Idempotent bounded C-semigroups

A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups.     

An interior-point trust-funnel algorithm for nonlinear optimization

We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. The prominent features of our algorithm are that (i) the subproblems that define each search direction may be solved with matrix-free methods so that derivative matrices need not be formed or factorized so long as matrix-vector products with them can be performed; (ii) the subproblems may be solved approximately in all iterations; (iii) in certain situations, the computed search directions represent inexact sequential quadratic optimization steps, which may be desirable for fast local convergence; (iv) criticality measures for feasibility and optimality aid in determining whether only a subset of computations need to be performed during a given iteration; and (v) no merit function or filter is needed to ensure global convergence.     

Concerning time and length scale estimates made from burst-mode LDA autocorrelation measurements

 An investigation was performed in grid-generated turbulence to highlight the difficulties in estimating integral and microscales from discrete autocorrelation measurements made using a burst-mode laser Doppler anemometer (LDA). Comparison was made to hot-wire results and the theoretical growth laws determined by the decay of turbulent energy. The chief concern was the presence of a spike in the measured autocorrelation coefficient functions at t=0. It was found that renormalizing the autocorrelation to a value at t=0 determined by “backfitting” a quadratic equation to the slots near t=0 led to microscale estimates that showed the same trend as the decay law and were in agreement with those determined using a hot-wire. Additionally, practical guidelines are presented for making accurate autocorrelation measurements by LDA. Received: 12 January 1995/Accepted: 9 June 1997     

N‐Alkoxyheterocycles As Irreversible Photooxidants

Irreversible photooxidation based on N–O bond fragmentation is demonstrated for N‐methoxyheterocycles in both the singlet and triplet excited state manifolds. The energetic requirements for bond fragmentation are studied in detail. Bond fragmentation in the excited singlet manifold is possible for ππ* singlet states with energies significantly larger than the N–O bond dissociation energy of ca 55 kcal mol^?1. For the nπ* triplet states, N–O bond fragmentation does not occur in the excited state for orbital overlap and energetic reasons. Irreversible photooxidation occurs in the singlet states by bond fragmentation followed by electron transfer. Irreversible photooxidation occurs in the triplet states via bimolecular electron transfer to the donor followed by bond fragmentation. Using these two sensitization schemes, donors can be irreversibly oxidized with oxidation potentials ranging from ca 1.6–2.2 V vs SCE. The corresponding N‐ethylheterocycles are characterized as conventional reversible photooxidants in their triplet states. The utility of these sensitizers is demonstrated by irreversibly generating the guanosine radical cation in buffered aqueous solution.     

Real-time cell electrophysiology using a multi-channel dielectrophoretic-dot microelectrode array

Dielectrophoresis (DEP) has been used for many years for the analysis of the electrophysiological properties of cells. However, such analyses have in the past been time-consuming, such that it can take 30 min or more to collect sufficient data to make valid interpretations from a single DEP spectrum. This has limited the application of the technology to a rapid tool for non-invasive, label-free research in areas from drug discovery to diagnostics. In this paper we present the development of a programmable, multi-channel DEP system for rapid biophysical assessment of populations of biological cells. A new assay format has been developed for continuous near-real-time monitoring, using simultaneous application of up to eight alternating current electrical signals to independently addressable dot microelectrodes in an array format, allowing a DEP spectrum to be measured in 20?s, with a total cycle time between measurements of 90?s. To demonstrate the system, human leukaemic K562 cells were monitored after exposure to staurosporine and valinomycin. The DEP response curves showed the timing and manner in which the membrane properties changed for the actions of these two drugs at the early phase of induction. This technology shows the great potential for increasing our understanding of the role of electrophysiology in drug action, by observing the changes in electrical characteristics as they occur.     

Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation,convergence and numerical results

An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for unconstrained optimization, generalizing at the same time an unpublished method due to Griewank (Technical Report NA/12, 1981, DAMTP, University of Cambridge), an algorithm by Nesterov and Polyak (Math Program 108(1):177–205, 2006) and a proposal by Weiser et al. (Optim Methods Softw 22(3):413–431, 2007). At each iteration of our approach, an approximate global minimizer of a local cubic regularisation of the objective function is determined, and this ensures a significant improvement in the objective so long as the Hessian of the objective is locally Lipschitz continuous. The new method uses an adaptive estimation of the local Lipschitz constant and approximations to the global model-minimizer which remain computationally-viable even for large-scale problems. We show that the excellent global and local convergence properties obtained by Nesterov and Polyak are retained, and sometimes extended to a wider class of problems, by our ARC approach. Preliminary numerical experiments with small-scale test problems from the CUTEr set show encouraging performance of the ARC algorithm when compared to a basic trust-region implementation.     

Axiomatisability problems for <Emphasis Type="Italic">S</Emphasis>-posets

Let \(\mathcal{C}\) be a class of ordered algebras of a given fixed type τ. Associated with the type is a first order language L _τ , which must also contain a binary predicate to be interpreted by the ordering in members of \(\mathcal{C}\). One can then ask the question, when is the class \(\mathcal{C}\) axiomatisable by sentences of L _τ ? In this paper we will be considering axiomatisability problems for classes of left S-posets over a pomonoid S (that is, a monoid S equipped with a partial order compatible with the binary operation). We aim to determine the pomonoids S such that certain categorically defined classes are axiomatisable. The classes we consider are the free S-posets, the projective S-posets and classes arising from flatness properties. Some of these cases have been studied in a recent article by Pervukhin and Stepanova. We present some general strategies to determine axiomatisability, from which their results for the classes of weakly po-flat and po-flat S-posets will follow. We also consider a number of classes not previously examined.     

On the Number of Inner Iterations Per Outer Iteration of a Globally Convergent Algorithm for Optimization with General Nonlinear Inequality Constraints and Simple Bounds

This paper considers the number of inner iterations required per outeriteration for the algorithm proposed by Conn et al.[9]. We show that asymptotically, under suitable reasonable assumptions, a single inner iteration suffices.