K-Theory of Azumaya Algebras over Schemes

Let X be a connected, noetherian scheme and A{script} be a sheaf of Azumaya algebras on X, which is a locally free O{script}-module of rank a. We show that the kernel and cokernel of K(X) ? K(A{script}) are torsion groups with exponent a for some m and any i = 0, when X is regular or X is of dimension d with an ample sheaf (in this case m = d + 1). As a consequence, K(X, Z/m) ? K(A{script}, Z/m), for any m relatively prime to a. © 2013 Copyright Taylor and Francis Group, LLC.

Topology synthesis of three-legged spherical parallel manipulators employing Lie group theory

Driven by the requirements of the bionic joint or tracking equipment for the spherical parallel manipulators (SPMs) with three rotational degrees-of-freedom (DoFs), this paper carries out the topology synthesis of a class of three-legged SPMs employing Lie group theory. In order to achieve the intersection of the displacement subgroups, the subgroup characteristics and operation principles are defined in this paper. Mainly drawing on the Lie group theory, the topology synthesis procedure of three-legged SPMs including four stages and two functional blocks is proposed, in which the assembly principles of three legs are defined. By introducing the circular track, a novel class of three-legged SPMs is synthesized, which is the important complement to the existing SPMs. Finally, four typical examples are given to demonstrate the finite displacements of the synthesized three-legged SPMs.

Graded/Gradient Porous Biomaterials

Biomaterials include bioceramics, biometals, biopolymers and biocomposites and they play important roles in the replacement and regeneration of human tissues. However, dense bioceramics and dense biometals pose the problem of stress shielding due to their high Young's moduli compared to those of bones. On the other hand, porous biomaterials exhibit the potential of bone ingrowth, which will depend on porous parameters such as pore size, pore interconnectivity, and porosity. Unfortunately, a highly porous biomaterial results in poor mechanical properties. To optimise the mechanical and the biological properties, porous biomaterials with graded/gradient porosity, pores size, and/or composition have been developed. Graded/gradient porous biomaterials have many advantages over graded/gradient dense biomaterials and uniform or homogenous porous biomaterials. The internal pore surfaces of graded/gradient porous biomaterials can be modified with organic, inorganic, or biological coatings and the internal pores themselves can also be filled with biocompatible and biodegradable materials or living cells. However, graded/gradient porous biomaterials are generally more difficult to fabricate than uniform or homogenous porous biomaterials. With the development of cost-effective processing techniques, graded/gradient porous biomaterials can find wide applications in bone defect filling, implant fixation, bone replacement, drug delivery, and tissue engineering.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).

Ideals of A(G) and bimodules over maximal abelian selfadjoint algebras

This paper is concerned with weak⁎ closed masa-bimodules generated by A(G)-invariant subspaces of VN(G). An annihilator formula is established, which is used to characterise the weak⁎ closed subspaces of B(L2(G)) which are invariant under both Schur multipliers and a canonical action of M(G) on B(L2(G)) via completely bounded maps. We study the special cases of extremal ideals with a given null set and, for a large class of groups, we establish a link between relative spectral synthesis and relative operator synthesis.

Cyclic nanoindentation and nano-impact fatigue characterisation of functionally graded TiN/TiNi shape memory film

This paper investigates the mechanism of nanoscale fatigue of functionally graded TiN/TiNi films using nano-impact and multiple-loading-cycle nanoindentation tests. The functionally graded films were deposited on silicon substrate, in which TiNi films maintain shape memory and pseudo elastic behavior, while a modified TiN surface layer provides tribological and anti-corrosion properties. Nanomechanical tests were performed to comprehend the localized film performance and failure modes of the functionally graded film using NanoTestTM equipped with Berkovich and conical indenter between 100 μN to 500 mN loads. The loading mechanism and load history are critical to define film failure modes (i.e. backward depth deviation) including the shape memory effect of the functionally graded layer. The results are sensitive to the applied load, loading type (e.g. semi-static, dynamic) and probe geometry. Based on indentation force-depth profiles, depth-time data and post-test surface observations of films, it is concluded that the shape of the nanoindenter is critical in inducing the localized indentation stress and film failure, including shape recovery at the lower load range. Elastic-plastic finite element (FE) simulation during nanoindentation loading indicated that the location of subsurface maximum stress near the interface influences the backward depth deviation type of film failure. A standalone, molecular dynamics simulation was performed with the help of a long range potential energy function to simulate the tensile test of TiN nanowire with two different aspect ratios to investigate the theory of its failure mechanism.

Temperature controlled motion of an antiferromagnet- ferromagnet interface within a dopant-graded FeRh epilayer

Chemically ordered B2 FeRh exhibits a remarkable antiferromagnetic-ferromagnetic phase transition that is first order. It thus shows phase coexistence, usually by proceeding though nucleation at random defect sites followed by propagation of phase boundary domain walls. The transition occurs at a temperature that can be varied by doping other metals onto the Rh site. We have taken advantage of this to yield control over the transition process by preparing an epilayer with oppositely directed doping gradients of Pd and Ir throughout its height, yielding a gradual transition that occurs between 350 K and 500 K. As the sample is heated, a horizontal antiferromagnetic-ferromagnetic phase boundary domain wall moves gradually up through the layer, its position controlled by the temperature. This mobile magnetic domain wall affects the magnetisation and resistivity of the layer in a way that can be controlled, and hence exploited, for novel device applications.

Norms of basic elementary operators on algebras of regular operators

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ L^r(E) and M_A,_B is the operator on L^r(E) defined by M_A,_B(T) = AT B then ||M_A,_B||r = ||A||_r||B||_r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.