operator norm localization property of metric spaces under finite decomposition complexity abstract the notions of operator norm localization property and finite decomposition complexity were recently introduced in metric geometry to study the coarse novikov conjecture and the stable borel conjecture in this paper we show that a metric space x has weak finite decomposition complexity with respect to the operator norm localization property if and only if x itself has the operator norm localization property it follows that any metric space with finite decomposition complexity has the operator norm localization property in particular we obtain an alternative way to prove a very recent result by e guentner r tessera and g yu that all countable linear groups have the operator norm localization property

self avoiding polygons on the square l and manhattan lattices transfer matrix techniques are used to extend the self avoiding polygon generating function on the square lattice to terms in x46 corresponding to 46 step polygons these techniques are then extended to apply to directed square lattices such as the l and manhattan lattice and the self avoiding polygon generating function to x48 is found for these lattices series analysis confirms that the specific heat exponent alpha 1 2 for the self avoiding walk problem and gives the following estimates for the connective constants mu sq 2 638155 or 0 000025 mu l 1 5657 or 0 0019 and mu man 1 7328 or 0 0005 some evidence for a correction to scaling exponent delta approximately 0 84 is found from square lattice series

complete distances of all negacyclic codes of length 2 s over bbz _ 2 a various kinds of distances of all negacyclic codes of length 2s over zopf2 a are completely determined using our structure theorems of negacyclic codes of length 2 s over zopf2 a we first calculate the hamming distances of all such negacyclic codes which particularly lead to the hamming weight distributions and hamming weight enumerators of several codes these hamming distances are then used to obtain their homogeneous lee and euclidean distances our techniques are extendable to the more general class of constacyclic codes namely the lambda constacyclic codes of length 2s over zopf2 a where lambda is any unit of zopf2 a with the form 4k 1 we establish the hamming homogeneous lee and euclidean distances of all such constacyclic codes

operator norm localization for linear groups and its application to k theory abstract we prove the operator norm localization property for linear groups as an application we prove the coarse novikov conjecture for box spaces of a linear group

polygons on the honeycomb lattice the authors enumerated the number of self avoiding polygons on the honeycomb lattice to 82 steps analysis of the resulting series gives for the connective constant mu 1 8477594 or 6 10 6 in agreement with nienhuis value 1984 of mu 2 2 12 1 84775906 the critical exponent alpha 0 4999 or 10 4 unbiased or alpha 0 49998 or 2 10 0 5 biased a non physical singularity on the negative real axis is accurately located and some curious results concerning the confluent singularity are obtained

the failure of a conjectured s4 symmetry in the three state checkerboard potts model low temperature expansions are obtained for the three state potts model on the checkerboard lattice the four boltzmann weights were set to various integer multiples of a low temperature variable x the series were evaluated to order x19 but it was found that the conjectured s4 symmetry failed at order x14 for the zero field partition function the spontaneous magnetisation and the zero field susceptibility

oscillations in the coefficients of power series the euler transformation van dyke quart j mech app math 27 1974 pp 423 450 pearce adv in phys 27 1978 pp 89 148 is a standard tool of series analysis for extending the range of convergence of a numerically determined series expansion in powers of some essentially positive physical parameter r because it can be used to map the physically significant range 0 r infty inside the unit circle the transformed series may in principle be useful for all positive r and for studying asymptotic behavior as r to infty in practice the deduction of this limiting behavior from a finite number of the coefficients of the transformed series is often complicated by substantial and slowly decaying oscillations in these coefficients we show that such oscillations can arise when r infty is a nonisolated or essential singularity we prove a generalization of darboux s theorem that applies to this case but show that the oscillations are due to components of the function that is

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

the maximal coarse baum connes conjecture for spaces which admit a fibred coarse embedding into hilbert space abstract we introduce a notion of fibred coarse embedding into hilbert space for metric spaces which is a generalization of gromov s notion of coarse embedding into hilbert space it turns out that a large class of expander graphs admit such an embedding we show that the maximal coarse baum connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into hilbert space

inclusion exclusion relations on the triangular lattice the combinatorial factors required for performing finite lattice series expansions on the triangular lattice are discussed series expansions can be obtained from a linear combination of free energies for finite convex hexagonal regions an algorithm for calculating the combinatorial weights is given a number of results are presented showing that many cancellations occur and that not all convex hexagons of less than a given size are required for a given degree of computational complexity as given by the size of the largest transfer matrix the expansion using hexagons of less than a certain perimeter and exploiting the full triangular symmetry gives 50 more series terms than the earlier approach which adds second neighbour bonds to the square lattice and only exploits square lattice symmetries

the coarse baum connes conjecture for spaces which admit a uniform embedding into hilbert space corollary 1 2 let be a finitely generated group if as a metric space with a word length metric admits a uniform embedding into hilbert space and its classifying space b has the homotopy type of a finite cw complex then the strong novikov conjecture holds for i e the index map from k b to k c r is injective corollary 1 2 follows from theorem 1 1 and the descent principle 23 by index theory the strong novikov conjecture implies the novikov conjecture on the homotopy invariance of higher signatures cf 8 for an excellent

constacyclic codes of length p s over fpm ufpm abstract for any prime p all constacyclic codes of length p s over the ring r f p m u f p m are considered the units of the ring r are of the forms and u where and are nonzero elements of f p m which provides p m p m 1 such constacyclic codes first the structure and hamming distances of all constacyclic codes of length p s over the finite field f p m are obtained they are used as a tool to establish the structure and hamming distances of all u constacyclic codes of length p s over r we then classify all cyclic codes of length p s over r and obtain the number of codewords in each of those cyclic codes finally a one to one correspondence between cyclic and constacyclic codes of length p s over r is constructed via ring isomorphism which carries over the results regarding cyclic codes corresponding to constacyclic codes of length p s over r

the number of convex polygons on the square and honeycomb lattices a subset of the set of self avoiding polygons sap embeddable on the square lattice which display the property of convexity is defined an algorithm for their enumeration is developed and from the available series coefficients the exact generating function is found the singularity structure appears similar to that of the unsolved sap problem but with different critical exponents and critical points the enumeration of convex polygons allows the extension of the existing series for the square lattice sap by one term for the honeycomb lattice similar results have been obtained despite a less natural definition of convexity

the coarse novikov conjecture and banach spaces with property h in this paper we prove the coarse novikov conjecture for metric spaces with bounded geometry which are coarsely embeddable into banach spaces with a geometric condition called property h introduced by g kasparov and g yu

k theory for the maximal roe algebra of certain expanders abstract we study in this paper the maximal version of the coarse baum connes assembly map for families of expanding graphs arising from residually finite groups unlike for the usual roe algebra we show that this assembly map is closely related to the maximal baum connes assembly map for the group and is an isomorphism for a class of expanders we also introduce a quantitative baum connes assembly map and discuss its connections to k theory of maximal roe algebras

series studies of the potts model i the simple cubic ising model the finite lattice method of series expansion is generalized to the q state potts model on the simple cubic lattice it is found that the computational effort grows exponentially with the square of the number of series terms obtained unlike two dimensional lattices where the computational requirements grow exponentially with the number of terms for the ising q 2 case the authors have extended the low temperature series for the partition functions magnetization and zero field susceptibility to u26 from u20 the high temperature series for the zero field partition function is extended from nu 18 to nu 22 subsequent analysis gives critical exponents in agreement with those from field theory

the trace description of irreducible quasi cyclic codes the notion of a q ary irreducible quasi cyclic code of block length n and index r is introduced a trace description of such a code is provided in a fashion similar to the trace description of irreducible cyclic codes in particular it is shown that an irreducible quasi cyclic code of dimension k is completely described by an irreducible cyclic code and r elements from a field of cardinality q sup k using this fact a number of binary irreducible quasi cyclic codes of index 2 are constructed and their weight spectra obtained

the high temperature susceptibility and spin spin correlation function of the three dimensional ising model the series analysis protocol developed in a preceding paper ibid vol 20 p 1839 1987 is applied to the susceptibility and correlation function of the three dimensional ising model for the spin 1 2 ising data the author argues that the protocol needs modification to take account of trends in the data which trends arise from the nature of the series in this way the author obtains gamma 1 239 or 0 003 for all cubic lattices and for a variety of spin values the diamond lattice data lies outside this range and it is argued that this series is effectively far shorter than the others the author also estimates nu 0 632 0 002 0 003 for the bcc lattice and obtains critical point estimates for all lattice and spin models studied

a note on the q ary image of a q sup m ary repeated root cyclic code for n q p sup s where p ch f sub q s spl ges 1 v a q sup m ary repeated root cyclic code of length n with generator polynomial g x we give a partial answer about whether the q ary image of v is cyclic or not with respect to a certain basis for f sub q m over f sub q

embeddings of uniform roe algebras in this paper we study embeddings of uniform roe algebras generally speaking given metric spaces x and y we are interested in which large scale geometric properties are stable under embedding of the uniform roe algebra of x into the uniform roe algebra of y

spaces of graphs boundary groupoids and the coarse baum connes conjecture we introduce a new variant of the coarse baum connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse baum connes conjecture we prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse baum connes conjecture in particular we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree we then connect the boundary conjecture to the coarse baum connes conjecture using homological methods which allows us to exhibit all the current uniformly discrete counterexamples to the coarse baum connes conjecture in an elementary way

on repeated root cyclic codes a parity check matrix for a q ary repeated root cyclic code is derived using the hasse derivative then the minimum distance of a q ary repeated root cyclic code is expressed in terms of the minimum distance of a certain simple root cyclic code with the help of this result several binary repeated root cyclic codes of lengths up to n 62 are shown to contain the largest known number of codewords for their given length and minimum distance the relative minimum distance d sub min n of q ary repeated root cyclic codes of rate r or r is proven to tend to zero as the largest multiplicity of a root of the generator g x increases to infinity it is further shown that repeated root cycle codes cannot be asymptotically better than simple root cyclic codes

repeated root cyclic codes in the theory of cyclic codes it is common practice to require that n q 1 where n is the word length and f sub q is the alphabet it is shown that the even weight subcodes of the shortened binary hamming codes form a sequence of repeated root cyclic codes that are optimal in nearly all other cases one does not find good cyclic codes by dropping the usual restriction that n and q must be relatively prime this statement is based on an analysis for lengths up to 100 a theorem shows why this was to be expected but it also leads to low complexity decoding methods this is an advantage especially for the codes that are not much worse than corresponding codes of odd length it is demonstrated that a binary cyclic code of length 2n n odd can be obtained from two cyclic codes of length n by the well known mod u mod u v mod construction this leads to an infinite sequence of optimal cyclic codes with distance 4 furthermore it is shown that low complexity decoding methods can be used for these codes the structure theorem generalizes to other characteristics and to other lengths some comparisons of the methods using earlier examples are given

ghostbusting and property a abstract we show that the roe algebra of a bounded geometry metric space contains non compact ghosts if and only if the space does not have property a

the q ary image of a q sup m ary cyclic code for n q 1 v a q sup m ary cyclic code of length n and with generator polynomial g x we show that there exists a basis for f q sup m over f sub q with respect to which the q ary image of v is cyclic if and only if i g x is over f sub q or ii g x g sub 0 x x spl gammasup q spl mu g sub 0 x is over f sub q f sub qspl ne f q sup k f sub q spl gamma spl sub f q sup m spl mu an integer modulo k and w sup m spl gamma has a divisor over f q sup k of degree e m k or iii g x g sub 0 x spl pisub spl muspl epsiv s x spl gamma q sup spl mu g sub 0 x is over f sub q f sub qspl ne f q sup k f sub q spl gamma spl sub f q sup m s a set of integers module k of cardinality k 1 and w sup m spl mu has a divisor over f q sup k of degree e m k in all of the above cases we determine all of the bases with respect to which the q ary image of v is cyclic

metric sparsification and operator norm localization abstract we study an operator norm localization property and its applications to the coarse novikov conjecture in operator k theory in particular we introduce a sufficient geometric condition called metric sparsification for the operator norm localization property this is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property we also show that a sequence of expanding graphs does not possess the operator norm localization property

self avoiding rings on the triangular lattice the finite lattice method of series expansion is used to extend the enumeration of self avoiding polygons on the triangular lattice through to rings of 35 steps the authors also give the enumeration of these triangular polygons grouped by perimeter and area of up to 21 unit triangles for perimeters up to 24 steps

on rigidity of roe algebras roe algebras are c algebras built using large scale or coarse aspects of a metric space x d in the special case that x is a finitely generated group and d is a word metric the simplest roe algebra associated to d is isomorphic to the crossed product c algebra l 1 r roe algebras are coarse invariants in the sense that if x and y are coarsely equivalent metric spaces then their roe algebras are isomorphic motivated in part by the coarse baum connes conjecture we ask if there is a converse to the above statement that is if x and y are metric spaces with isomorphic roe algebras must x and y be coarsely equivalent we show that for very large classes of spaces the answer to this question and some related questions is yes this can be thought of as a c rigidity result it shows that the roe algebra construction preserves a large amount of information about the space and is thus surprisingly rigid as an example of our results in the group case we have that if and are finitely generated elementary amenable hyperbolic or linear groups

a metric approach to limit operators we extend the limit operator machinery of rabinovich roch and silbermann from z n to bounded geometry strongly discrete metric spaces we do not assume the presence of any group structure or action on our metric spaces using this machinery and recent ideas of lindner and seidel we show that if a metric space x has yu s property a then a band dominated operator on x is fredholm if and only if all of its limit operators are invertible we also show that this always fails for metric spaces without property a

on the essential spectrum of elliptic differential operators abstract let a be a c algebra of bounded uniformly continuous functions on a finite dimensional real vector space x such that a is stable under translations and contains the continuous functions that have a limit at infinity denote a the boundary of x in the character space of a then to each operator a in the crossed product a x one may naturally associate a family of bounded operators a on l 2 x indexed by the characters a we show that the essential spectrum of a is the union of the spectra of the operators a the applications cover very general classes of singular elliptic operators

constacyclic codes of length 2 s over galois extension rings of bbf _ 2 u bbf _2 we study all constacyclic codes of length 2s over gr rfr m the galois extension ring of dimension m of the ring rfr f2 uf2 the units of the ring gr rfr m are of the forms alpha and alpha ubeta where alpha beta are nonzero elements of f2m which correspond to 2 m 2m 1 such constacyclic codes first the structure and hamming distances of 1 ugamma constacyclic codes are established we then classify all cyclic codes of length 2s over gr rfr m and obtain a formula for the number of those cyclic codes as well as the number of codewords in each code finally one to one correspondences between cyclic and alpha constacyclic codes as well as 1 ugamma constacyclic and alpha ubeta constacyclic codes are provided via ring isomorphisms that allow us to carry over the results about cyclic and 1 ugamma constacyclic accordingly to all constacyclic codes of length 2s over gr rfr m

negacyclic codes of length 2 sup s over galois rings codes over the ring of integers modulo 4 have been studied by many researchers negacyclic codes such that the length n of the code is odd have been characterized over the alphabet zopf4 and furthermore have been generalized to the case of the alphabet being a finite commutative chain ring in this paper we investigate negacyclic codes of length 2s over galois rings the structure of negacyclic codes of length 2s over the galois rings gr 2a m as well as that of their duals are completely obtained the hamming distances of negacyclic codes over gr 2a m in general and over zopf2 a in particular are studied among other more general results the hamming distances of all negacyclic codes over zopf2 a of length 4 8 and 16 are given the weight distributions of such negacyclic codes are also discussed

two three state potts models the universality of confluent corrections to scaling the authors present a study of an extended 35 power low temperature series for the susceptibility of the ordinary two site three state potts model on the square lattice as well as reanalyses of several extant series for the three site three state potts model on the triangular lattice dominant and confluent singularities are investigated and the exponents of both are found to be universal and in agreement with known and conjectured exact values

geometrization of the strong novikov conjecture for residually finite groups in this paper we prove that the strong novikov conjecture for a residually finite group is essentially equivalent to the coarse geometric novikov conjecture for a certain metric space associated to the group as an application we obtain the coarse geometric novikov conjecture for a large class of sequences of expanders

quasi locality and property a abstract let x be a metric space with bounded geometry p 0 1 and let e be a banach space the main result of this paper is that either if x has yu s property a and p 1 or without any condition on x when p 0 1 then quasi local operators on l p x e belong to the appropriate variant of the roe algebra of x this generalises the existing results of this type by lange and rabinovich engel tikuisis and the first author and li wang and the second author as consequences we obtain that uniform l p roe algebras of spaces with property a are closed under taking inverses and another condition characterising property a akin to the operator norm localisation for quasi local operators

high temperature series expansions for the 2 1 dimensional ising model using efficient cluster expansion methods the known high temperature series for the vacuum energy specific heat susceptibility and mass gap of the 2 1 dimensional ising model on the square and triangular lattices have been extended by several terms estimates of the critical indices demonstrate very convincing universality with the euclidean version of the model

on the corrections to scaling in three dimensional ising models the leading correction to scaling amplitudes for the spin 1 2 nearest neighbor sc bcc and fee ising models are considered with the particular aim of determining their signs on the basis of previous two variable series analyses by chen fisher and nickel and renormalization group 4 d expansions it is concluded that the correction amplitudes for the susceptibility correlation length specific heat and spontaneous magnetization arenegative for all three lattices thus for example the effective exponent eff t asymptotically approaches the true susceptibility exponent fromabove other earlier and more recent high temperature series and field theoretic analyses are seen to be consistent with this result however the usual nonasymptotic perturbative field theoretic approaches are essentially committed to positive correction amplitudes the question of the signs therefore relates directly to the applicability of these non asymptotic field theoretic calculations to three dimensional ising models as well as to different experimental systems

the size and number of rings on the square lattice the authors have calculated the number of self avoiding polygons on the square lattice to 56 steps and the caliper size to 54 steps analysis of the generating function permits estimates of the connective constant mu 2 638 1585 or 10 6 and the critical exponents alpha 0 500 06 or 0 000 06 and v 0 753 or 0 007 the singularity structure of the polygon generating function is found to be consistent with a correction to the scaling exponent delta 1 5 as predicted by nienhuis 1982 1984 the confluent part however maps into the additive analytic term due to the value of the exponent alpha

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension