Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Fine root condition relates to visible crown damage in Norway spruce on acidified soils

Allochthonous Norway spruce stands in the Kysucké Beskydy Mts. (north-western Slovakia) have been exposed to substantial acid deposition in the recent past and grow in acidified soil conditions with mean pH of about 4.0 in the topsoil. We selected 90 spruce trees representing 30 triples of different crown status: healthy, stressed and declining to assess the relationship between crown and fine root status. Sequential coring and in-growth bags were applied to each triplet to investigate fine root biomass and growth in the soil depths of 0-10 and 10-20 cm. Fine root quantity (biomass and necromass), turnover (production over standing stock), morphological features (specific root length, root tip density) and chemical properties (Ca:Al molar ratio) were compared among the abovementioned health status categories. Living fine root biomass decreased with increasing stress, while the ratio of living to dead biomass increased. Annual fine root production decreased and specific root length increased in stressed trees when compared to healthy or declining trees, a situation which may be related to the position of trees in the canopy (healthy and declining – dominant, stressed – co-dominant). The Ca:Al ratio decreased with increasing crown damage, indicating a decreased ability to filter out aluminium. In conclusion, fine root status appears to be linked to visible crown damage and can be used as a tree health indicator.

The status of literature: English teaching and the condition of literature teaching in schools

Although the curriculum subject of English is continually reviewed and revised in all English speaking countries, the status of literature is rarely questioned i.e. that it is of high cultural value and all students should be taught about it. The concerns of any review, in any country, are typically about what counts as literature, especially in terms of national heritage and then how much of the curriculum should it occupy. This article reports on three inter-related pieces of research that examine the views of in-service, and pre-service, English teachers about their experiences of teaching literature and their perceptions of its ‘status’ and significance at official level and in the actual classroom; it draws attention to how England compares to some other English speaking countries and draws attention to the need to learn from the negative outcomes of political policy in England. The findings suggest that the nature of engagement with literature for teachers and their students has been distorted by official rhetorics and assessment regimes and that English teachers are deeply concerned to reverse this pattern.

Cardioprotective effects of insulin: how intensive insulin therapy may benefit cardiac surgery patients

Interest in the effects of insulin on the heart came with the recognition that hyperglycemia in the context of myocardial infarction is associated with increased risks of mortality, congestive heart failure, or cardiogenic shock. More recently, instigated by research findings on stress hyperglycemia in critical illness, this interest has been extended to the influence of insulin on clinical outcome after cardiac surgery. Even in nondiabetic individuals, stress hyperglycemia commonly occurs as a key metabolic response to critical illness, eg, after surgical trauma. It is recognized as a major pathophysiological feature of organ dysfunction in the critically ill. The condition stems from insulin resistance brought about by dysregulation of key homeostatic processes, which implicates immune/inflammatory, endocrine, and metabolic pathways. It has been associated with adverse clinical outcomes, including increased mortality, increased duration of mechanical ventilation, increased intensive care unit (ICU) and hospital stay, and increased risk of infection. Hyperglycemia in critical illness is managed with exogenous insulin as standard treatment; however, there is considerable disagreement among experts in the field as to what target blood glucose level is optimal for the critically ill patient. Conventionally, the aim of insulin therapy has been to maintain blood glucose levels below the renal threshold, typically 220 mg/dL (12.2 mmol/L). In recent years, some have advocated tight glycemic control (TGC) with intensive insulin therapy (IIT) to normalize blood glucose levels to within the euglycemic range, typically 80 to 110 mg/dL (4.4–6.1 mmol/L).

A study of the microstructure and condition of thin sheets of painting support ivory using SEM and ESEM

This paper outlines a study of the microstructure of thin sheets of ivory used as a painting support for portrait miniatures. Warping of the ivory support is one of the main problems commonly found in portrait miniatures from the late eighteenth century and early nineteenth century. Portrait miniatures from this period are painted on very thin sheets of ivory that are often only 0.2 mm in thickness. Warping can lead to cracking of the ivory and can also accentuate flaking of the paint layer. The problem of warping in ivory has thus been of long-term interest to conservators who deal with portrait miniatures, including those at the Victoria and Albert (V&A) Museum. The causes of warping are complex. However, it should be noted that artists normally stuck the thin ivory sheets onto paper or card before commencing the painting. The possible causes of warping therefore are thought to relate to the differential reactions of the ivory/adhesive/paper or card layers to changes in relative humidity (RH). It is well known that ivory is hygroscopic and anisotropic.1 However, only a few scientific studies have been carried out related to this subject and systematic analyses of the morphological and microstructural changes due to changes in RH or moisture in such thin sheets of ivory have yet to be investigated.

What variables condition syntactic transfer? A look at the L3 initial state

This study investigates transfer at the third-language (L3) initial state, testing between the following possibilities: (1) the first language (L1) transfer hypothesis (an L1 effect for all adult acquisition), (2) the second language (L2) transfer hypothesis, where the L2 blocks L1 transfer (often referred to in the recent literature as the ‘L2 status factor’; Williams and Hammarberg, 1998), and (3) the Cumulative Enhancement Model (Flynn et al., 2004), which proposes selective transfer from all previous linguistic knowledge. We provide data from successful English-speaking learners of L2 Spanish at the initial state of acquiring L3 French and L3 Italian relating to properties of the Null-Subject Parameter (e.g. Chomsky, 1981; Rizzi, 1982). We compare these groups to each other, as well as to groups of English learners of L2 French and L2 Italian at the initial state, and conclude that the data are consistent with the predictions of the ‘L2 status factor’. However, we discuss an alternative possible interpretation based on (psycho)typologically-motivated transfer (borrowing from Kellerman, 1983), providing a methodology for future research in this domain to meaningfully tease apart the ‘L2 status factor’ from this alternative account.

Influence of dietary protein intake and glycemic index on the association between TCF7L2 HapA and weight gain

BACKGROUND: Genetic polymorphisms of transcription factor 7-like 2 (TCF7L2) have been associated with type 2 diabetes and BMI. OBJECTIVE: The objective was to investigate whether TCF7L2 HapA is associated with weight development and whether such an association is modulated by protein intake or by the glycemic index (GI). DESIGN: The investigation was based on prospective data from 5 cohort studies nested within the European Prospective Investigation into Cancer and Nutrition. Weight change was followed up for a mean (±SD) of 6.8 ± 2.5 y. TCF7L2 rs7903146 and rs10885406 were successfully genotyped in 11,069 individuals and used to derive HapA. Multiple logistic and linear regression analysis was applied to test for the main effect of HapA and its interaction with dietary protein or GI. Analyses from the cohorts were combined by random-effects meta-analysis. RESULTS: HapA was associated neither with baseline BMI (0.03 ± 0.07 BMI units per allele; P = 0.6) nor with annual weight change (8.8 ± 11.7 g/y per allele; P = 0.5). However, a previously shown positive association between intake of protein, particularly of animal origin, and subsequent weight change in this population proved to be attenuated by TCF7L2 HapA (P-interaction = 0.01). We showed that weight gain becomes independent of protein intake with an increasing number of HapA alleles. Substitution of protein with either fat or carbohydrates showed the same effects. No interaction with GI was observed. CONCLUSION: TCF7L2 HapA attenuates the positive association between animal protein intake and long-term body weight change in middle-aged Europeans but does not interact with the GI of the diet.

Glycemic Index, glycemic control and beyond

It is currently estimated that over 370 million individuals have diabetes, making diabetes a major public health issue contributing significantly to global morbidity and mortality. The steep rise in diabetes prevalence over the past decades is attributable, in a large part, to lifestyle changes, with dietary habits and behaviour significant contributors. Despite the relatively wide availability of anti-diabetic medicine, it is lifestyle approaches that still remain the cornerstone of diabetes prevention and treatment. Glycemic index (GI) is a nutritional tool, which represents the glycemic response to carbohydrate ingestion. In light of the major impact of nutrition on diabetes pathophysiology, with the rising need to combat the escalating diabetes epidemic, this review will focus on the role of GI in glycemic control, the primary target of diabetic treatment and beyond. The review will present the evidence relating GI and diabetes treatment and prevention, as well as weight loss, weight maintenance and CVD risk factors.

Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum-that is, due to the surrounding continuum with magnetic permeability mu(BC)-on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.

Novel flavours paired with glutamate condition increased intake in older adults in the absence of changes in liking

Previous research on the repeat exposure to a novel flavour combined with monosodium glutamate (MSG) has shown an increase in liking and consumption for the particular flavour. The aim of the current work was to investigate whether this could also be observed in the case of older people, since they are most affected by undernutrition in the developed world and ways to increase consumption of food are of significant importance for this particular age group. For this study, 40 older adults (age 65-88) repeatedly consumed potato soup with two novel flavours (lemongrass and cumin) which were either with or without a high level of MSG (5%w/w). A randomized single blind within-subject design was implemented, where each participant was exposed to both soup flavours three times over 6 days, with one of the soup flavours containing MSG. After three repeat exposures, consumption increased significantly for the soups where the flavours had contained MSG during the repeated exposure (mean weight consumed increased from 123 to 164 g, p=0.017), implying that glutamate conditioned for increased wanting and consumption, despite the fact that the liking for the soup had not increased.

Asymmetric information, credit market condition, and entrepreneurial finance

The issue of imperfect information plays a much more important role in financing “informationally opaque” small businesses than in financing large companies.1 This chapter examines the asymmetric information issue in entrepreneurial finance from two perspectives: the effects of relationship lending and the impacts of credit market concentration on entrepreneurial financial behavior. These two perspectives are strongly linked to each other via the asymmetric information issue in entrepreneurial finance. Existing literature has recognized the important role played by relationship lending in alleviating the problem of asymmetric information. However, mixed empirical results have been reported. For example, it has been found that the development of relationship lending can improve the availability of finance for small businesses borrowers (Petersen and Rajan, 1994) and reduce the costs of finance (Berger and Udell, 1995). Meanwhile, with monopoly power, banks may extract rents, in terms of charging higher-than-market interest rates, from small businesscustomers who have very concentrated banking relationships (Ongena and Smith, 2001). In addition, both favorable and unfavorable effects of credit market concentration on financing small businesses have been acknowledged. Small business borrowers may have to pay a higher-than-market price on loans (Degryse and Ongena, 2005) and are more likely to be financially constrained (Cetorelli, 2004) than in competitive markets. On the other hand, empirical studies have shown that market concentration create a strong motive for lenders to invest in private information from small business customers, and therefore a concentrated market is more efficient in terms of private information acquisition (Han et al., 2009b). The objective of this chapter is to investigate, by reviewing existing literature, the role played by relationship lending and the effects of market concentration on financing entrepreneurial businesses that are supposed to be informationally opaque. In the first section we review literature on the important role played by asymmetric information in entrepreneurial finance from two perspectives: asymmetric information and relationship lending, and the theoretical modeling of asymmetric information. Then we examine the relationship between capital market conditions and entrepreneurial finance and attempt to answer two questions: Why is the capital market condition important for entrepreneurial finance? and What are the effects of capital market conditions on entrepreneurial financial behavior in terms of discouraged borrowers, cash holding, and the availability and costs of finance?