The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Detection and molecular characterisation of Pyrenopeziza brassicae isolates resistant to methyl benzimidazole carbamates

BACKGROUND Methyl benzimidazole carbamate (MBC) fungicides are used to control the oilseed rape pathogen Pyrenopeziza brassicae. Resistance to MBCs has been reported in P. brassicae, but the molecular mechanism(s) associated with reductions in sensitivity have not been verified in this species. Elucidation of the genetic changes responsible for resistance, hypothesised to be target-site mutations in β-tubulin, will enable resistance diagnostics and thereby inform resistance management strategies. RESULTS P. brassicae isolates were classified as sensitive, moderately resistant or resistant to MBCs. Crossing P. brassicae isolates of different MBC sensitivities indicated that resistance was conferred by a single gene. The MBC-target encoding gene β-tubulin was cloned and sequenced. Reduced MBC sensitivity of field isolates correlated with β-tubulin amino acid substitutions L240F and E198A. The highest level of MBC resistance was measured for isolates carrying E198A. Negative cross-resistance between MBCs and the fungicides diethofencarb and zoxamide was only measured in E198A isolates. PCR-RFLP was used to screen isolates for the presence of L240F and E198A. The substitutions E198G and F200Y were also detected in DNA samples from P. brassicae populations after cloning and sequencing of PCR products. The frequencies of L240F and E198A in different P. brassicae populations were quantified by pyrosequencing. There were no differences in the frequencies of these alleles between P. brassicae populations sampled from different locations or after fungicide treatment regimes. CONCLUSIONS The molecular mechanisms affecting sensitivity to MBCs in P. brassicae have been identified. Pyrosequencing assays are a powerful tool for quantifying fungicide-resistant alleles in pathogen populations.

Small states, great power? Gaining influence through intrinsic, derivative, and collective power

In recent years, scholars have devoted increased attention to the agency of small states in International Relations. However, the conventional wisdom remains that while not completely powerful, small states are unlikely to achieve much of significance when faced by great power opposition. This argument, however, implicitly rests on resource-based and compulsory understandings of power. This article explores the implicit connections between the concept of "small state" and diverse concepts of power, asking how we should understand these states' attempts to gain influence and achieve their international political objectives. By connecting the study of small states with additional understandings of power, the article elaborates the broader avenues for influence that are open to many states but are particularly relevant for small states. The article argues that small states' power can be best understood as originating in three categories: “derivative,” collective, and particular-intrinsic. Derivative power, coined by Michael Handel, relies upon the relationship with a great power. Collective power involves building coalitions of supportive states, often through institutions. Particular-intrinsic power relies on the assets of the small state trying to do the influencing. Small states specialize in the bases and means of these types of power, which may have unconventional compulsory, institutional, structural, and productive aspects.

Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Force constants and dipole‐moment derivatives of molecules from perturbed Hartree–Fock calculations

General expressions for the force constants and dipole‐moment derivatives of molecules are derived, and the problems arising in their practical application are reviewed. Great emphasis is placed on the use of the Hartree–Fock function as an approximate wavefunction, and a number of its properties are discussed and re‐emphasised. The main content of this paper is the development of a perturbed Hartree–Fock theory that makes possible the direct calculation of force constants and dipole‐moment derivatives from SCF–MO wavefunctions. Essentially the theory yields ∂ϕi / ∂RJα, the derivative of an MO with respect to a nuclear coordinate.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.

The microwave spectrum of thietan-2,2,4,4-d4

The microwave spectrum for thietan-2,2,4,4-d4 is analysed in six of its lowest puckering states and up to J = 25. The close lying pairs of states of vp = 0/1, 2/3 and 4/5 are treated with a vibration-rotation hamiltonian which includes an off-diagonal coupling term in vp. Additional corrections to this coupling term in higher powers of the angular momentum operator are derived and their importance for improving the fit of calculated to observed data is tested. The variation of the centrifugal distortion constants with vp follows the model of Creswell and Mills (1974, J. molec. Spectrosc., 52, 392). A value is determined for the derivative with respect to the puckering coordinate of the ac-component of the inverse moment of inertia tensor.

Integrable evolution equations in time-dependent domains

We discuss the implementation of a method of solving initial boundary value problems in the case of integrable evolution equations in a time-dependent domain. This method is applied to a dispersive linear evolution equation with spatial derivatives of arbitrary order and to the defocusing nonlinear Schrödinger equation, in the domain l(t)derivative is monotonic, and T is a fixed positive constant.

Alternatives to linear analysis of energy balance data from lactating dairy cows

The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (MEm), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k(l)), 3) growth (k(g)), and the efficiency of utilization of body stores for milk production (k(t)). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k(g) and k(t). Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k(g) and k(t) using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k(g) and 0.82 to 0.84 for k(t). Using the estimated values of k(g) and k(t), the data were corrected to allow for body tissue changes. Based on the definition of k(l) as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, MEm and k(l) were determined. Meta-analysis of the pooled data showed that the average k(l) ranged from 0.50 to 0.58 and MEm ranged between 0.34 and 0.64 MJ/kg of BW0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.

Field evaluation of systemic inducing resistance chemicals at different growth stages for the control of apple (Venturia inaequalis) and pear (Venturia pirina) scab

Two field trials were conducted using established apple (Malus cv. Golden Delicious) and pear (Pyrus communis 'Williams' Bon Chretien') to assess the efficacy of three commercially available systemic inducing resistance (SIR) products, Messenger (a.i. Harpin protein), Phoenix (a.i. Potassium phosphite) and Rigel (a.i. Salicylic acid derivative) applied at four different growth stages of tree development (bud break, green cluster, 90% petal fall, early fruitlet) against the foliar pathogens Venturia inaequalis and Venturia pirina which cause apple and pear scab respectively. A conventional synthetic fungicide (penconazole) used within the UK for apple and pear scab control was included for comparison. Little efficacy as scab protectants was demonstrated when each SIR product and penconazole was applied at only two growth stages (bud break, green cluster). However when the above compounds were applied at three or more growth stages efficacy as scab protectants was confirmed. The synthetic fungicide penconazole provided greatest protection against apple and pear scab in both the 2006 and 2007 field trials. There was little difference in the magnitude of scab protection conferred by each SIR agent. Results suggest application of at least three sprays during bud break to early fruitlet formation with an appropriate SIR agent may provide a useful addition to existing methods of apple and pear scab management under field conditions. (C) 2009 Published by Elsevier Ltd.

Development and application of in vivo expression technology (IVET) for analysing microbial gene expression in complex environments

Establishing the mechanisms by which microbes interact with their environment, including eukaryotic hosts, is a major challenge that is essential for the economic utilisation of microbes and their products. Techniques for determining global gene expression profiles of microbes, such as microarray analyses, are often hampered by methodological restraints, particularly the recovery of bacterial transcripts (RNA) from complex mixtures and rapid degradation of RNA. A pioneering technology that avoids this problem is In Vivo Expression Technology (IVET). IVET is a 'promoter-trapping' methodology that can be used to capture nearly all bacterial promoters (genes) upregulated during a microbe-environment interaction. IVET is especially useful because there is virtually no limit to the type of environment used (examples to date include soil, oomycete, a host plant or animal) to select for active microbial promoters. Furthermore, IVET provides a powerful method to identify genes that are often overlooked during genomic annotation, and has proven to be a flexible technology that can provide even more information than identification of gene expression profiles. A derivative of IVET, termed resolvase-IVET (RIVET), can be used to provide spatio-temporal information about environment-specific gene expression. More recently, niche-specific genes captured during an IVET screen have been exploited to identify the regulatory mechanisms controlling their expression. Overall, IVET and its various spin-offs have proven to be a valuable and robust set of tools for analysing microbial gene expression in complex environments and providing new targets for biotechnological development.

The mechanism of bacterial indigo reduction

The reduction of water-insoluble indigo by the recently isolated moderate thermophile, Clostridium isatidis, has been studied with the aim of developing a sustainable technology for industrial indigo reduction. The ability to reduce indigo was not shared with C. aurantibutyricum, C. celatum and C. papyrosolvens, but C. papyrosolvens could reduce indigo carmine (5,5-indigosulfonic acid), a soluble indigo derivative. The supernatant from cultures of C. isatidis, but not from cultures of the other bacteria tested, decreased indigo particle size to one-tenth diameter. Addition of madder powder, anthraquinone-2,6-disulfonic acid, and humic acid all stimulated indigo reduction by C. isatidis. Redox potentials of cultures of C. isatidis were about 100 mV more negative than those of C. aurantibutyricum, C. celatum and C. papyrosolvens, and reached –600 mV versus the SCE in the presence of indigo, but potentials were not consistently affected by the addition of the quinone compounds, which probably act by modifying the surface of the bacteria or indigo particles. It is concluded that C. isatidis can reduce indigo because (1) it produces an extracellular factor that decreases indigo particle size, and (2) it generates a sufficiently reducing potential.

1,3-Dipolar cycloadditions to unsymmetrical ketone-derived chiral stabilized azomethine ylides: strategies for the synthesis of highly substituted amino acids

We report herein, the first generation of unsymmetrical ketone-derived chiral stabilized azomethine ylides. Intrairiolecular and intermolecular cycloaddition strategies have been utilized to synthesize both an enantiornerically pure bicyclic proline derivative and an enantionierically pure beta-hydroxy-alpha-amino acid.