Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

Silica templating of a self-assembling peptide amphiphile that forms nanotapes

The peptide amphiphile C16-KTTKS templates silica polymerization, enabling the production of silica nanotape structures, imaged via electron microscopy (TEM and SEM). X-ray scattering shows that the nanotapes comprise stacked layers, as for the parent peptide amphiphile, but with a substantially increased layer spacing resulting from silica polymerization.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Autobiographical memory and well-being in aging: the central role of semantic self-images

Higher levels of well-being are associated with longer life expectancies and better physical health. Previous studies suggest that processes involving the self and autobiographical memory are related to well-being, yet these relationships are poorly understood. The present study tested 32 older and 32 younger adults using scales measuring well-being and the affective valence of two types of autobiographical memory: episodic autobiographical memories and semantic self-images. Results showed that valence of semantic self-images, but not episodic autobiographical memories, was highly correlated with well-being,particularly in older adults. In contrast, well-being in older adults was unrelated to performance across a range of standardised memory tasks. These results highlight the role of semantic self-images in well-being, and have implications for the development of therapeutic interventions for well-being in aging.

Protocol for a feasibility study of a self help cognitive behavioural therapy resource for the reduction of dental anxiety in young people

Background Childhood dental anxiety is very common, with 10–20 % of children and young people reporting high levels of dental anxiety. It is distressing and has a negative impact on the quality of life of young people and their parents as well as being associated with poor oral health. Affected individuals may develop a lifelong reliance on general anaesthetic or sedation for necessary dental treatment thus requiring the support of specialist dental services. Children and young people with dental anxiety therefore require additional clinical time and can be costly to treat in the long term. The reduction of dental anxiety through the use of effective psychological techniques is, therefore, of high importance. However, there is a lack of high-quality research investigating the impact of cognitive behavioural therapy (CBT) approaches when applied to young people’s dental anxiety. Methods/design The first part of the study will develop a profile of dentally anxious young people using a prospective questionnaire sent to a consecutive sample of 100 young people referred to the Paediatric Dentistry Department, Charles Clifford Dental Hospital, in Sheffield. The second part will involve interviewing a purposive sample of 15–20 dental team members on their perceptions of a CBT self-help resource for dental anxiety, their opinions on whether they might use such a resource with patients, and their willingness to recruit participants to a future randomised controlled trial (RCT) to evaluate the resource. The third part of the study will investigate the most appropriate outcome measures to include in a trial, the acceptability of the resource, and retention and completion rates of treatment with a sample of 60 dentally anxious young people using the CBT resource. Discussion This study will provide information on the profile of dentally anxious young people who could potentially be helped by a guided self-help CBT resource. It will gain the perceptions of dental care team members of guided self-help CBT for dental anxiety in young people and their willingness to recruit participants to a trial. Acceptability of the resource to participants and retention and completion rates will also be investigated to inform a future RCT.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Control of nanomaterial self-assembly in ultrasonically levitated droplets

We demonstrate that acoustic trapping can be used to levitate and manipulate droplets of soft matter, in particular, lyotropic mesophases formed from selfassembly of different surfactants and lipids, which can be analyzed in a contact-less manner by X-ray scattering in a controlled gas-phase environment. On the macroscopic length scale, the dimensions and the orientation of the particle are shaped by the ultrasonic field, while on the microscopic length scale the nanostructure can be controlled by varying the humidity of the atmosphere around the droplet. We demonstrate levitation and in situ phase transitions of micellar, hexagonal, bicontinuous cubic, and lamellar phases. The technique opens up a wide range of new experimental approaches of fundamental importance for environmental, biological, and chemical research.

Engineering of 3D self-directed quantum dot ordering in multilayer InGaAs/GaAs nanostructures by means of flux gas composition

Lateral ordering of InGaAs quantum dots on the GaAs (001) surface has been achieved in earlier reports, resembling an anisotropic pattern. In this work, we present a method of breaking the anisotropy of ordered quantum dots (QDs) by changing the growth environment. We show experimentally that using As(2) molecules instead of As(4) as a background flux is efficient in controlling the diffusion of distant Ga adatoms to make it possible to produce isotropic ordering of InGaAs QDs over GaAs (001). The control of the lateral ordering of QDs under As(2) flux has enabled us to improve their optical properties. Our results are consistent with reported experimental and theoretical data for structure and diffusion on the GaAs surface.

THE FUNDAMENTAL GROUP OF THE SPACE OF MAPS FROM A SURFACE INTO THE PROJECTIVE PLANE

In this work we compute the fundamental group of each connected component of the function space of maps from it closed surface into the projective space

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Immobilized analogues of sunflower trypsin inhibitor-1 constitute a versatile group of affinity sorbents for selective isolation of serine proteases

Sunflower trypsin inhibitor-1 (SFI-1), a natural 14-residue cyclic peptide, and some of its synthetic acyclic variants are potent protease inhibitors displaying peculiar inhibitory profiles. Here we describe the synthesis and use of affinity sorbents prepared by coupling SFTI-1 analogues to agarose resin. Chymotrypsinand trypsin-like proteases could then be selectively isolated from pancreatin; similarly, other proteases were obtained from distinct biological sources. The binding capacity of [Lys5]-SFTI-1-agarose for trypsin was estimated at over 10 mg/mL of packed gel. SFTI-1-based resins could find application either to improve the performance of current purification protocols or as novel protease-discovery tools in different areas of biological investigation. (C) 2009 Elsevier B.V. All rights reserved.

A group of Litho students at the New York Trade School

A group of students from the New York Trade School studying lithography pose for a group photo. Black and white photograph mounted on paper.