anticommutation in the presentations of theta deformed spheres abstract we consider an analogue of the deformed even spheres modifying the relations demanded of the self adjoint generator x in the usual presentation in this analogue x is given anticommutation relations with all of the other generators as opposed to being central the main result shows that these algebras satisfy a borsuk ulam property that is visible in even k theory

inverse problem of non homogeneous residual stress identification in thin plates abstract vibration of solid bodies with residual stresses has been attracting attention of researchers from different countries for a long time problems of residual stress analysis have its applications in fields of building mechanical engineering aircraft construction biomechanics manufacturing of composite and functionally gradient materials the most common model of residual stresses or prestresses is the homogeneous prestress state model however in fact the prestress state is often non homogeneous under natural conditions one of the most powerful nondestructive methods of reconstruction of non homogeneous prestress state is the acoustical method in the present paper the direct problem formulations for 3d bodies and thin plates with non homogeneous prestress fields are described a formulation of the inverse problem on a reconstruction of non homogeneous prestress state is given on the basis of acoustical method the problem is reduced to the iterative process at each step of the latter the direct problem and the integral fredholm equation of the first kind are solved two ways of obtaining operator equations of the inverse problem are presented for two oscillation regimes in plane and out of plane plate vibration modes numerical results of solving the inverse problem on a reconstruction of the uniaxial prestress function in case of out of plane vibration for a thin rectangular plate are presented features and characteristics of the solutions obtained are revealed the most auspicious conditions for a better quality of the identification procedure are pointed out

approximations for expected generation number a deterministic formula is commonly used to approximate the expected generation number of a population of growing cells however this can give misleading results because it does not allow for natural variation in the times that individual cells take to reproduce here we present more accurate approximations for both symmetric and asymmetric cell division based on the first two moments of the generation time distribution these approximations are also robust we illustrate the improved approximations using data that arise from monitoring individual yeast cells under a microscope and also demonstrate how the approximations can be used when such detailed data are not available

equivariant deformations of homogeneous spaces abstract c algebraic deformations of homogeneous spaces g are constructed by completing dense subspaces of c 0 g in a different multiplication and c norm these deformations are equivariant in the sense that they still carry a natural action of g by left translation the motivating examples are the noncommutative heisenberg manifolds of rieffel but the construction given here is based on the authors twisted dual group algebras which are equivariant deformations of c 0 g the procedure is general enough to give other recently studied families of noncommutative spaces and some interesting new examples of simple c algebras

free products of compact quantum groups we construct and study compact quantum groups from free products ofc algebras in this connection we discover two mysterious classes of natural compact quantum groups a u m anda o m thea u m s respectivelya o m s are non isomorphic to each other for differentm s and are not obtainable by the ordinary quantization method we also clarify some basic concepts in the theory of compact quantum groups

deformation of operator algebras by borel cocycles abstract assume that we are given a coaction of a locally compact group g on a c algebra a and a t valued borel 2 cocycle on g motivated by the approach of kasprzak to rieffel s deformation we define a deformation a of a among other properties of a we show that a k l 2 g is canonically isomorphic to a g g this together with a slight extension of a result of echterhoff et al implies that for groups satisfying the baum connes conjecture the k theory of a remains invariant under homotopies of

deformation quantization for actions of qpd abstract the main objective of this article is to develop the theory of deformation of c algebras endowed with a group action from the perspective of non formal equivariant quantization this program initiated in 4 aims to extend rieffel s deformation theory 27 for more general groups than r d in 4 we have constructed such a theory for a class of non abelian lie groups in the present article we study the somehow opposite situation of abelian but non lie groups more specifically we construct here a deformation theory of c algebras endowed with an action of a finite dimensional vector space over a non archimedean local field of characteristic different from 2 at the root of our construction stands the p adic version of the weyl quantization introduced by haran 12 and further extended by bechata 1 and unterberger 34

systemes dynamiques non commutatifs et moyennabilite on introduit la notion de fonction de type positif relativement a un systeme dynamique c dont les proprietes sont analogues a celles des fonctions de type positif classiques on montre que dans le cas d un groupe discret g agissant sur une algebre de von neumann m la moyennabilite de l action est equivalente a l existence d une suite bornee de fonctions de type positif sur g a support fini a valeurs dans le centre z m de m qui converge vers 1 pour la topologie de la convergence simple ultrafaible

an equivariant brauer semigroup and the symmetric imprimitivity theorem suppose that x g is a second countable locally compact transformation group we let sg x denote the set of morita equivalence classes of separable dynamical systems a g where a is a c0 x algebra and is compatible with the given g action on x we prove that sg x is a commutative semigroup with identity with respect to the binary operation a g b g a x b g x for an appropriately defined balanced tensor product on c0 x algebras if g and h act freely and properly on the left and right of a space x then we prove that sg x h and sh g x are isomorphic as semigroups if the isomorphism maps the class of a g to the class of b h then a o g is morita equivalent to b o h

the brauer group of a locally compact groupoid we define the brauer group br g of a locally compact groupoid g to be the set of morita equivalence classes of pairs a consisting of an elementary c bundle a over g 0 satisfying fell s condition and an action of g on a by isomorphisms when g is the transformation groupoid x h then br g is the equivariant brauer group br h x in addition to proving that br g is a group we prove three isomorphism results first we show that if g and h are equivalent groupoids then br g and br h are isomorphic this generalizes the result that if g and h are groups acting freely and properly on a space x say g on the left and h on the right then br g x h and br h g x are isomorphic secondly we show that the subgroup br0 g of br g consisting of classes a with a having trivial dixmier douady invariant is isomorphic to a quotient e g of the collection tw g of twists over g finally we prove that br g is isomorphic to the inductive limit ext g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of the groups e g x where x varies over all principal g spaces x and g x is the imprimitivity groupoid associated to x

a new stable inverse method for identification of the elastic constants of a three dimensional generally anisotropic solid abstract this article presents a new approach for inverse identification of all elastic constants of a 3d generally anisotropic solid with arbitrary geometry via measured strain data to eradicate the nonlinear inequality constraints posed on the elastic constants the problem is first transformed to an unconstrained one by the cholesky factorization theorem the cost function is defined by the tikhonov regularization method and the inverse problem is solved using the damped gauss newton technique where a meshless method is employed for the direct and sensitivity analyses to demonstrate the effectiveness of the proposed approach several examples are presented in the end where all experimental data are numerically simulated analyses of these examples show that all twenty one elastic constants of an example material can be correctly identified even when measurement errors are relatively large and initial guesses are far from exact values

a smoothed inverse eigenstrain method for reconstruction of the regularized residual fields abstract a smoothed inverse eigenstrain method is developed for reconstruction of residual field from limited strain measurements a framework for appropriate choice of shape functions based on the prior knowledge of expected residual distribution is presented which results in stabilized numerical behavior the analytical method is successfully applied to three case studies where residual stresses are introduced by inelastic beam bending laser forming and shot peening the well rehearsed advantage of the proposed eigenstrain based formulation is that it not only minimizes the deviation of measurements from its approximations but also will result in an inverse solution satisfying a full range of continuum mechanics requirements the smoothed inverse eigenstrain approach allows suppressing fluctuations that are contrary to the physics of the problem furthermore a comprehensive discussion is performed on regularity of the asymptotic solution in the tikhonov scheme and the regularization parameter is then exactly determined utilizing morozov discrepancy principle gradient iterative regularization method is also examined and shown to have an excellent convergence to the tikhonov morozov regularization results

new approximations to the malthusian parameter approximations to the malthusian parameter of an age dependent branching process are obtained in terms of the moments of the lifetime distribution by exploiting a link with renewal theory in several examples the new approximations are more accurate than those currently in use even when based on only the first two moments the new approximations are extended to include a form of asymmetric cell division that occurs in some species of yeast when used for inference the new approximations are shown to have high efficiency

symmetry of quantum torus with crossed product algebra in this paper we study the symmetry of quantum torus with the concept of crossed product algebra as a classical counterpart we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function an invariant function under the group action is constructed as a variant of the classical theta function then our main issue the crossed product algebra representation of a quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding we perform this analysis with manin s so called model ii quantum theta function approach the symplectic group sp 2n z satisfies the consistency condition of a crossed product algebra representation of quantum torus times the algebra of functions on the siegel space however only a subgroup of sp 2n z satisfies the consistency condition for orbifolding of the quantum torus

noncommutative instantons from twisted conformal symmetries we construct a five parameter family of gauge nonequivalent su 2 instantons on a noncommutative four sphere s theta 4 and of topological charge equal to 1 these instantons are critical points of a gauge functional and satisfy self duality equations with respect to a hodge star operator on forms on s theta 4 they are obtained by acting with a twisted conformal symmetry on a basic instanton canonically associated with a noncommutative instanton bundle on the sphere a completeness argument for this family is obtained by means of index theorems the dimension of the tangent space to the moduli space is computed as the index of a twisted dirac operator and turns out to be equal to five a number that survives deformation

induction in stages for crossed products of c algebras by maximal coactions let be a maximal coaction of a locally compact group g on a c algebra b and let n and h be closed normal subgroups of g with n h we show that the process indg hg which uses mansfield s bimodule to induce representations of b g from those of b g h is equivalent to the two stage induction process indg ng indg hg n the proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces

a new look at crossed product correspondences and associated c algebras abstract when a locally compact group acts on a c correspondence it also acts on the associated cuntz pimsner algebra in a natural way hao and ng have shown that when the group is amenable the cuntz pimsner algebra of the crossed product correspondence is isomorphic to the crossed product of the cuntz pimsner algebra in this paper we have a closer look at this isomorphism in the case where the group is not necessarily amenable we also consider what happens at the level of toeplitz algebras

k theory of equivariant quantization abstract using an equivariant version of connes thom isomorphism we prove that equivariant k theory is invariant under strict deformation quantization for a compact lie group action

deformation quantization and the baum connes conjecture alternative titles of this paper would have been index theory without index or the baum connes conjecture without baum

noncommutative manifolds the instanton algebra and isospectral deformations we give new examples of noncommutative manifolds that are less standard than the nc torus or moyal deformations of n they arise naturally from basic considerations of noncommutative differential topology and have non trivial global features

basis functions for residual stresses abstract we consider arbitrary preexisting residual stress states in arbitrarily shaped unloaded bodies these stresses must be self equilibrating and traction free common treatments of the topic tend to focus on either the mechanical origins of the stress or methods of stress measurement at certain locations here we take the stress field as given and consider the problem of approximating any such stress field in a given body as a linear combination of predetermined fields which can serve as a basis we consider planar stress states in detail and introduce an extremization problem that leads to a linear eigenvalue problem eigenfunctions of that problem form an orthonormal basis for all possible residual stress states of sufficient smoothness in numerical examples convergence of the approximating stress fields is demonstrated in the l2 norm for continuous stress fields as well as for a stress field with a simple discontinuity finally we outline the extension of our theory to three dimensional bodies and states of stress our approach can be used to describe arbitrary preexisting residual stress states in arbitrarily shaped bodies using basis functions that are determined by the body geometry alone

on an inverse problem for inhomogeneous thermoelastic rod abstract in recent years different fields of engineering have been increasingly incorporating functionally graded materials with variable physical properties that significantly improve a quality of elements of designs the efficiency of practical application of thermoelastic inhomogeneous materials depends on knowledge of exact laws of heterogeneity and to define them it is necessary to solve coefficient inverse problems of thermoelasticity in the present research a scheme of solving the inverse problem for an inhomogeneous thermoelastic rod is presented two statements of the inverse problem are considered in the laplace transform space and in the actual space the direct problem solving is reduced to a system of the fredholm integral equations of the 2nd kind in the laplace transform space and an inversion of the solutions obtained on the basis of the theory of residues the inverse problem solving is reduced to an iterative procedure at its each step it is necessary to solve the fredholm integral equation of the 1st kind to solve it the tikhonov method is used specific examples of a reconstruction of variable characteristics required are given

continuous orbit equivalence flow equivalence of markov shifts and circle actions on cuntz krieger algebras we will study circle actions on cuntz krieger algebras trivially acting on its canonical maximal abelian c subalgebras from the view points of continuous orbit equivalence of one sided topological markov shifts and flow equivalence of two sided topological markov shifts

proper actions on imprimitivity bimodules and decompositions of morita equivalences we consider a class of proper actions of locally compact groups on imprimitivity bimodules over c algebras which behave like the proper actions on c algebras introduced by rieffel in 1988 we prove that every such action gives rise to a morita equivalence between a crossed product and a generalized fixed point algebra and in doing so make several innovations which improve the applicability of rieffel s theory we then show how our construction can be used to obtain canonical tensor product decompositions of important morita equivalences our results show for example that the different proofs of the symmetric imprimitivity theorem for actions on graph algebras yield isomorphic equivalences and this gives new information about the amenability of actions on graph algebras

an analogue of the thom isomorphism for crossed products of a c algebra by an action of r abstract in this paper we show the existence and uniqueness of a natural isomorphism oj of kj a with kj 1 a r j z 2 where a r is a c dynamical r system k is the functor of topological k theory and a r is the crossed product of a by the action of r the pimsner voiculescu exact sequence is obtained as a corollary we show that given an invariant trace on a with dual trace gt one has gto 1 u 1 2 i u u for any unitary u in the domain of the derivation of a associated to the action finally we show that the crossed product of c s3 continuous functions on the 3 sphere by a minimal diffeomorphism is a simple c algebra with no nontrivial idempotent

isomorphism and morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of sl2 z abstract let be irrational numbers and a b be matrices in s l 2 z of infinite order we compute the k theory of the crossed product a a z and show that a a z and a b z are isomorphic if and only if mod z and i a 1 is matrix equivalent to i b 1 combining this result and an explicit construction of equivariant bimodules we show that a a z and a b z are morita equivalent if and only if and are in the same g l 2 z orbit and i a 1 is matrix equivalent to i b 1 finally we determine the morita equivalence class of a f for any finite subgroup f of s l 2 z

enveloping actions and takai duality for partial actions we show that any partial action on a topological space x is the restriction of a suitable global action called enveloping action that is essentially unique in the case of c algebras we prove that any partial action has a unique enveloping action up to morita equivalence and that the corresponding reduced crossed products are morita equivalent the study of the enveloping action up to morita equivalence reveals the form that takai duality takes for partial actions by applying our constructions we prove that the reduced crossed product of the reduced cross sectional algebra of a fell bundle by the dual coaction is liminal postliminal or nuclear if and only if so is the unit fiber of the bundle we also give a non commutative generalization of the well known fact that the integral curves of a vector field on a compact manifold are defined on all of r

non compact quantum groups associated with abelian subgroups letg be a lie group for any abelian subalgebra mathfrak h of the lie algebra g ofg and any r in mathfrak h lambda mathfrak h the difference of the left and right translates ofr gives a compatible poisson bracket ong we show how to construct the corresponding quantum group in thec algebra setting the main tool used is the general deformation quantization construction developed earlier by the author for actions of vector groups onc algebras

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

an equivariant brauer group and actions of groups onc algebras suppose that g t is a second countable locally compact trans formation group given by a homomorphism l g homeo t and that a is a separable continuous trace c algebra with spectrum t an action g aut a is said to cover l if the induced action of g on t coincides with the original one we prove that the set brg t of morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product a b a c0 t b and we refer to brg t as the equivariant brauer group we give a detailed analysis of the structure of brg t in terms of the moore cohomology of the group g and the integral cohomology of the space t using this we can characterize the stable continuous trace c algebras with spectrum t which admit actions covering l in particular we prove that if g r then every stable continuous trace c algebra admits an essentially unique action covering l thereby substantially improving results of raeburn and rosenberg

on the structure of twisted group c algebras we first give general structural results for the twisted group algebras c g of a locally compact group g with large abelian subgroups in particular we use a theorem of williams to realise c g as the sections of a c bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras next we use a device of rosenberg to show that when is a discrete subgroup of a solvable lie group g the k groups k c are isomorphic to certain twisted k groups k g of the homogeneous space g and we discuss how the twisting class h 3 g z depends on the cocycle

noncommutative finite dimensional manifolds i spherical manifolds and related examples we exhibit large classes of examples of noncommutative finite dimensional manifolds which are non formal deformations of classical manifolds the main result of this paper is a complete description of noncommutative three dimensional spherical manifolds a noncommutative version of the sphere s 3 defined by basic k theoretic equations we find a 3 parameter family of deformations of the standard 3 sphere s 3 and a corresponding 3 parameter deformation of the 4 dimensional euclidean space 4 for generic values of the deformation parameters we show that the obtained algebras of polynomials on the deformed 4 u only depend on two parameters and are isomorphic to the algebras introduced by sklyanin in connection with the yang baxter equation it follows that different can span the same this equivalence generates a foliation of the parameter space this foliation admits singular leaves reduced to a point these critical points are either isolated or fall in two 1 parameter families up to the simple operation of taking the fixed algebra by an involution these two families are identical and we concentrate here on c for the above isomorphism with the sklyanin algebra breaks down and the corresponding algebras are special cases of deformations a notion which we generalize in any dimension and various contexts and study in some detail here and this point is crucial the dimension is not an artifact i e the dimension of the classical model but is the hochschild dimension of the corresponding algebra which remains constant during the deformation besides the standard noncommutative tori examples of deformations include the recently defined noncommutative 4 sphere as well as m dimensional generalizations noncommutative versions of spaces and quantum groups which are deformations of various classical groups we develop general tools such as the twisting of the clifford algebras in order to exhibit the spherical property of the hermitian projections corresponding to the noncommutative dimensional spherical manifolds a key result is the differential self duality properties of these projections which generalize the self duality of the round instanton

branching process results in terms of moments of the generation time distribution a number of simple formulae concerning the growth rate doubling time and age distribution of cell populations are in common usage many of these are invalid unless the generation times have no variation a situation which occurs rarely the correct formulae which are available from the theory of age dependent branching processes are often ignored in the biological literature perhaps due to their complexity in this paper the major formulae from the theory of age dependent branching processes are reorganised in terms of the mean coefficient of variation and skewness of the generation times this leads to a greater insight into the theory and some simple formulae which account for the variability

reconstruction of inhomogeneous properties of orthotropic viscoelastic layer abstract the consecutive scheme of reconstructing the functions characterizing the instantaneous and long termed modules for inhomogeneous orthotropic viscoelastic layer whose properties continuously vary through a thickness is proposed the identification problem is solved on the basis of the additional information on the integral characteristics of displacement fields measured on top border of a layer iterative process of reconstruction of six unknown functions is formulated to reconstruct the rest six functions systems of fredholm s integral equations of the first kind with smooth kernels are received computational experiment on a reconstruction of various laws of inhomogeneity is conducted a comparative analysis of the results obtained is carried out

k groups of c algebras deformed by actions of rd abstract we show that the topological k groups of a c algebra deformed by an action of r d are isomorphic to those of the original c a1gebra we do this by exhibiting the deformed algebra as a suitable generalized fixed point algebra this also shows that the deformed algebra is nuclear if the original one is

exotic crossed products and the baum connes conjecture we study general properties of exotic crossed product functors and characterise those which extend to functors on equivariant c algebra categories based on correspondences we show that every such functor allows the construction of a descent in kk theory and we use this to show that all crossed products by correspondence functors of k amenable groups are kk equivalent we also show that for second countable groups the minimal exact morita compatible crossed product functor used in the new formulation of the baum connes conjecture by baum guentner and willett 4 extends to correspondences when restricted to separable g c algebras it therefore allows a descent in kk theory for separable systems

duality of restriction and induction for c coactions consider a coaction of a locally compact group g on a c algebra a and a closed normal subgroup n of g we prove following results of echterhoff for abelian g that mansfield s imprimitivity between a g n and a g r n implements equivalences between mansfield induction of representations from a g n to a g and restriction of representations froma g rn to a g and between restriction of representations from a g to a g n and green induction of representations from a g to a g r n this allows us to deduce properties of mansfield induction from the known theory of ordinary crossed products