Time operators for one parameter semigroups

We develop two simple approaches to the construction of time operators for semigroups of continuous linear operators in Hilbert spaces provided that the generators of these semigroups are normal operators. The first approach enables us to give explicit formulas (in the spectral representations) both for the time operators and for their eigenfunctions. The other approach provides no explicit formula. However, it enables us to find necessary and sufficient conditions for the existence of time operators for semigroups of continuous linear operators in separable Hilbert spaces with normal generators. Time superoperators corresponding to unitary groups are also discussed.

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

Extended spectral decompositions of the Renyi map

We present new general methods to obtain spectral decompositions of dynamical systems in rigged Hilbert spaces and investigate the existence of resonances and the completeness of the associated eigenfunctions. The results are illustrated explicitly for the simplest chaotic endomorphism, namely the Renyi map.

Intelligent Assembly Time Analysis Using a Digital Knowledge-Based Approach

The implementation of effective time analysis methods fast and accurately in the era of digital manufacturing has become a significant challenge for aerospace manufacturers hoping to build and maintain a competitive advantage. This paper proposes a structure oriented, knowledge-based approach for intelligent time analysis of aircraft assembly processes within a digital manufacturing framework. A knowledge system is developed so that the design knowledge can be intelligently retrieved for implementing assembly time analysis automatically. A time estimation method based on MOST, is reviewed and employed. Knowledge capture, transfer and storage within the digital manufacturing environment are extensively discussed. Configured plantypes, GUIs and functional modules are designed and developed for the automated time analysis. An exemplar study using an aircraft panel assembly from a regional jet is also presented. Although the method currently focuses on aircraft assembly, it can also be well utilized in other industry sectors, such as transportation, automobile and shipbuilding. The main contribution of the work is to present a methodology that facilitates the integration of time analysis with design and manufacturing using a digital manufacturing platform solution.

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Cohomology of Banach algebras of operators and geometry of Banach spaces.

In the paper we give an exposition of the major results concerning the relation between first order cohomology of Banach algebras of operators on a Banach space with coefficients in specified modules and the geometry of the underlying Banach space. In particular we shall compare the properties weak amenability and amenability for Banach algebras A(X), the approximable operators on a Banach space X. Whereas amenability is a local property of the Banach space X, weak amenability is often the consequence of properties of large scale geometry.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

An Educational Initative in Anaesthetic Nursing Practice

The National Board for Nurses, Midwives and Health Visitors in Northern Ireland (NBNI) has adopted the principles of the UKCC's recommendations for specialist nursing practice and Incorporated these within their continuing education framework. Stage two of this framework decrees the standard required for specialist nursing practice (NBNI, 1995) and, as a result, a specialist anaesthetic nursing course has been instigated. The course extends over 44 weeks and includes 8 weeks of consolidation practice, comprising seven modules at degree and diploma level. The course gives the students an opportunity to deepen their knowledge, skills and attitudes in the field of anaesthetic nursing. Nurses were taught the necessary skills to work in collaboration with other professionals, patients and families in order to coordinate a patient-centred approach to perianaesthetic care. The role of the anaesthetic nurse specialist should be viewed as complementary to that of the anaesthetist. This course facilitates and encourages practitioners to move beyond registered practice on qualifying to a more specialized role where care is delivered in an innovative and creative manner.

Group Design-Build-Test Projects as the Core of an Integrated Curriculum in Product Design and Development

The School of Mechanical and Aerospace Engineering at Queen’s University Belfast introduced a new degree programme in Product Design and Development (PDD) in 2004. As well as setting out to meet all UK-SPEC requirements, the entirely new curriculum was developed in line with the syllabus and standards defined by the CDIO Initiative, an international collaboration of universities aiming to improve the education of engineering students. The CDIO ethos is that students are taught in the context of conceiving, designing, implementing and operating a product or system. Fundamental to this is an integrated curriculum with multiple Design-Build-Test (DBT) experiences at the core. Unlike most traditional engineering courses the PDD degree features group DBT projects in all years of the programme. The projects increase in complexity and challenge in a staged manner, with learning outcomes guided by Bloom’s taxonomy of learning domains. The integrated course structure enables the immediate application of disciplinary knowledge, gained from other modules, as well as development of professional skills and attributes in the context of the DBT activity. This has a positive impact on student engagement and the embedding of these relevant skills, identified from a stakeholder survey, has also been shown to better prepare students for professional practice. This paper will detail the methodology used in the development of the curriculum, refinements that have been made during the first five years of operation and discuss the resource and staffing issues raised in facilitating such a learning environment.

Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator V and a rank 2 operator R acting on a Hilbert space H are constructed such that V + R is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.

CCN3-A key regulator of the hematopoietic compartment

CCN3, a founding member of the CCN family of growth regulators, was linked with hematology in 2003(1) when it was detected in human serum. CCN3 is expressed and secreted by hematopoietic progenitor cells in normal bone marrow. CCN3 acts through the core stem cell signalling pathways including Notch and Bone Morphogenic Protein, connecting CCN3 with the modulation of self-renewal and maturation of a number of cell lineages including hematopoietic, osteogenic and chondrogenic. CCN3 expression is disrupted in Chronic Myeloid Leukemia as a consequence of the BCR-ABL oncogene and allows the leukemic clone to evade growth regulation. In contrast, naive cord blood progenitors undergo enhanced clonal expansion in response to CCN3. Altered CCN3 expression is associated with numerous solid tumors including glioblastoma, melanoma. adrenocortical tumours, prostate cancer and bone malignancies including osteosarcoma. Mature CCN3 protein has five distinct modules and truncated protein variants with altered function are found in many cancers. Regulation by CCN3 is therefore cell type and isoform specific. CCN3 has emerged as a key player in stem cell regulation, hematopoiesis and a crucial component within the bone marrow microenvironment. (c) 2008 Elsevier Ltd. All rights reserved.

Faithful test of nonlocal realism with entangled coherent states

We investigate the violation of Leggett's inequality for nonlocal realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the nonlocal realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows one to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original arguments to continuous-variable states.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.