Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Global exponential periodicity of a class of neural networks with recent-history distributed delays

In this paper, we propose to study a class of neural networks with recent-history distributed delays. A sufficient condition is derived for the global exponential periodicity of the proposed neural networks, which has the advantage that it assumes neither the differentiability nor monotonicity of the activation function of each neuron nor the symmetry of the feedback matrix or delayed feedback matrix. Our criterion is shown to be valid by applying it to an illustrative system. (c) 2005 Elsevier Ltd. All rights reserved.

Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series. The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Analysis of the seasonal cycle within the first international urban land-surface model comparison

A number of urban land-surface models have been developed in recent years to satisfy the growing requirements for urban weather and climate interactions and prediction. These models vary considerably in their complexity and the processes that they represent. Although the models have been evaluated, the observational datasets have typically been of short duration and so are not suitable to assess the performance over the seasonal cycle. The First International Urban Land-Surface Model comparison used an observational dataset that spanned a period greater than a year, which enables an analysis over the seasonal cycle, whilst the variety of models that took part in the comparison allows the analysis to include a full range of model complexity. The results show that, in general, urban models do capture the seasonal cycle for each of the surface fluxes, but have larger errors in the summer months than in the winter. The net all-wave radiation has the smallest errors at all times of the year but with a negative bias. The latent heat flux and the net storage heat flux are also underestimated, whereas the sensible heat flux generally has a positive bias throughout the seasonal cycle. A representation of vegetation is a necessary, but not sufficient, condition for modelling the latent heat flux and associated sensible heat flux at all times of the year. Models that include a temporal variation in anthropogenic heat flux show some increased skill in the sensible heat flux at night during the winter, although their daytime values are consistently overestimated at all times of the year. Models that use the net all-wave radiation to determine the net storage heat flux have the best agreement with observed values of this flux during the daytime in summer, but perform worse during the winter months. The latter could result from a bias of summer periods in the observational datasets used to derive the relations with net all-wave radiation. Apart from these models, all of the other model categories considered in the analysis result in a mean net storage heat flux that is close to zero throughout the seasonal cycle, which is not seen in the observations. Models with a simple treatment of the physical processes generally perform at least as well as models with greater complexity.

Some necessary and sufficient conditions for eigenstructure assignment

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.

Sufficiency of Favard's condition for a class of band-dominated operators on the axis

The purpose of this paper is to show that, for a large class of band-dominated operators on $\ell^\infty(Z,U)$, with $U$ being a complex Banach space, the injectivity of all limit operators of $A$ already implies their invertibility and the uniform boundedness of their inverses. The latter property is known to be equivalent to the invertibility at infinity of $A$, which, on the other hand, is often equivalent to the Fredholmness of $A$. As a consequence, for operators $A$ in the Wiener algebra, we can characterize the essential spectrum of $A$ on $\ell^p(Z,U)$, regardless of $p\in[1,\infty]$, as the union of point spectra of its limit operators considered as acting on $\ell^p(Z,U)$.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Iron Uptake and Homeostasis in Microorganisms

Preface. Iron is considered to be a minor element employed, in a variety of forms, by nearly all living organisms. In some cases, it is utilised in large quantities, for instance for the formation of magnetosomes within magnetotactic bacteria or during use of iron as a respiratory donor or acceptor by iron oxidising or reducing bacteria. However, in most cases the role of iron is restricted to its use as a cofactor or prosthetic group assisting the biological activity of many different types of protein. The key metabolic processes that are dependent on iron as a cofactor are numerous; they include respiration, light harvesting, nitrogen fixation, the Krebs cycle, redox stress resistance, amino acid synthesis and oxygen transport. Indeed, it is clear that Life in its current form would be impossible in the absence of iron. One of the main reasons for the reliance of Life upon this metal is the ability of iron to exist in multiple redox states, in particular the relatively stable ferrous (Fe2+) and ferric (Fe3+) forms. The availability of these stable oxidation states allows iron to engage in redox reactions over a wide range of midpoint potentials, depending on the coordination environment, making it an extremely adaptable mediator of electron exchange processes. Iron is also one of the most common elements within the Earth’s crust (5% abundance) and thus is considered to have been readily available when Life evolved on our early, anaerobic planet. However, as oxygen accumulated (the ‘Great oxidation event’) within the atmosphere some 2.4 billion years ago, and as the oceans became less acidic, the iron within primordial oceans was converted from its soluble reduced form to its weakly-soluble oxidised ferric form, which precipitated (~1.8 billion years ago) to form the ‘banded iron formations’ (BIFs) observed today in Precambrian sedimentary rocks around the world. These BIFs provide a geological record marking a transition point away from the ancient anaerobic world towards modern aerobic Earth. They also indicate a period over which the bio-availability of iron shifted from abundance to limitation, a condition that extends to the modern day. Thus, it is considered likely that the vast majority of extant organisms face the common problem of securing sufficient iron from their environment – a problem that Life on Earth has had to cope with for some 2 billion years. This struggle for iron is exemplified by the competition for this metal amongst co-habiting microorganisms who resort to stealing (pirating) each others iron supplies! The reliance of micro-organisms upon iron can be disadvantageous to them, and to our innate immune system it represents a chink in the microbial armour, offering an opportunity that can be exploited to ward off pathogenic invaders. In order to infect body tissues and cause disease, pathogens must secure all their iron from the host. To fight such infections, the host specifically withdraws available iron through the action of various iron depleting processes (e.g. the release of lactoferrin and lipocalin-2) – this represents an important strategy in our defence against disease. However, pathogens are frequently able to deploy iron acquisition systems that target host iron sources such as transferrin, lactoferrin and hemoproteins, and thus counteract the iron-withdrawal approaches of the host. Inactivation of such host-targeting iron-uptake systems often attenuates the pathogenicity of the invading microbe, illustrating the importance of ‘the battle for iron’ in the infection process. The role of iron sequestration systems in facilitating microbial infections has been a major driving force in research aimed at unravelling the complexities of microbial iron transport processes. But also, the intricacy of such systems offers a challenge that stimulates the curiosity. One such challenge is to understand how balanced levels of free iron within the cytosol are achieved in a way that avoids toxicity whilst providing sufficient levels for metabolic purposes – this is a requirement that all organisms have to meet. Although the systems involved in achieving this balance can be highly variable amongst different microorganisms, the overall strategy is common. On a coarse level, the homeostatic control of cellular iron is maintained through strict control of the uptake, storage and utilisation of available iron, and is co-ordinated by integrated iron-regulatory networks. However, much yet remains to be discovered concerning the fine details of these different iron regulatory processes. As already indicated, perhaps the most difficult task in maintaining iron homeostasis is simply the procurement of sufficient iron from external sources. The importance of this problem is demonstrated by the plethora of distinct iron transporters often found within a single bacterium, each targeting different forms (complex or redox state) of iron or a different environmental condition. Thus, microbes devote considerable cellular resource to securing iron from their surroundings, reflecting how successful acquisition of iron can be crucial in the competition for survival. The aim of this book is provide the reader with an overview of iron transport processes within a range of microorganisms and to provide an indication of how microbial iron levels are controlled. This aim is promoted through the inclusion of expert reviews on several well studied examples that illustrate the current state of play concerning our comprehension of how iron is translocated into the bacterial (or fungal) cell and how iron homeostasis is controlled within microbes. The first two chapters (1-2) consider the general properties of microbial iron-chelating compounds (known as ‘siderophores’), and the mechanisms used by bacteria to acquire haem and utilise it as an iron source. The following twelve chapters (3-14) focus on specific types of microorganism that are of key interest, covering both an array of pathogens for humans, animals and plants (e.g. species of Bordetella, Shigella, , Erwinia, Vibrio, Aeromonas, Francisella, Campylobacter and Staphylococci, and EHEC) as well as a number of prominent non-pathogens (e.g. the rhizobia, E. coli K-12, Bacteroides spp., cyanobacteria, Bacillus spp. and yeasts). The chapters relay the common themes in microbial iron uptake approaches (e.g. the use of siderophores, TonB-dependent transporters, and ABC transport systems), but also highlight many distinctions (such as use of different types iron regulator and the impact of the presence/absence of a cell wall) in the strategies employed. We hope that those both within and outside the field will find this book useful, stimulating and interesting. We intend that it will provide a source for reference that will assist relevant researchers and provide an entry point for those initiating their studies within this subject. Finally, it is important that we acknowledge and thank wholeheartedly the many contributors who have provided the 14 excellent chapters from which this book is composed. Without their considerable efforts, this book, and the understanding that it relays, would not have been possible. Simon C Andrews and Pierre Cornelis

Autopoietic organization of firm: an illustration for the construction industry

Generally poor productivity, delays, low profitability and exceeded budgets are Common problems in modern construction management, however it seems that a basic obstacle lies far deeper in the understanding of a firm's fundamental mission, its existence. The main objective of this paper therefore is to examine the operational living of a construction firm and by doing that to reveal the key problem or the solution for a construction firm - its organization. A firm as a social system in which interactions between its constitutive components (employees) are surordinated to its maintenance (keeping a system alive) is an autopoietic social system. Two domains of external perturbations are uncovered to which a construction firm has to adapt (market driven and project driven perturbations). Constructed conceptual model of an autopoietic organization is based upon two necessary and sufficient operational domains that a firm has to create in order to become an autopoietic, adaptive social system. The first one is a domain of interactions between employees and other operationally external systems, which is representing an idea-generating domain of interactions. The second is employee's autonomous operational domain, which embodies employee's autonomy and individuality and represents a necessary condition for the establishment of an idea-generating domain. Finally, it is recognized that interactions within these four domains keep a construction firm alive.