value u 0 u 0 by using the waveform relaxation wr technique and the diagonalization technique with a suitable parameter alpha the wr technique generates a functional sequence u k t via the dynamic iterations dot u k f t u k u k 0 alpha u k t alpha u k 1 t u 0 and at convergence we get u infty t u t each wr iterate represents a periodic like differential equation which is very suitable for applying the diagonalization technique yielding direct parallel in time computation the parameter alpha controls both the roundoff error arising from the diagonalization procedure and the convergence factor of the wr iterations and we perform a detailed analysis for the influence of the parameter alpha on the method we show that the roundoff error is proportional to epsilon 2n 1 max alpha 2 alpha 2 n t vardelta t and epsilon is the machine precision and the convergence factor can be bounded by alpha e tl 1 alpha e tl where l ge 0 is the one sided lipschitz constant of f we also perform a convergence analysis at the discrete level and the effect of temporal discretizations is explored our analysis includes the heat and wave equations as special cases numerical results are given to support our findings

waveform relaxation methods for fractional differential equations with the caputo derivatives in this paper we report new waveform relaxation methods for fractional differential equations with the caputo derivatives the convergence properties of the waveform relaxation methods are studied under linear and nonlinear conditions for the right hand side of equations some convergent splittings are given this is the first time for studying the waveform relaxation methods for fractional differential equations in references

characteristic classes and distortion of diffeomorphisms let m and n be manifolds of bounded geometry that is the absolute value of their curvatures as well as their covariant derivatives are bounded from above and their injectivity radii are bounded from below a map f m n has bounded d stortion if there is an upper bound on the norm of the derivative d f a bounded distortion diffeomorphism cb d d is assumed to have an inverse which also has bounded distortion similarly homotopies are assumed to have bounded distortion note that this implies that homotopic maps are a finite distance apart we prove the following theorem that describes when characteristic classes of a compact manifold obstruct the existence of bounded distortion diffeomorphisms of universal covers theorem there are compact manifolds a and b with fundamental group r and a map f a b with jcpcb i pca for some rational pontrjagin class p whose universal cover is b d homotopic to a b d diffeomorphism if and only if r is nonamenable

np problems are tractable in the space of cellular automata in the hyperbolic plane in this paper we define cellular automata on a grid of the hyperbolic plane that is based on the tessellation obtained from the regular pentagon with right angles owing to the properties of that grid we show that 3 sat can be solved in polynomial time in that peculiar setting then we extend that result for any np problem on this ground several directions are indicated

residual restarting and richardson iteration for the matrix exponential a well known problem in computing some matrix functions iteratively is the lack of a clear commonly accepted residual notion an important matrix function for which this is the case is the matrix exponential suppose the matrix exponential of a given matrix times a given vector has to be computed we develop the approach of druskin greenbaum and knizhnerman siam j sci comput 19 1998 pp 38 54 and interpret the sought after vector as the value of a vector function satisfying the linear system of ordinary differential equations odes whose coefficients form the given matrix the residual is then defined with respect to the initial value problem for this ode system the residual introduced in this way can be seen as a backward error we show how the residual can be computed efficiently within several iterative methods for the matrix exponential this resolves the question of reliable stopping criteria for these methods further we show that the residual concept can be used to construct new residual based iterative methods in particular a variant of the richardson method for the new residual appears to provide an efficient way to restart krylov subspace methods for evaluating the matrix exponential

equicontinuous foliated spaces riemannian foliations are characterized as those foliations whose holonomy pseudogroup consists of local isometries of a riemannian manifold their main structural features are well understood since the work of molina in this paper we analyze the more general concept of equicontinuous pseudogroup of homeomorphisms which gives rise to the notion of equicontinuous foliated space we show that equicontinuous foliated spaces have structural properties similar to those known for riemannian foliations the universal covers of their leaves are in the same quasi isometry class leaf closures are homogeneous spaces and the holonomy pseudogroup is indeed given by local isometries

computing periodic solutions of linear differential algebraic equations by waveform relaxation we propose an algorithm which is based on the waveform relaxation wr approach to compute the periodic solutions of a linear system described by differential algebraic equations for this kind of two point boundary problems we derive an analytic expression of the spectral set for the periodic wr operator we show that the periodic wr algorithm is convergent if the supremum value of the spectral radii for a series of matrices derived from the system is less than 1 numerical examples where discrete waveforms are computed with a backward difference formula further illustrate the correctness of the theoretical work in this paper

multigrid waveform relaxation on spatial finite element meshes the continuous time case the waveform relaxation method and its multigrid acceleration are studied as solution procedures for the system of ordinary differential equations obtained by finite element discretisation of a linear parabolic initial boundary value problem the convergence properties of the continuous time algorithm are theoretically investigated on finite length and infinite length time intervals in addition quantitative convergence estimates and numerical results are presented for one dimensional and two dimensional model problems

amenability and uniform roe algebras abstract amenability for groups can be extended to metric spaces algebras over commutative fields and c algebras by adapting the notion of folner nets in the present article we investigate the close ties among these extensions and show that these three pictures unify in the context of the uniform roe algebra c u x over a metric space x d with bounded geometry in particular we show that the following conditions are equivalent 1 x d is amenable 2 the translation algebra generating c u x is algebraically amenable 3 c u x has a tracial state 4 c u x is not properly infinite 5 1 0 0 0 in the k 0 group k 0 c u x 6 c u x does not contain the leavitt algebra as a unital subalgebra 7 c u x is a folner c algebra in the sense that it admits a net of unital completely positive maps into matrices which is asymptotically multiplicative in the normalized trace norm we also show that every possible tracial state of the uniform roe algebra c u x is amenable

relative property a and relative amenability for countable groups abstract we define a relative property a for a countable group with respect to a finite family of subgroups many characterizations for relative property a are given in particular a relative bounded cohomological characterization shows that if g has property a relative to a family of subgroups h and if each h h has property a then g has property a this result leads to new classes of groups that have property a in particular groups are of property a if they act cocompactly on locally finite property a spaces of bounded geometry with any stabilizer of property a specializing the definition of relative property a an analogue definition of relative amenability for discrete groups is introduced and similar results are obtained

minimal configurations for the frenkel kontorova model on a quasicrystal in this paper we consider the frenkel kontorova model of a one dimensional chain of atoms submitted to a potential this potential splits into an interaction potential and a potential induced by an underlying substrate which is a quasicrystal under standard hypotheses we show that every minimal configuration has a rotation number that the rotation number varies continuously with the minimal configuration and that every non negative real number is the rotation number of a minimal configuration this generalizes well known results obtained by s aubry and p y le daeron in the case of a crystalline substrate

the pinwheel tilings of the plane prototiles in euclidean n space en for n 2 the prototiles are usually required to be rather nice topologically at least homeomorphs of the closed unit ball one then makes arbitrarily many congruent copies called tiles of these prototiles and considers all ways called tilings that such tiles may provide a simultaneous covering and packing of en a tiling is thus an unordered collection of tiles for which the union is all of en but such that the interiors of each pair of tiles do not intersect wang s original problem was to determine if it was possible to have a finite set of prototiles with associated tilings of space for which all the tilings were nonperiodic a tiling is nonperiodic if it is not invariant under any single simultaneous translation of its tiles this was settled in the affirmative in the thesis of wang s student robert berger 1

the z theorem for compact lie groups keywords categories of finite p subgroups z theorem compact lie group control of fusion p toral subgroups mod p cohomology reference ctg article 1991 001doi 10 1007 bf01445193 record created on 2008 12 16 modified on 2017 05 12

waveform relaxation with fast direct methods as preconditioner for a restricted class of parabolic pdes one can devise a practical numerical solver with a parallel complexity that is theoretically optimal the method uses a multidimensional fft to decouple the unknowns in the spatial domain into independent scalar odes these are discretized to give recurrence relations in the time dimension solved by parallel cyclic reduction this is the fft cr algorithm we discuss the use of fft cr as a preconditioner to iteratively solve more general parabolic pdes this approach naturally leads to a waveform relaxation scheme waveform relaxation was developed as an iterative method for solving large systems of odes it is the continuous in time analogue of stationary iterative methods for linear algebraic equations using the fft cr solver as a preconditioner preserves most of the potential for concurrency that accounts for the attractiveness of waveform relaxation with simple preconditioners like jacobi or red black gauss seidel while showing an important advantage the convergence rate of the resulting iteration is independent of the mesh size used in the spatial discretization the method can be accelerated by applying an appropriate scaling of the system before preconditioning

convergence analysis of waveform relaxation methods for neutral differential functional systems in this paper the problems of convergence and superlinear convergence of continuous time waveform relaxation method applied to volterra type systems of neutral functional differential equations are discussed under a lipschitz condition with time and delay dependent right hand side imposed on the so called splitting function more suitable conditions about convergence and superlinear convergence of continuous time wr method are obtained we also investigate the initial interval acceleration strategy for the practical implementation of the continuous time waveform relaxation method i e discrete time waveform relaxation method it is shown by numerical results that this strategy is efficacious and has the essential acceleration effect for the whole computation process

isoperimetry of group actions the isoperimetric profile of a discrete group was introduced by vershik however it is well defined only for a restrictive class amenable groups we generalize the notion of isoperimetric profile beyond the world of amenable groups by defining isoperimetric profiles of amenable actions of finitely generated groups on compact topological spaces this allows to extend the definition of the isoperimetric profile to all groups which are exact in such a way that for amenable groups it is equal to vershik s isoperimetric profile the main feature of our construction is that it preserves many of the properties known from the classical case we use these results to compute exact asymptotics of the isoperimetric profiles for several classes of non amenable groups

a strongly aperiodic set of tiles in the hyperbolic plane we construct the first known example of a strongly aperiodic set of tiles in the hyperbolic plane such a set of tiles does admit a tiling but admits no tiling with an infinite cyclic symmetry this can also be regarded as a regular production system 5 that does admit bi infinite orbits but admits no periodic orbits

an etale approach to the novikov conjecture we show that the rational novikov conjecture for a group of finite homological type follows from the mod 2 acyclicity of the higson compactification of an e we then show that for groups of finite asymptotic dimension the higson compactification is mod p acyclic for all p and deduce the integral novikov conjecture for these groups 2007 wiley periodicals inc

uniform k homology theory we define a uniform version of analytic k homology theory for separable proper metric spaces furthermore we define an index map from this theory into the k theory of uniform roe c algebras analogous to the coarse assembly map from analytic k homology into the k theory of roe c algebras we show that our theory has a mayer vietoris sequence we prove that for a torsion free countable discrete group the direct limit of the uniform k homology of the rips complexes of limd k u pd is isomorphic to k top l the left hand side of the baum connes conjecture with coefficients in l in particular this provides a computation of the uniform k homology groups for some torsion free groups as an application of uniform k homology we prove a criterion for amenability in terms of vanishing of a fundamental class in spirit of similar criteria in uniformly finite homology and k theory of uniform roe algebras

a universal cellular automaton on the heptagrid of the hyperbolic plane with four states in this paper we construct a new weakly universal cellular automaton on the ternary heptagrid this significantly improves the previous result obtained by the same author in the same grid with six states this time the number of states is four this is the best result up to date for cellular automata in the hyperbolic plane with true planar motions

homotopy classification of self maps of bg via g actions to complete the classification of self maps of bg theorem 4 2 it remains to prove theorem 4 1 i e to show that the higher limits of certain functors n 1h 2 f p g z p wall vanish and that h0 mp g f i has the expected value in this section these limits h mp g hi will be calculated in the easy cases when g is a simply connected classical group i e one of the groups su n sp n or spin n or when i 2 the computation of h mp g hi for the simply connected exceptional lie groups will be put off until section 6 we begin with some general properties of higher limits let 6 be any small discrete category it is convenient when dealing with higher limits of functors on to let 4 moldenote the category of contravariant functors from v to ad then for any f e w muok we can identify

aperiodic tilings positive scalar curvature and amenability of spaces the object of this paper is to begin a geometric study of noncompact spaces whose local structure has bounded complexity manifolds of this sort arise as leaves of foliations of compact manifolds and as their universal covers we shall introduce a coarse homology theory using chains of bounded complexity and study some of its first properties the most interesting result characterizes when h uf x vanishes as an analogue and strengthening of f0lner s amenability criterion for groups in terms of isoperimetric inequalities see 4 one can view this result as producing a successful infinite ponzi scheme on any nonamenable space each point with only finite resources gives to some of its neighbors some of these resources yet receives more from the remaining neighbors as one can imagine this is useful for eliminating obstructions on noncompact spaces this has a number of applications we present two of them the first produces tilings that are unbalanced on any nonamenable polyhedron unbalanced tilings are automatically aperiodic and this gives many examples of sets of tiles that tile only aperiodically unfortunately imbalance is a particularly unsubtle reason for aperiodicity so that the aperiodic tilings of euclidean space penrose tilings are necessarily not accessible to our method on the other hand most other simply connected noncompact symmetric spaces even have unbalanced tilings using our criterion the second application regards characteristic numbers of manifolds whose universal covers have positive scalar curvature we prove a converse to a theorem of roe we show that for any nonamenable group f one can find a spin manifold with fundamental group f with nonzero a genus whose universal cover has a uniformly positive scalar curvature metric of bounded geometry in the natural strict quasi isometry class

tiling spaces are inverse limits let m be an arbitrary riemannian homogeneous space and let be a space of tilings of m with finite local complexity relative to some symmetry group and closed in the natural topology then is the inverse limit of a sequence of compact finite dimensional branched manifolds the branched manifolds are finite unions of cells constructed from the tiles themselves and the group this result extends previous results of anderson and putnam of ormes radin and sadun of bellissard benedetti and gambaudo and of gahler in particular the construction in this paper is a natural generalization of gahler s

an index theorem on open manifolds ii on decrit et on applique un nouveau theoreme d indice pour des operateurs elliptiques sur certaines varietes non compactes on calcule un indice a valeur reelle pour des operateurs de type dirac sur des varietes non compactes de geometrie bornee

bilipschitz equivalence is not equivalent to quasi isometric equivalence for finitely generated groups we show that certain lamplighter groups that are quasi isometric to each other are not bilipschitz equivalent this gives a positive answer to a question of de la harpe

time domain model order reduction of general orthogonal polynomials for linear input output systems for a class of large linear input output systems we present a new model order reduction algorithm based on general orthogonal polynomials in the time domain the main idea of the algorithm is first to expand the unknown state variables in the space spanned by orthogonal polynomials then the coefficient terms of polynomial expansion are calculated by a recurrence formula the basic procedure is to use the coefficient terms to generate a projection matrix many classic methods with orthogonal polynomials are special cases of the general approach the proposed approach has a good computational efficiency and preserves the stability and passivity under certain condition numerical experiments are reported to verify the theoretical analysis

model order reduction methods for coupled systems in the time domain using laguerre polynomials in this paper based on laguerre polynomials we present new methods for model reduction of coupled systems in the time domain by appropriately selected projection matrices a reduced order system is produced to retain the topology structure of the original system meanwhile it preserves a desired number of laguerre coefficients of the system s output thereby providing good approximation accuracy we also study the two sided projection method in the time domain as well as the stability of reduced order systems two numerical examples are used to illustrate the efficiency of the proposed methods

the large scale geometry of strongly aperiodic subshifts of finite type abstract a subshift on a group g is a closed g invariant subset of a g for some finite set a it is said to be a subshift of finite type sft if it is defined by a finite collection of forbidden patterns to be strongly aperiodic if all point stabilizers are trivial and weakly aperiodic if all point stabilizers are infinite index in g we show that groups with at least 2 ends have a strongly aperiodic sft and that having such an sft is a qi invariant for finitely presented groups we show that a finitely presented torsion free group with no weakly aperiodic sft must be qi rigid the domino problem on g asks whether the sft specified by a given set of forbidden patterns is empty we show that decidability of the domino problem is a qi invariant

monotone waveform relaxation for systems of nonlinear differential algebraic equations we present a monotone waveform relaxation algorithm which produces very tight upper and lower bounds of the transient response of a class of systems described by nonlinear differential algebraic equations daes that satisfy certain lipschitz conditions the choice of initial iteration is critical and we give two methods of finding it we show that the class of systems in which monotone convergence of waveform relaxation is possible is actually larger than previously reported numerical experiments are given to confirm the monotonicity of convergence of the algorithm

on time domain simulation of lossless transmission lines with nonlinear terminations a time domain approach is presented to solve nonlinear circuits with lossless transmission lines mathematically the circuits are described by a special kind of nonlinear differential algebraic equations daes with multiple constant delays in order to directly compute these delay systems in time domain decoupling by waveform relaxation wr is applied to the systems for the relaxation based method we provide a new convergence proof numerical experiments are given to illustrate the novel approach

exotic cohomology and index theory the main result of this paper is a version of the atiyah singer index theorem for dirac type operators on noncompact complete riemannian manifolds the statement of the theorem involves a novel cohomology theory for such manifolds this theory called exotic cohomology depends on the structure at infinity of a space more precisely it depends on the way that large bounded sets fit together for each cohomology class in this theory we define a higher index of a dirac type operator enjoying the stability and vanishing properties of the usual atiyah singer index these higher indices are analogous to the novikov higher signatures our main theorem will compute these higher indices in terms of standard topological invariants applications of this index theorem include a different approach to some of the results of gromov and lawson 10 on topological obstructions to positive scalar curvature the concept of index that we will use involves the a theory functors k0 and kx for operator algebras 3 14 suppose that b is an ideal in a unital algebra c and let t e c be invertible modulo b in the classical atiyah singer index theorem one takes c to be the bounded operators on the l space of some compact manifold b the compact operators and t an elliptic pseudodifferential operator of order zero then t has an index in the theory group kq b in the classical case this is just z and one recovers the usual fredholm index now let m be a complete riemannian manifold possibly noncompact in 18 i introduced an algebra m which is defined as follows sf m consists of all bounded operators a on l m that have a kernel representation

nonnegative solutions of fractional functional differential equations in this paper we discuss the existence and monotone iterative method of nonnegative solutions for fractional functional differential equations the main conclusion is that the nonnegative solutions can be derived from the monotone iterative method which starts off with a nonnegative upper solution or the zero function under different conditions our approach of obtaining nonnegative solutions is feasible for computational purposes

quantitative algebraic topology and lipschitz homotopy we consider when it is possible to bound the lipschitz constant a priori in a homotopy between lipschitz maps if one wants uniform bounds this is essentially a finiteness condition on homotopy this contrasts strongly with the question of whether one can homotop the maps through lipschitz maps we also give an application to cobordism and discuss analogous isotopy questions