a stabilized conforming nodal integration for galerkin mesh free methods domain integration by gauss quadrature in the galerkin mesh free methods adds considerable complexity to solution procedures direct nodal integration on the other hand leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration for convergence an integration constraint ic is introduced as a necessary condition for a linear exactness in the mesh free galerkin approximation the gradient matrix of strain smoothing is shown to satisfy ic using a divergence theorem no numerical control parameter is involved in the proposed strain smoothing stabilization the numerical results show that the accuracy and convergent rates in the mesh free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method it is also demonstrated that the gauss integration method fails to meet ic in mesh free discretization for this reason the proposed method provides even better accuracy than gauss integration for galerkin mesh free method as presented in several numerical examples copyright 2001 john wiley sons ltd

a new cloud based hp finite element method a hybrid computational method for solving boundary value problems is introduced which combines features of the meshless hp cloud methods with features of conventional finite elements the method admits straightforward nonuniform hp type approximations easy implementation of essential boundary conditions is robust under severe distortions of the mesh and can deliver exponential rates of convergence results of numerical experiments are presented

on tracial approximation let c be a class of unital c algebras the class tac of c algebras which can be tracially approximated in the egorov like sense first considered by lin by the c algebras in c is studied lin considered the case that c consists of finite dimensional c algebras or the tensor products of such with c 0 1 in particular the question is considered whether for any simple separable a tac there is a c algebra b which is a simple inductive limit of certain basic homogeneous c algebras together with c algebras in c such that the elliott invariant of a is isomorphic to the elliott invariant of b an interesting case of this question is answered in the final part of the paper the question is also considered which properties of c algebras are inherited by tracial approximation results of this kind are obtained which are used in the proof of the main theorem of the paper and also in the proof of the classification theorem of the second author given in z niu a classification of tracially approximately splitting tree algebra in preparation and z niu a classification of certain tracially approximately subhomogeneous c algebras phd thesis university of toronto 2005 which also uses the main result of the present paper

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

the partition of unity method for the elastically supported beam abstract the partition of unity method pum is used to solve the timoshenko beam with elastic support some important features of this new method are addressed but the main concern is to overcome locking and to resolve boundary layer we prove that by a proper selection of the local basis functions the method is free of locking at the thin beam limit and exhibits no numerical boundary layer for strong elastic support optimal convergent rate is established in the energy norm and it is uniformly valid with respect to the thickness of the beam and toughness of the elastic support furthermore the computed shear stress is also convergent uniformly with optimal rate

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

scaling of the average weighted receiving time on a family of double weighted hierarchical networks abstract in this paper we introduce a family of double weighted hierarchical networks which is depended on the initial complete bipartite graph and two weight factors r w 0 r 1 0 w 1 then we consider the biased walk in the double weighted hierarchical networks what is more we define two weighted times the mean weighted first passing time mwfpt and the average weighted receiving time awrt according to the definition we calculate the exact expressions of the mwfpt and the awrt on the double weighted hierarchical networks the expressions we obtain in this paper illustrate that the awrt tends to a constant when the size of the networks increases while if n 2 4 n 1 n 2 1 w 2 where n 1 and n 2 denote the number of nodes in initial complete bipartite graph and n n 1 n 2 holds the awrt grows as a power law function of network order with the exponent denoted by log n n k

orbital hp clouds for solving schrodinger equation in quantum mechanics solving schrodinger equation in quantum mechanics presents a challenging task in numerical methods due to the high order behavior and high dimension characteristics in the wave functions in addition to the highly coupled nature between wave functions this work introduces orbital and polynomial enrichment functions to the partition of unity for solution of schrodinger equation under the framework of hp clouds an intrinsic enrichment of orbital function and extrinsic enrichment of monomial functions are proposed due to the employment of higher order basis functions a higher order stabilized conforming nodal integration is developed the proposed methods are implemented using the density functional theory for solution of schrodinger equation analysis of several single and multi electron nucleus structures demonstrates the effectiveness of the proposed method

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

random walks in modular scale free networks with multiple traps extensive empirical investigation has shown that a plethora of real networks synchronously exhibit scale free and modular structure and it is thus of great importance to uncover the effects of these two striking properties on various dynamical processes occurring on such networks in this paper we examine two cases of random walks performed on a class of modular scale free networks with multiple traps located at several given nodes we first derive a formula of the mean first passage time mfpt for a general network which is the mean of the expected time to absorption originating from a specific node averaged over all nontrap starting nodes although the computation is complex the expression of the formula is exact moreover the computational approach and procedure are independent of the number and position of the traps we then determine analytically the mfpt for the two random walks being considered the obtained analytical results are in complete agreement with the numerical ones our results show that the number and location of traps play an important role in the behavior of the mfpt since for both cases the mfpt grows as a power law function of the number of nodes but their exponents are quite different we demonstrate that the root of the difference in the behavior of mfpt is attributed to the modular and scale free topologies of the networks this work can deepen the understanding of diffusion on networks with modular and scale free architecture and motivate relevant studies for random walks running on complex random networks with multiple traps

classification ofc algebras of real rank zero and unsuspendede equivalence types abstract in this article examples are given to prove that the graded scaled ordered k group is not the complete invariant for a c algebra in the class of unital separable nuclear c algebras of real rank zero and stable rank one even for a c algebra in the subclass which consists of those real rank zero stable rank one c algebras being expressed as inductive limits of k n i 1 m n i c x n i where x n i are two dimensional finite cw complexes and n i are positive integers in the case of simple such c algebras it has been proved that the above invariant is the complete invariant by george elliott and the author these examples prove that the classification conjecture of elliott for the case of non simple real rank zero c algebras should be revised one needs extra invariants the obstruction preventing two such c algebras with the same graded scaled ordered k group from being isomorphic is that they have different unsuspended e equivalence types a refinement of kk equivalence type of c algebras due to connes and higson in this article it is proved that for the above class of inductive limit c algebras the obstruction of unsuspended e equivalence type is the only obstruction i e if two c algebras in the class are unsuspended e equivalence then they are isomorphic it is a surprise that in the case of simple such c algebras or even the case of c algebras with finitely many ideals the obstruction will disappear see section 4

c algebras generated by stable relations abstract presentations of certain c algebras such as c0 0 1 mn by generators and relations are proven to be stable by the weakest definition of stability a set p1 pn of star polynomials is stable if operators a1 an which almost satisfy these relations meaning pi a1 an can be perturbed within c a1 an to satisfy these relations exactly homotopy and perturbation results for these c algebras are corollaries in particular we prove some new results about the dimension drop c algebras a n c 0 1 m n 0 1 c i we show that an is semiprojective answering a question of effros and kaminker also we show that whenever an b is a homomorphism approximately contained in a sub c algebra b0 b there is a nearby homomorphism of an into b0 this answers a question raised by elliott we prove technical results regarding mn c0 0 1 which should be useful elsewhere first we show this is projective meaning a star homomorphism mn c0 0 1 b j always lifts to a star homomorphism mn c0 0 1 b secondly we show that for a finitely generated m n a m n c 0 0 1 c 0 0 1 a if the amalgamation is done properly

a class of simple c algebras with stable rank one abstract we study the limits of inductive sequences a i i where each a i is a direct sum of full matrix algebras over compact metric spaces and each partial map of i is diagonal we give a new characterisation of simplicity for such algebras and apply it to prove that the said algebras have stable rank one whenever they are simple and unital significantly our results do not require any dimension growth assumption

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

theory of strongly irreducible operators and its applications in the matrix theory of finite dimensional space the famous jordan canonical form theorem sufficiently reveals the internal structure of matrices in the survey we will give similar jordan canonical form theorems of operator theory in a complex separable infinite dimensional hilbert space by the way we also show their applications in other mathematical branches

target problem on small world networks in this work we focus on reactions on small world networks swn s disordered graphs of much recent interest we study the target problem since it allows an exact solution on regular lattices on swn s we find that the decay of the targets for which we extend the formalism to disordered lattices is again related to s n the mean number of distinct sites visited in n steps although the s n vs n dependence changes here drastically in going from regular linear chains to their swn

k group and similarity classification of operators abstract let h be a complex separable hilbert space and l h denote the collection of bounded linear operators on h an operator a in l h is said to be a cowen douglas operator if there exist a connected open subset of complex plane c and n a positive integer such that a a z c a z is not invertible b ran a z y a z x y x h h for z in c z ker a z h and d dim ker a z n for z in in the paper we give a similarity classification of cowen douglas operators by using the ordered k group of the commutant algebra as an invariant and characterize the maximal ideals of the commutant algebras of cowen douglas operators the theorem greatly generalizes the main result in canada j math 156 4 2004 742 by simply removing the restriction of strong irreducibility of the operators the research is also partially inspired by the recent classification theory of simple ah algebras of elliott gong in documenta math 7 2002 255 on the classification of simple inductive limit c algebras ii the isomorphism theorem preprint also see j funct anal 1998 1 ann math 144 1996 497 amer j math 1996 187

a particle method for history dependent materials abstract a broad class of engineering problems including penetration impact and large rotations of solid bodies causes severe numerical problems for these problems the constitutive equations are history dependent so material points must be followed this is difficult to implement in a eulerian scheme on the other hand purely lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables a process which can introduce errors proposed here is an extension of the particle in cell method in which particles are interpreted to be material points that are followed through the complete loading process a fixed eulerian grid provides the means for determining a spatial gradient because the grid can also be interpreted as an updated lagrangian frame the usual convection term in the acceleration associated with eulerian formulations does not appear with the use of maps between material points and the grid the advantages of both eulerian and lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced also it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

the modified box dimension and average weighted receiving time of the weighted hierarchical graph abstract in this paper we study the weighted hierarchical graph which is generated from bipartite graph with n n 1 n 2 vertices in which the weights of edges have been assigned to different values with certain scale firstly we introduce the definition of the modified box dimension then for the weighted hierarchical graph we deduce the modified box dimension dim m b g n n n log r n depending on the weighted factor r and the number n of copies secondly we mainly study their two average weighted receiving times awrts t i n and t ii n of the weighted hierarchical graph on random walk we discuss two cases in the case of n 1 n 2 r n 2 n 1 we deduce both awrts grow as a power law function of the network size v g n with the postive exponent represented by log n n n 1 n 2 or log n r 1 dim m b g n n n which means that the bigger the value of the modified box dimension is the slower the process of receiving information is in the case of n 1 n 2 r n 2 n 1 both awrts tend to constant if n n 1 n 2 the awrts grow with increasing order as log n v g n if n n 1 n 2 and both awrts grow as a power law function of the network size v g n with the exponent represented by log n n n 1 n 2 0 if n n 1 n 2

orbital enriched flat top partition of unity method for the schrodinger eigenproblem abstract quantum mechanical calculations require the repeated solution of a schrodinger equation for the wavefunctions of the system from which materials properties follow recent work has shown the effectiveness of enriched finite element type galerkin methods at significantly reducing the degrees of freedom required to obtain accurate solutions however time to solution has been adversely affected by the need to solve a generalized rather than standard eigenvalue problem and the ill conditioning of associated system matrices in this work we address both issues by proposing a stable and efficient orbital enriched partition of unity method to solve the schrodinger boundary value problem in a parallelepiped unit cell subject to bloch periodic boundary conditions in the proposed partition of unity method the three dimensional domain is covered by overlapping patches with a compactly supported weight function associated with each patch a key ingredient in our approach is the use of non negative weight functions that possess the flat top property i e each weight function is identically equal to unity over some finite subset of its support this flat top property provides a pathway to devise a stable approximation over the whole domain on each patch we use p th degree orthogonal legendre polynomials that ensure p th order completeness and in addition include eigenfunctions of the radial schrodinger equation furthermore we adopt a variational lumping approach to construct a block diagonal overlap matrix that yields a standard eigenvalue problem for which there exist efficient eigensolvers the accuracy stability and efficiency of the proposed method is demonstrated for the schrodinger equation with a harmonic potential as well as a localized gaussian potential we show that the proposed approach delivers optimal rates of convergence in the energy and the use of orbital enrichment significantly reduces the number of degrees of freedom for a given desired accuracy in the energy eigenvalues while the stability of the enriched approach is fully maintained

non linear version of stabilized conforming nodal integration for galerkin mesh free methods a stabilized conforming sc nodal integration which meets the integration constraint in the galerkin meshfree approximation is generalized for nonlinear problems in sc nodal integration a strain smoothing stabilization is introduced and applied to the deformation gradient using a lagrangian meshfree discretization the assumed strain method expressed in terms of deformation gradient is employed to formulate an efficient meshfree discrete equation for nonlinear problems a significant gain in computational efficiency is achieved as well as enhanced accuracy in comparison to the solution of meshfree method using gauss integration method the performance of the proposed method appears to be quite robust when dealing with irregular discretization

classification of unital extensions of at algebras abstract we prove that the six term exact sequence in k theory together with the elliott invariants of the ideal and quotient is a complete invariant for certain unital extensions of a t algebras up to stable isomorphism we also give some necessary and sufficient conditions for such extensions being a t algebras or quasidiagonal extensions and prove the above invariant with the equivalence class of unit is a complete invariant for unital quasidiagonal extensions of a t algebras up to isomorphism

nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems convective transport terms in eulerian conservation laws lead to numerical instability in the solution of bubnov galerkin methods for these non self adjoint pdes stabilized petrov galerkin methods overcome this difficulty however gradient terms are required to construct the test functions which are typically expensive for meshfree methods in this work the implicit gradient reproducing kernel particle method is introduced which avoids explicit differentiation of test functions stabilization is accomplished by including gradient terms in the reproducing condition of the reproducing kernel approximation the proposed method is computationally efficient and simplifies stabilization procedures it is also shown that the implicit gradient resembles the diffuse derivative originally introduced in the diffuse element method in nayroles et al 1992 and maintains the desirable properties of the full derivative since careful attention must be paid to efficiency of domain integration in meshfree methods nodal integration is examined for this class of problems and a nodal integration method with enhanced accuracy and stability is introduced numerical examples are provided to show the effectiveness of the proposed method for both steady and transient problems

exact scaling properties of a hierarchical network model we report on the exact results for the degree k the diameter d the clustering coefficient c and the betweenness centrality b of a hierarchical network model with a replication factor m such quantities are calculated exactly with the help of recursion relations using the results we show that i the degree distribution follows a power law p k approximately k gamma with gamma 1 ln m ln m 1 ii the diameter grows logarithmically as d approximately ln n with the number of nodes n iii the clustering coefficient of each node is inversely proportional to its degree c proportional variant 1 k and the average clustering coefficient is nonzero in the infinite n limit and iv the betweenness centrality distribution follows a power law p b approximately b 2 we discuss a classification scheme of scale free networks into the universality class with the clustering property and the betweenness centrality distribution

distance between unitary orbits of normal elements in simple c algebras of real rank zero let x y x y be two normal elements in a unital simple c c algebra a we introduce a function d c x y d c x y and show that in a unital simple af algebra there is a constant 1 c 0 1 c 0 such that c d c x y dist u x u y d c x y c d c x y dist u x u y d c x y where u x u x and u y u y are the closures of the unitary orbits of x and of y respectively we also generalize this to unital simple c c algebras with real rank zero stable rank one and weakly unperforated k 0 k 0 group more complicated estimates are given in the presence of non trivial k 1 k 1 information

on the classification of simple inductive limit c algebras ii the isomorphism theorem in this article it is proved that the invariant consisting of the scaled ordered k group and the space of tracial states together with the natural pairing between them is a complete invariant for the class of unital simple c algebras which can be expressed as the inductive limit of a sequence a 1 to a 2 to cdots to a n to cdots with a n bigoplus i 1 t n p n i m n i c x n i p n i where xn i is a compact metrizable space and pn i is a projection in m n i c xn i for each n and i and the spaces xn i are of uniformly bounded finite dimension note that the c algebras in the present class are not assumed to be of real rank zero as they were in eg2

non commutative spheres iii irrational rotations leta be the irrational rotation algebra i e thec algebra generated by two unitariesu v satisfyingvu e 2 i uv with irrational and consider the fixed point subalgebrab under the flip automorphismu u 1 v v 1 we prove thatb is an af algebra

average receiving scaling of the weighted polygon koch networks with the weight dependent walk based on the weighted koch networks and the self similarity of fractals we present a family of weighted polygon koch networks with a weight factor r 0 r 1 we study the average receiving time art on weight dependent walk i e the walker moves to any of its neighbors with probability proportional to the weight of edge linking them whose key step is to calculate the sum of mean first passage times mfpts for all nodes absorpt at a hub node we use a recursive division method to divide the weighted polygon koch networks in order to calculate the art scaling more conveniently we show that the art scaling exhibits a sublinear or linear dependence on network order thus the weighted polygon koch networks are more efficient than expended koch networks in receiving information finally compared with other previous studies results i e koch networks weighted koch networks we find out that our models are more general

element free galerkin methods for static and dynamic fracture abstract element free galerkin efg methods are presented and applied to static and dynamic fracture problems efg methods which are based on moving least square mls interpolants require only nodal data no element connectivity is needed the description of the geometry and numerical model of the problem consists only of a set of nodes and a description of exterior boundaries and interior boundaries from any cracks this makes the method particularly attractive for growing crack problems since only minimal remeshing is needed to follow crack growth in moving least square interpolants the dependent variable at any point is obtained by minimizing a function in terms of the nodal values of the dependent variable in the domain of influence of the point numerical examples involving fatigue crack growth and dynamic crack propagation are presented to illustrate the performance and potential of this method

a generalized finite element method for solving the helmholtz equation in two dimensions with minimal pollution when using the galerkin fem for solving the helmholtz equation in two dimensions the error of the corresponding solution differs substantially from the error of the best approximation and this effect increases with higher wave number k in this paper we will design a generalized finite element method gfem for the helmholtz equation such that the pollution effect is minimal

effect of numerical integration on meshless methods abstract in this paper we present the effect of numerical integration on meshless methods with shape functions that reproduce polynomials of degree k 1 the meshless method was used on a second order neumann problem and we derived an estimate for the energy norm of the error between the exact solution and the approximate solution from the meshless method under the presence of numerical integration this estimate was obtained under the assumption that the numerical integration scheme satisfied a form of green s formula we also indicated how to obtain numerical integration schemes satisfying this property

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

universal coefficient theorems for the stable ext groups let a be a unital separable nuclear c algebra and let b be a stable c algebra using k theory and kk theory we establish universal coefficient theorems for the stable ext groups of unital extensions of a by b when a and b have certain properties which generalize a result of l brown and m dadarlat for the strong ext groups the class of extensions being studied are also enlarged

simple nuclear c algebras of tracial topological rank one we give a classification theorem for unital separable nuclear c algebras with tracial rank no more than one let a and b be two unital separable simple nuclear c algebras with tr a tr b 1 which satisfy the universal coefficient theorem we show that a b if and only if there is an order and unit preserving isomorphism 0 1 2 k0 a k0 a 1a k1 a t a k0 b k0 b 1b k1 b t b where 2 1 x 0 x for each x k0 a and t b

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

mathbb z actions on ah algebras and mathbb z 2 actions on af algebras we consider mathbb z actions single automorphisms on a unital simple ah algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the rohlin property under some technical assumptions moreover two mathbb z actions with the rohlin property on such a c algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent we also prove that locally approximately inner and uniformly outer mathbb z 2 actions on a unital simple af algebra with a unique trace have the rohlin property and classify them up to cocycle conjugacy employing the orderext group as classification invariants

weighted fractal networks abstract in this paper we define a new class of weighted complex networks sharing several properties with fractal sets and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension general networks with fractal or hierarchical structures can be set in the proposed framework that moreover could be used to provide some answers to the widespread emergence of fractal structures in nature

regularity properties in the classification program for separable amenable c algebras we report on recent progress in the program to classify separable amenable c algebras our emphasis is on the newly apparent role of regularity properties such as finite decomposition rank strict comparison of positive elements and z stability and on the importance of the cuntz semigroup we include a brief history of the program s successes since 1989 a more detailed look at the villadsen type algebras which have so dramatically changed the landscape and a collection of announcements on the structure and properties of the cuntz semigroup

similarity classification of holomorphic curves abstract let h be a complex separable hilbert space for an open connected subset of c we shall say that a map f gr n h is a holomorphic curve if there exist n holomorphic h valued functions 1 2 n on such that f 1 n where gr n h denotes the grassmann manifold the set of all n dimensional subspaces of h in the paper we give a similarity classification of some holomorphic curves by using the k group of its commutant algebra as an invariant

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

the classification of separable simple c algebras which are inductive limits of continuous trace c algebras with spectrum homeomorphic to the closed interval 0 1 abstract a classification is given of certain separable nuclear c algebras not necessarily of real rank zero namely the class of separable simple c algebras which are inductive limits of continuous trace c algebras whose building blocks have spectrum homeomorphic to the closed interval 0 1 or to a disjoint union of copies of this space also the range of the invariant is calculated

nodal integration of the element free galerkin method abstract spatial integration of the element free galerkin efg method is achieved by evaluating the integrals of the weak form only at the nodes in previous efg formulations a grid of cells was used to perform gaussian quadrature over the domain the absence of a cell structure for nodal integration results in a completely meshless method similar in simplicity to particle methods such as smooth particle hydrodynamics sph it is shown that nodal integration like sph suffers from spurious singular modes this spatial instability results from underintegration of the weak form and it is treated by the addition to the potential energy functional of a stabilization term which contains the square of the residual of the equilibrium equation example problems illustrate the effect of the stabilization and provide the basis for convergence studies

the classification of certain non simple c algebras of tracial rank zero abstract it is proved that the z 2 graded ordered k theory group with order unit k a k a 1 a is a complete invariant for the class of unital c algebras which are inductive limits of finite direct sums of unital amenable separable simple c algebras with tracial rank zero which satisfy the uct

random walks on complex trees we study the properties of random walks on complex trees we observe that the absence of loops is reflected in physical observables showing large differences with respect to their looped counterparts first both the vertex discovery rate and the mean topological displacement from the origin present a considerable slowing down in the tree case second the mean first passage time mfpt displays a logarithmic degree dependence in contrast to the inverse degree shape exhibited in looped networks this deviation can be ascribed to the dominance of source target topological distance in trees to show this we study the distance dependence of a symmetrized mfpt and derive its logarithmic profile obtaining good agreement with simulation results these unique properties shed light on the recently reported anomalies observed in diffusive dynamical systems on trees

trapping on modular scale free and small world networks with multiple hubs abstract in this paper we introduce a new kind of scale free and small world networks with multiple hubs based on classic networks and present the trapping problem on them we show that in the multiple hub networks the growth of mfpt with the traps located on the hub or peripheral nodes displays quite a difference from the single hub networks our conclusions are directed to possible applications in rumor or epidemic spreading phenomena

hp cloud approximation of the dirac eigenvalue problem the way of stability we apply hp cloud method to the radial dirac eigenvalue problem the difficulty of occurrence of spurious eigenvalues among the genuine ones in the computation is resolved the method of treatment is based on assuming hp cloud petrov galerkin scheme to construct the weak formulation of the problem which adds a consistent diffusivity to the variational formulation the size of the artificially added diffusion term is controlled by a stability parameter tau the derivation of tau assumes the limit behavior of the eigenvalues at infinity the parameter tau is applicable for generic basis functions this is combined with the choice of appropriate intrinsic enrichments in the construction of the cloud shape functions c 2014 elsevier inc all rights reserved

first passage properties of the erdos renyi random graph we study the mean time for a random walk to traverse between two arbitrary sites of the erd s renyi random graph we develop an effective medium approximation that predicts that the mean first passage time between pairs of nodes as well as all moments of this first passage time are insensitive to the fraction p of occupied links this prediction qualitatively agrees with numerical simulations away from the percolation threshold near the percolation threshold the statistically meaningful quantity is the mean transit rate namely the inverse of the first passage time this rate varies non monotonically with p near the percolation transition much of this behaviour can be understood by simple heuristic arguments

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

classification of simple c algebras inductive limits of matrix algebras over one dimensional spaces abstract in this article we will give a complete classification of simple c algebras which can be written as inductive limits of algebras of the form a n i 1 k n m n i c x n i where x n i are arbitrary variable one dimensional compact metrizable spaces the results unify and generalize the previous results for the case x n i s 1 and for the case of x n i being trees we obtain our classification results by reducing the case of general one dimensional spaces to the case of circles the techniques in this paper play important roles in the study of the case of higher dimensional spaces

on inductive limits of matrix algebras over the two torus it will be shown in this paper that certain real rank zero c algebras which are inductive limits of c algebras of the form i m k i c inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i can be expressed as inductive limits of c algebras of the form i m k i c s 1 in particular if both a and b are of real rank zero and are inductive limits of c algebras of the form i m k i c s 1 then also a b is an inductive limit of c algebras of the form i m k i c s 1 hence a b can be classified by its k theory this is a key step in the general classification theory of inductive limit c algebras

at structure of ah algebras with the ideal property and torsion free k theory abstract let a be an ah algebra that is a is the inductive limit c algebra of a 1 1 2 a 2 2 3 a 3 a n with a n i 1 t n p n i m n i c x n i p n i where x n i are compact metric spaces t n and n i are positive integers and p n i m n i c x n i are projections suppose that a has the ideal property each closed two sided ideal of a is generated by the projections inside the ideal as a closed two sided ideal suppose that sup n i dim x n i this condition can be relaxed to a certain condition called very slow dimension growth in this article we prove that if we further assume that k a is torsion free then a is an approximate circle algebra or an a t algebra that is a can be written as the inductive limit of b 1 b 2 b n where b n i 1 s n m n i c s 1 one of the main technical results of this article called the decomposition theorem is proved for the general case i e without the assumption that k a is torsion free this decomposition theorem will play an essential role in the proof of a general reduction theorem where the condition that k a is torsion free is dropped in the subsequent paper gong et al preprint 31 of course in that case in addition to space s 1 we will also need the spaces t ii k t iii k and s 2 as in gong 2002 29