a generalisation to birkhoff von neumann theorem abstract the classic birkhoff von neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices in this paper we study a generalisation of this theorem in the type ii 1 setting namely we replace a doubly stochastic matrix with a collection of measure preserving partial isomorphisms of the unit interval with similar properties we show that a weaker version of this theorem still holds

sofic groups and direct finiteness abstract we construct an analogue of von neumann s affiliated algebras for sofic group algebras over arbitrary fields consequently we settle kaplansky s direct finiteness conjecture for sofic groups

c stability of discrete groups abstract a group may be considered c stable if almost representations of the group in a c algebra are always close to actual representations we initiate a systematic study of which discrete groups are c stable or only stable with respect to some subclass of c algebras e g finite dimensional c algebras we provide criteria and invariants for stability of groups and this allows us to completely determine stability non stability of crystallographic groups surface groups virtually free groups and certain baumslag solitar groups we also show that among the non trivial finitely generated torsion free 2 step nilpotent groups the only c stable group is z

sofic groups and diophantine approximation we prove the algebraic eigenvalue conjecture of j dodziuk p linnell v mathai t schick and s yates see 2 for sofic groups moreover we give restrictions on the spectral measure of elements in the integral group ring finally we define integer operators and prove a quantization of the operator norm below 2 to the knowledge of the author there is no group known that is not sofic

the strong atiyah and luck approximation conjectures for one relator groups it is shown that the strong atiyah conjecture and the luck approximation conjecture in the space of marked groups hold for locally indicable groups in particular this implies that one relator groups satisfy both conjectures we also show that the center conjecture the independence conjecture and the strong eigenvalue conjecture hold for these groups as a byproduct we prove that the group algebra of a locally indicable group over a field of characteristic zero has a hughes free epic division algebra and in particular it is embedded in a division algebra

stability of group relations under small hilbert schmidt perturbations abstract if matrices almost satisfying a group relation are close to matrices exactly satisfying the relation then we say that a group is matricially stable here almost and close are in terms of the hilbert schmidt norm using tracial 2 norm on i i 1 factors we similarly define i i 1 factor stability for groups our main result is that all 1 relator groups with non trivial center are i i 1 factor stable many of them are also matricially stable and rfd for amenable groups we give a complete characterization of matricial stability in terms of the following approximation property for characters each character must be a pointwise limit of traces of finite dimensional representations this allows us to prove matricial stability for the discrete heisenberg group h 3 and for all virtually abelian groups for non amenable groups the same approximation property is a necessary condition for being matricially stable we study this approximation property and show that rf groups with character rigidity have it

morphisms of extensions of c algebras pushing forward the busby invariant abstract we study completions of diagrams of extensions of c algebras in which all three c algebras in one of the rows and either the ideal or the quotient in the other are given along with the three morphisms between them we find universal solutions to all four of these problems under restrictions of varying severity on the given vertical maps and describe the solutions in terms of push outs and pull backs of certain diagrams our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products this leads to new results about the k theory of amalgamated free products verifying the cuntz conjecture in certain cases we also obtain new results about extensions of matricial field c algebras verifying partially a conjecture of blackadar and kirchberg finally we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes

on the relation between an operator and its self commutator we show that a bounded operator a on a hilbert space belongs to a certain set associated with its self commutator a a provided that a zi can be approximated by invertible operators for all complex numbers z the theorem remains valid in a general c algebra of real rank zero under the assumption that a zi belong to the closure of the connected component of unity in the set of invertible elements this result implies the brown douglas fillmore theorem and huaxin lin s theorem on almost commuting matrices moreover it allows us to refine the former and to extend the latter to operators of infinite rank and other norms including the schatten norms on the space of matrices the proof is based on an abstract theorem which states that a normal element of a c algebra of real rank zero satisfying the above condition has a resolution of the identity associated with any open cover of its spectrum

variance balanced change over designs for dependent observations we show that variance balanced change over designs can be obtained from orthogonal arrays for many dependence structures some examples and design comparisons are given

sofic groups and profinite topology on free groups abstract we give a definition of weakly sofic groups w sofic groups our definition is a rather natural extension of the definition of sofic groups where instead of the hamming metric on symmetric groups we use general bi invariant metrics on finite groups the existence of non w sofic groups is equivalent to some conjecture about profinite topology on free groups

approximations of groups characterizations of sofic groups and equations over groups we give new characterizations of sofic groups a group g is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups a group g is sofic if and only if any system of equations solvable in all alternating groups is solvable over g the last characterization allows to express soficity of an existentially closed group by sentences

constraint metric approximations and equations in groups abstract we introduce notions of a constraint metric approximation and of a constraint stability of a metric approximation this is done in the language of group equations with coefficients we give an example of a group which is not constraintly sofic in building it we find a sofic representation of free group with trivial commutant among extreme points of the convex structure on the space of sofic representations we consider the centralizer equation in permutations as an instance of this new general setting we characterize permutations p s k whose centralizer is stable in permutations with respect to the normalized hamming distance that is a permutation which almost centralizes p is near a centralizing permutation this answers a question of gorenstein sandler mills 1962

statistical model of nearly complete elastic rough surface contact abstract in the area of homogeneous isotropic linear elastic rough surface normal contact many classic statistical models have been developed which are only valid in the early contact when real area of contact is infinitesimally small e g the greenwood williamson gw model in this article newly developed statistical models built under the framework of the i gw ii nayak bush and iii greenwood s simplified elliptic models extend the range of application of the classic statistical models to the case of nearly complete contact nearly complete contact is the stage when the ratio of the real area of contact to the nominal contact area approaches unity at nearly complete contact the non contact area consists of a finite number of the non contact regions over a finite nominal contact area each non contact region is treated as a mode i crack the area of each non contact region and the corresponding trapped volume within each non contact region are determined by the analytical solutions in the linear elastic fracture mechanics respectively for a certain average contact pressure not only can the real area of contact be determined by the newly developed statistical models but also the average interfacial gap rough surface is restricted to the geometrically isotropic surface i e the corresponding statistical parameters are independent of the direction of measurement relations between the average contact pressure non contact area and average interfacial gap for different combinations of statistical parameters are compared between newly developed statistical models the relations between non contact area and average contact pressure predicted by the current models are also compared with that by persson s theory of contact the analogies between the classic statistical models and the newly developed models are also explored

convex hulls of unitary orbits of normal elements in c algebras with tracial rank zero abstract let a be a unital separable simple c algebra with tracial rank zero and let x y a be two normal elements we show that x is in the closure of the convex hull of the unitary orbit of y if and only if there exists a sequence of unital completely positive linear maps n from a to a such that the sequence n y converges to x in norm and also approximately preserves the trace values a purely measure theoretical description for normal elements in the closure of the convex hull of unitary orbit of y is also given in the case that a has a unique tracial state some classical results about the closure of the convex hull of the unitary orbits in von neumann algebras are proved to hold in the c algebraic setting

on sofic actions and equivalence relations abstract the notion of sofic equivalence relation was introduced by gabor elek and gabor lippner their technics employ some graph theory here we define this notion in a more operator algebraic context starting from connes embedding problem and prove the equivalence of these two definitions we introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic we also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic

similarity and fractality in the modelling of roughness by a multilevel profile with hierarchical structure some modern scaling and fractal approaches to the characterization of surface roughness are under consideration a new mathematical model of a multilevel profile suitable for flexible simulation of roughness is presented as a development from these approaches the iterative construction of the model is described it is shown that the profile is a hierarchical structure with self affine and fractal features its geometrical properties are studied both analytically and numerically and some of them are proved to be of the renormalization type the profile contour length can be finite or infinite depending on the chosen values of the structural parameters some characteristics including the bearing curve and the upper volume function of the profile and the corresponding prestructures are calculated

a new application of random matrices ext c _ mathrm red f_2 is not a group in the process of developing the theory of free probability and free entropy voiculescu introduced in 1991 a random matrix model for a free semicircular system since then random matrices have played a key role in von neumann algebra theory cf v8 v9 the main result of this paper is the following extension of voiculescui s random matrix result let x n 1 x n r be a system of r stochastically independent n i n gaussian self adjoint random matrices as in voiculescui s random matrix paper v4 and let x1 xr be a semi circular system in a c probability space then for every polynomial p in r noncommuting variables lim niaeia p x n 1 o x n r o p x1 xr for almost all o in the underlying probability space we use the result to show that the ext invariant for the reduced c algebra of the free group on 2 generators is not a group but only a semi group this problem has been open since anderson in 1978 found the first example of a c algebra a for which ext a is not a group

matrix commutators their asymptotic metric properties and relation to approximate joint diagonalization abstract we analyze the properties of the norm of the commutator of two hermitian matrices showing that asymptotically it behaves like a metric and establish its relation to joint approximate diagonalization of matrices showing that almost commuting matrices are almost jointly diagonalizable and vice versa we show an application of our results in the field of 3d shape analysis

integrality of l 2 betti numbers the atiyah conjecture predicts that the l 2 betti numbers of a finite cw complex with torsion free fundamental group are integers we establish the atiyah conjecture under the condition that it holds for g and that h lhd g is a normal subgroup for amalgamated free products g h h rtimes f here f is a free group and h rtimes f is an arbitrary semi direct product this includes free products g f and semi direct products g rtimes f we also show that the atiyah conjecture holds with an additional technical condition for direct and inverse limits of groups for which it is true as a corollary it holds for positive 1 relator groups with torsion free abelianization putting everything together we establish a new bigger class of groups for which the atiyah conjecture holds which contains all free groups and in particular is closed under taking subgroups direct sums free products extensions with torsion free elementary amenable quotient or with free quotient and under certain direct and inverse limits

orthogonal free quantum group factors are strongly 1 bounded abstract we prove that the orthogonal free quantum group factors l f o n are strongly 1 bounded in the sense of jung in particular they are not isomorphic to free group factors this result is obtained by establishing a spectral regularity result for the edge reversing operator on the quantum cayley tree associated to f o n and combining this result with a recent free entropy dimension rank theorem of jung and shlyakhtenko

almost commuting orthogonal matrices abstract we show that two almost commuting real orthogonal matrices are uniformly close to exactly commuting real orthogonal matrices we prove the same for symplectic unitary matrices this is in contrast to the general complex case where not all pairs of almost commuting unitaries are close to commuting pairs our techniques also yield results about almost normal matrices over the reals and the quaternions we conclude with an example where the k theoretical obstructions to approximation cannot be avoided our example is inspired by the physical systems known as topological superconductors

adhesive contact of the weierstrass profile the weierstrass series was considered in ciavarella et al ciavarella et al 2000 proc r soc lond a 456 387405 doi 10 1098 rspa 2000 0522 to describe a linear contact problem between a ri

stability for product groups and property τ abstract we study the notion of permutation stability or p stability for countable groups our main result provides a wide class of non amenable product groups which are not p stable this class includes the product group whenever admits a non abelian free quotient and admits an infinite cyclic quotient in particular we obtain that the groups f m z d and f m f n are not p stable for any integers m n 2 and d 1 this implies that p stability is not closed under the direct product construction which answers a question of becker lubotzky and thom the proof of our main result relies on a construction of asymptotic homomorphisms from to finite symmetric groups starting from sequences of finite index subgroups in and with and without property our method is sufficiently robust to show that the groups covered are not even flexibly p stable thus giving the first such non amenable residually finite examples

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

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

approximating macroscopic observables in quantum spin systems with commuting matrices abstract macroscopic observables in a quantum spin system are given by sequences of spatial means of local elements 1 2 n 1 j n n j a i n n i 1 m in a uhf algebra one of their properties is that they commute asymptotically as n goes to infinity it is not true that any given set of asymptotically commuting matrices can be approximated by commuting ones in the norm topology in this paper we show that for macroscopic observables this is true

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

operator algebraic superridigity for sl n ℤ n 3 for n 3 let sln we prove the following superridigity result for in the context of operator algebras let l be the von neumann algebra generated by the left regular representation of let m be a finite factor and let u m be its unitary group let u m be a group homomorphism such that m then either

optimal crossover designs for the comparison of two treatments in the presence of carryover effects and autocorrelated errors summary a model for responses in a crossover experiment that includes direct and first order carryover treatment effects together with an autocorrelated error term is considered when there are two treatments a method for generating designs that minimize the variance of the estimated treatment effects is proposed and explicit results are given for the three and four period cases efficiencies of some practical designs are calculated

character rigidity for special linear groups in this paper we study characters on special linear groups sln r where r is either an infinite field or the localization of an order in a number field we give several applications to the theory of measure preserving actions operator algebraic superrigidity and almost homomorphisms

cross over designs for two treatments and correlated errors summary the paper aims to derive optimal two treatment cross over designs for experiments with many periods when the observations are correlated and residual effects are present the case of small numbers of periods was treated by laska meisner 1985 and matthews 1987 their results are substantially affected by end effects arising because the first and last periods behave differently we look at designs which maximize an upper bound of the information matrix and show that these designs are highly efficient especially when the number of periods is large assume we have b experimental units each of which is exposed to a series of treatments the number of treatments is t and each unit receives k different or identical treatments in successive periods the design d determines which treatment is applied to which unit at which period we denote the set of all such cross over designs by ft b k the measurement on the jth period of the uth unit is denoted by yd u j if design d e itb k is applied williams 1949 introduced a model for this situation which assumes that

conductance of rough random profiles abstract recently the real contact area and the compliance and electrical resistance for a rough surface defined with a weierstrass series have been studied under the assumption that superposed self affine sine waves had well separated wavelengths extending the celebrated procedures pioneered by archard archard j f 1957 elastic deformation and the laws of friction proc r soc lond a 243 190 205 here more realistic fractal rough surface profiles are considered by using the weierstrass series with random phases and with much lower separation of the various scales using a full or a hybrid numerical analytical technique a non linear layer algorithm is developed which is a very efficient approximate tool to study this problem avoiding the need for averaging over various realizations of profiles with random phases the multiscale problem is solved by a cascade of 2 scales problems each of which is solved with a few elements for an imposed contact area deriving load as a function of indentation and the conductance by differentiation using barber s analogy theorem dimensionless results for the conductance as a function of applied pressures show that the conductance seems to be close to a power law at low loads and is nearly linear at intermediate loads following the normalized single sinusoidal case except at the origin at high loads the conductance becomes strongly dependent on fractal dimension because of weak dependence on the contribution of small wavelength scales higher order terms in the series since roughness tends to be squeezed out the conductance tends to increase more than linearly more so the smaller is the fractal dimension however another limit could be found in terms of the finite size of the specimen which may suggest reaching a finite limit the resulting curves could then be sigmoidal as confirmed by qualitative comparisons with experiments in the literature

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

making almost commuting matrices commute suppose two hermitian matrices a b almost commute vert a b vert leq delta are they close to a commuting pair of hermitian matrices a b with vert a a vert vert b b vert leq epsilon a theorem of h lin 3 shows that this is uniformly true in that for every epsilon 0 there exists a 0 independent of the size n of the matrices for which almost commuting implies being close to a commuting pair however this theorem does not specify how depends on epsilon we give uniform bounds relating and epsilon the proof is constructive giving an explicit algorithm to construct a and b we provide tighter bounds in the case of block tridiagonal and tridiagonal matrices within the context of quantum measurement this implies an algorithm to construct a basis in which we can make a projective measurement that approximately measures two approximately commuting operators simultaneously finally we comment briefly on the case of approximately measuring three or more approximately commuting operators using povms positive operator valued measures instead of projective measurements

characters l 2 betti numbers and an equivariant approximation theorem let g be a group with a finite subgroup h we define the l 2 multiplicity of an irreducible representation of h in the l 2 homology of a proper g cw complex these invariants generalize the l 2 betti numbers our main results are approximation theorems for l 2 multiplicities which extend the approximation theorems for l 2 betti numbers of luck farber and elek szabo respectively the main ingredient is the theory of characters of infinite groups and a method to induce characters from finite subgroups we discuss applications to the cohomology of arithmetic groups

group ring elements with large spectral density given delta 0 we construct a group g and a group ring element s in mathbb z g such that the spectral measure mu of s fulfils mu 0 varepsilon frac c log varepsilon 1 delta for small varepsilon in particular the novikov shubin invariant of any such s is 0 the constructed examples show that the best known upper bounds on mu 0 varepsilon are not far from being optimal

a variational approach to optimal two treatment crossover designs application to carryover effect models abstract a variational method is used to obtain sufficient conditions for an optimal two treatment p period design given a repeated measures model with arbitrary within subject covariance the design minimizes the variance of the estimator of treatment differences over all possible allocations of n subjects to the 2 p possible treatment sequences the method is applied to a model that includes carryover effects when subject effects are random with equicorrelated observations designs are optimal if they are a strongly balanced b uniform on the rows and c either uniform on the subjects p is even and greater than 2 or uniform on the first p 1 periods if p is odd for two periods the optimal design is ab ba aa bb the same designs are optimal when baseline measurements are obtained in each period baseline observations improve efficiency considerably for p 2 only slightly for p odd and are of no help for p even and greater than 2 a second model of errors in which a subject s response ha

sofic mean dimension abstract we introduce mean dimensions for continuous actions of countable sofic groups on compact metrizable spaces these generalize the gromov lindenstrauss weiss mean dimensions for actions of countable amenable groups and are useful for distinguishing continuous actions of countable sofic groups with infinite entropy

optimal repeated measurements designs the linear optimality equations in approximate design theory necessary and sufficient conditions that a repeated measurements design be universally optimal are given as linear equations whose unknowns are the proportions of subjects on the treatment sequences both the number of periods and the number of treatments in the designs are arbitrary as is the covariance matrix of the normal response model the existence of universally optimal symmetric designs is proved the single linear equation which the proportions satisfy is given a formula for the information matrix of a universally optimal design is derived

on turing dynamical systems and the atiyah problem main theorems of the article concern the problem of atiyah on possible values of l 2 betti numbers it is shown that all non negative real numbers are l 2 betti numbers and that many for example all non negative algebraic real numbers are l 2 betti numbers of simply connected manifolds with respect to a free cocompact action also an explicit example is constructed which leads to a simply connected manifold with a transcendental l 2 betti number with respect to an action of the threefold direct product of the lamplighter group mathbb z 2 mathbb z wr mathbb z the main new idea is embedding turing machines into integral group rings the main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids

hyperlinearity essentially free actions and l2 invariants the sofic property we prove that connes embedding conjecture holds for the von neumann algebras of sofic groups that is sofic groups are hyperlinear hence we provide some new examples of hyperlinearity we also show that the determinant conjecture holds for sofic groups as well we introduce the notion of essentially free actions and amenable actions and study their properties

quasidiagonality of nuclear c algebras we prove that faithful traces on separable and nuclear c algebras in the uct class are quasidiagonal this has a number of consequences firstly by results of many hands the classification of unital separable simple and nuclear c algebras of finite nuclear dimension which satisfy the uct is now complete secondly our result links the finite to the general version of the toms winter conjecture in the expected way and hence clarifies the relation between decomposition rank and nuclear dimension finally we confirm the rosenberg conjecture discrete amenable groups have quasidiagonal c algebras

exponential rank of c algebras with real rank zero and the brown pedersen conjectures abstract we show that every c algebra with real rank zero has exponential rank 1 consequently c algebras with real rank zero have the property weak fu we also show that if a is a unital c algebra with real rank zero stable rank one and trivial k1 group then its multiplier algebra has real rank zero if a is a unital stable c algebra with stable rank one we show that its multiplier algebra has real rank zero if and only if a has real rank zero and k1 a 0

separability properties of certain tree products of groups abstract we introduce the concept of finite compatibility to prove certain double coset separability of tree products of central subgroup separable groups we also prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a central subgroup in one of the factors using this we prove that tree products of finitely many central subgroup separable and conjugacy separable groups are conjugacy separable we apply the results to polycyclic by finite groups and groups of linkages of torus knots

linear elastic contact of the weierstrass profile a contact problem is considered in which an elastic half plane is pressed against a rigid fractally rough surface whose profile is defined by a weierstrass series it is shown that no applied mean pressure is sufficiently large to ensure full contact and indeed there are not even any contact areas of finite dimension the contact area consists of a set of fractal character for all values of the geometric and loading parameters a solution for the partial contact of a sinusoidal surface is used to develop a relation between the contact pressure distribution at scale n 1 and that at scale n recursive numerical integration of this relation yields the contact area as a function of scale an analytical solution to the same problem appropriate at large n is constructed following a technique due to archard this is found to give a very good approximation to the numerical results even at small n except for cases where the dimensionless applied load is large the contact area is found to decrease continuously with n tending to a power law behaviour at large n which corresponds to a limiting fractal dimension of 2 d where d is the fractal dimension of the surface profile however it is not a simple fractal in the sense that it deviates from the power law form at low n at which there is also a dependence on the applied load contact segment lengths become smaller at small scales but an appropriately normalized size distribution tends to a limiting function at large n the authors dedicate this paper to the memory of dr j f archard 1918 1989

harmonic models and spanning forests of residually finite groups abstract we prove a number of identities relating the sofic entropy of a certain class of non expansive algebraic dynamical systems the sofic entropy of the wired spanning forest and the tree entropy of cayley graphs of residually finite groups we also show that homoclinic points and periodic points in harmonic models are dense under general conditions

almost commuting permutations are near commuting permutations abstract we prove that the commutator is stable in permutations endowed with the hamming distance that is two permutations that almost commute are near two commuting permutations our result extends to k tuples of almost commuting permutations for any given k and allows restrictions for instance to even permutations

group stability and property t abstract in recent years there has been a considerable amount of interest in the stability of a finitely generated group with respect to a sequence of groups g n n 1 equipped with bi invariant metrics d n n 1 we consider the case g n u n resp g n sym n equipped with the normalized hilbert schmidt metric d n hs resp the normalized hamming metric d n hamming our main result is that if is infinite hyperlinear resp sofic and has property t then it is not stable with respect to u n d n hs resp sym n d n hamming this answers a question of hadwin and shulman regarding the stability of sl 3 z we also deduce that the mapping class group mcg g g 3 and aut f n n 3 are not stable with respect to sym n d n hamming our main result exhibits a difference between stability with respect to the normalized hilbert schmidt metric on u n and the unnormalized p schatten metrics since many groups with property t are stable with respect to the latter metrics as shown by de chiffre glebsky lubotzky thom and lubotzky oppenheim we suggest a more flexible notion of stability that may repair this deficiency of stability with respect to u n d n hs and sym n d n hamming

optimal repeated measurements designs for correlated observations and analysis by weighted least squares summary we consider a model for repeated measurements designs where the measurements on the same unit are assumed to be correlated with known correlation coefficient it is shown that latin squares with an additional balancing property are e optimal for the weighted least squares estimate

entropy determinants and l 2 torsion we show that for any amenable group and any z module m of type fl with vanishing euler characteristic the entropy of the natural action on the pontryagin dual of m is equal to the l 2 torsion of m as a particular case the entropy of the principal algebraic action associated with the module z z f is equal to the logarithm of the fuglede kadison determinant of f whenever f is a non zero divisor in z this conrms a conjecture of deninger as a key step in the proof we provide a general szeg o type approximation theorem for the fuglede kadison determinant on the group von neumann algebra of an amenable group as a consequence of the equality between l 2 torsion and entropy we show that the l 2 torsion of a non trivial amenable group with nite classifying space vanishes this was conjectured by luck finally we establish a milnor turaev formula for the l 2 torsion of a nite acyclic chain complex

c algebras with weak fn letabe a simplec algebra of real rank zero and stable rank one we show that for any normal elementx awith x inv0 a forall sp x there is a sequence of normal elementsxn awith finite spectra such thatx limn xn we show this for more generalc algebras we also point out that the condition thatais simple cannot be removed

optimality and efficiency of two treatment repeated measurements designs for an arbitrary covariance matrix and any number of treatments and periods necessary and sufficient conditions for the optimality of a repeated measurements i e crossover or changeover design were given in the as yet unpublished report by h b kushner optimal repeated measurements designs the linear optimality equations kushner report here we specialise the results to the two treatment case we give linear equations whose solutions are the proportions of subjects allocated to each treatment sequence in the most general optimal design the treatment effects information matrix of an optimal design is also presented the results are applied to several situations for arbitrary covariance matrices we show that designs consisting of at most two treatment sequences and their duals must necessarily be dual balanced to be optimal for autoregressive covariance matrices we confirm that designs of matthews 1987 for three and four periods are optimal and we derive new optimal designs for five and six periods some optimality results of laska meisner 1985 are extended a simple formula for the efficiency of a dual balanced nonoptimal design is provided and used to compute the exact efficiencies of some of kunert s 1991 designs

incipient sliding of rough surfaces in contact a multiscale numerical analysis in this paper the cattaneo theory of frictional contact is extended to elastic half spaces in contact through rough disordered interfaces the discrete version of the cattaneo theorem is provided and represents the basis of a multiscale numerical contact algorithm mathematical surfaces with imposed roughness as well as experimentally digitised ones are analysed by means of a numerical method the evolution of the contact domain at different resolution is investigated roughness of the interfaces provides lacunarity of the contact domains whose fractal dimension is always smaller than 2 0 when a tangential force is applied the extent of the stick area decreases in the same way as the contact area develops with increasing pressure and the slip area is found to be proportional to the tangential force as predicted by cattaneo theory the evolution of the shear centroid as well as the amount of dissipated energy up to full sliding are provided finally it is shown that at a sufficient level of discretization the distribution of contact pressures is multifractal

when almost multiplicative morphisms are close to homomorphisms absrract it is shown that approximately multiplicative contractive positive morphisms from c x with dim x 2 into a simple c algebra a of real rank zero and of stable rank one are close to homomorphisms provided that certain k theoretical obstacles vanish as a corollary we show that a homomorphism h c x a is approximated by homomorphisms with finite dimensional range if h gives no k theoretical obstacle

on the lattice of normal subgroups in ultraproducts of compact simple groups we prove that the lattice of normal subgroups of ultraproducts of compact simple non abelian groups is distributive in the case of ultraproducts of finite simple groups or compact connected simple lie groups of bounded rank the set of normal subgroups is shown to be linearly ordered by inclusion 2010 mathematics subject classification 03c20 20d30 primary 20f69 20d06 22e46 secondary

optimal design and refinement of the linera model with applications to repeated measurements designs the information matrices of one design in a finer and a simpler linear model are compared to each other the orthogonality condition ensuring that both matrices are equal is examined in the model for repeated measurements designs which was considered e g by cheng and wu 1980 examples of unbalanced designs fulfilling the orthogonality condition are shown to be optimum moreover nearly strongly balanced generalized latin squares are introduced and their universal optimality is proved if the numbers of units and periods are sufficiently large

a unified theory of surface roughness the properties of the peaks and summits of a rough surface are predicted on the assumption that the surface is two dimensional random noise the important result is that in non dimensional form the answers depend only to a minor degree on the parameters describing the surface or on the sampling interval used on the other hand the absolute values are strongly dependent on the sampling interval experimental results on a real surface agree remarkably well with the predictions