Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

Investigation of the M2/G2/1/ ∞, N Queue with Restricted Admission of Priority Customers and its Application to HSDPA Mobile Systems

This paper investigates a queuing system for QoS optimization of multimedia traffic consisting of aggregated streams with diverse QoS requirements transmitted to a mobile terminal over a common downlink shared channel. The queuing system, proposed for buffer management of aggregated single-user traffic in the base station of High-Speed Downlink Packet Access (HSDPA), allows for optimum loss/delay/jitter performance for end-user multimedia traffic with delay-tolerant non-real-time streams and partially loss tolerant real-time streams. In the queuing system, the real-time stream has non-preemptive priority in service but the number of the packets in the system is restricted by a constant. The non-real-time stream has no service priority but is allowed unlimited access to the system. Both types of packets arrive in the stationary Poisson flow. Service times follow general distribution depending on the packet type. Stability condition for the model is derived. Queue length distribution for both types of customers is calculated at arbitrary epochs and service completion epochs. Loss probability for priority packets is computed. Waiting time distribution in terms of Laplace-Stieltjes transform is obtained for both types of packets. Mean waiting time and jitter are computed. Numerical examples presented demonstrate the effectiveness of the queuing system for QoS optimization of buffered end-user multimedia traffic with aggregated real-time and non-real-time streams.

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.

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.

Contribution of rarity and commonness to patterns of species richness

There is little understanding in ecology as to how biodiversity patterns emerge from the distribution patterns of individual species. Here we consider the question of the contributions of rare (restricted range) and common (widespread) species to richness patterns. Considering a species richness pattern, is most of the spatial structure, in terms of where the peaks and troughs of diversity lie, caused by the common species or the rare species (or neither)? Using southern African and British bird richness patterns, we show here that commoner species are most responsible for richness patterns. While rare and common species show markedly different species richness patterns, most spatial patterning in richness is caused by relatively few, more common, species. The level of redundancy we found suggests that a broad understanding of what determines the majority of spatial variation in biodiversity may be had by considering only a minority of species.

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.

Two dimensional unital Riesz algebras, their representations and norms

We describe all two dimensional unital Riesz algebras and study representations of them in Riesz algebras of regular operators. Although our results are not complete, we do demonstrate that very varied behaviour can occur even though all these algebras can be given a Banach lattice algebra norm.

BubR1 is required for the mitotic block induced by combretastatin-A4 and a novel cis-restricted ß-lactam analogue in human cancer cells

BubR1 is a well-defined guardian of the mitotic spindle, initiating mitotic arrest in response to the lack of tension and/or chromosome alignment across the mitotic plate. However, the role of BubR1 in combretastatin-induced cell death remains unknown. In this study, we describe the effects of combretastatin A-4 (CA-4) and a synthetic cis-restricted 3,4-diaryl-2-azetidinone (ß-lactam) analogue (CA-432) on the modulation and phosphorylation of BubR1 in human cervical cancer-derived cells. We demonstrate that CA-4 and CA-432 depolymerise the microtubular network of human cervical carcinoma-derived cells. Both compounds induced the disassembly of the microtubules and the loss of microtubule tension led to the early phosphorylation of BubR1 and the late cleavage of BubR1. The phosphorylation of BubR1 correlated with the onset of G2M cell cycle arrest whilst the cleavage of BubR1 coincided with apoptosis induced by the combretastatins. The combretastatin-induced apoptosis and the BubR1 cleavage were caspase-dependent. In vitro enzyme digests demonstrated that combretastatin-activated BubR1 is a substrate for caspase-3. Gene silencing of BubR1 with small interfering RNA severely compromised combretastatin-induced G2M cell cycle arrest with a corresponding increase in the formation of polyploid cells in both cervical and breast cancer-derived cells. In summary, BubR1 is required to maintain the G2M arrest and limit the formation of polyploid cells in response to continued combretastatin exposure. Moreover, substitution of the ethylene bridge with 3,4-diaryl-2-azetidinone did not alter the tubulin depolymerising properties or the subsequent mitotic spindle checkpoint response to CA-4 in human cancer cells.