The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

Does measurement technique explain the mismatch between European head size and WHO charts?

Objective To test whether different measuring techniques produce systematic differences in head size that could explain the large head circumferences found in Northern European children compared with the WHO standard. Design: Cross-sectional observational study. Setting: Scotland, UK. Patients: Study 1: 68 healthy children aged 0.4–18 months from mother and baby groups and a medical students teaching session. Study 2: 81 children aged 0.4 to 25 months from hospital wards and neonatal follow-up clinics. Interventions: Study 1: heads measured with plastic tape using both the WHO tight and UK loose technique. Study 2: heads measured using WHO research technique and a metal measuring tape and compared with routinely acquired measurements. Main outcome measures: Mean difference in head z-scores using WHO standard between the two methods. Results: The tight technique resulted in a mean (95% CI) z-score difference of 0.41 (0.27 to 0.54, p<0.001) in study 1 and 0.44 (0.36 to 0.53, p<0.001) in study 2. However, the mean WHO measurements in the healthy infants still produced a mean z-score that was two-third of a centile space (0.54 SD (0.28 to 0.79) p<0.001) above the 50th centile. Conclusion: The WHO measurement techniques produced significantly lower measures of head size, but average healthy Scottish children still had larger heads than the WHO standard using this method

The effect of different frequencies of ultrasound on the activity of horseradish peroxidase

Ultrasound technology has been studied by food researchers as an alternative method for thermal processing. The use of ultrasound as a way to inactivate and/or activate enzymes has been widely studied at low frequencies (20–40 kHz), however, little research on the effect of high frequencies has been reported. Thus, the effect of high and low frequency ultrasound on commercial horseradish peroxidase with a concentration of 0.005 mg mL−1 is described. Experiments were performed for 60 min using 20, 378, 583, 862, 995, 1144 and 1175 kHz ultrasound at power levels (acoustic energy) between 2.1 and 64 W. Residual activity was monitored using a spectrophotometric method and data analysis was performed using ANOVA. A significant enhancement of enzyme inactivation (p < 0.05) was observed at each frequency with an increase of sonication time and power. Inactivation of peroxidase by ultrasound followed first order kinetics and an increase of the rate constant with the power applied was observed for all the frequencies studied. Overall, low frequency (20 kHz) and low power are not effective on the enzyme inactivation and the level of residual activity remained high. The use of 378 and 583 kHz (48 W) is particularly effective for complete enzyme inactivation

A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces

Let $G/K$ be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of $G$ sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms of a root system of $G$. As an example of application, we give the list of the first eigenvalues for the spin compact irreducible symmetric spaces endowed with a quaternion-K\"{a}hler structure

Stimulation of bioprocesses by ultrasound

Ultrasound (US) has become a ubiquitous technological process in a large variety of scientific disciplines. However, little information exists on the use of ultrasound to enhance biological processes and/or processing and consequently this paper provides an overview of work reported to date on this topic. This review provides a brief introduction to ultrasound and the history of ultrasound as applied to bioprocesses. This is followed by a discussion of the influence of US on discrete enzyme systems, enzymes used in bioremediation, microbial fermentations and enzymatic hydrolysis of biopolymers. Augmentation of anaerobic digestion by US is then considered along with enhancement of enzymes in food science and technology. The use of ultrasonically stimulated enzymes in synthesis is then considered and other relevant miscellaneous topics are described. It is concluded that the precise mechanism of action of US in bio-processing remains to be elucidated though a variety of plausible suggestions are made

Time-resolved fluorescence observation of di-tyrosine formation in horseradish peroxidase upon ultrasound treatment leading to enzyme inactivation

The application of ultrasound to a solution can induce cavitional phenomena and generate high localised temperatures and pressures. These are dependent of the frequency used and have enabled ultrasound application in areas such as synthetic, green and food chemistry. High frequency (100 kHz to 1 MHz) in particular is promising in food chemistry as a means to inactivate enzymes, replacing the need to use periods of high temperature. A plant enzyme, horseradish peroxidase, was studied using time-resolved fluorescence techniques as a means to assess the effect of high frequency (378 kHz and 583 kHz) ultrasound treatment at equivalent acoustic powers. This uncovered the fluorescence emission from a newly formed species, attributed to the formation of di-tyrosine within the horseradish peroxidase structure caused by auto-oxidation, and linked to enzyme inactivation

School gardens and the school food plan: contributing to a culture of healthy living

Significantly revised and updated the second edition now includes 7 brand new chapters on: · Methods of Assessment and Evaluation · Global perspectives on Outdoor Learning · Developing whole school approaches to indoor and outdoor ..

Coping with Persistent Pain, Effectiveness Research into Self-management (COPERS): statistical analysis plan for a randomised controlled trial

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated

Four types of special functions of G_2 and their discretization

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the other two (S^L- and S^S-functions) are not found elsewhere in the literature. It is shown explicitly that all four families have similar properties. In particular, they are orthogonal when integrated over a finite region F of the Euclidean space, and they are discretely orthogonal when their values, sampled at the lattice points F_M \subset F, are added up with a weight function appropriate for each family. Products of ten types among the four families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S, S^LS^S and S^LS^L, are completely decomposable into the finite sum of the functions. Uncommon arithmetic properties of the functions are pointed out and questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table

Overcoming the uncanny valley: Displays of emotions reduce the uncanniness of humanlike robots

In this paper we show empirically that highly humanlike robots make thoughts of death more accessible, leading to perceptions of uncanniness and eeriness of such robots. Rather than reducing the humanlikeness of robots, our research suggests the addition of emotion displays to decrease a sense of uncanniness. We show that a highly humanlike robot displaying emotions in a social context reduces death-thought accessibility (DTA), which in turn reduces uncanniness. In a pre-test with N = 95 participants, we established that not all humanoid robots elicit thoughts of death and that the extent to which a robot appears humanlike may be linked to DTA. In our Main Study, N = 44 participants briefly interacted with a highly humanlike robotic head that either showed appropriate basic emotions or reacted by blinking. The display of emotions significantly reduced perceptions of uncanniness, which was mediated by a corresponding reduction in DTA. Implications for the design of humanoid robots are proposed.EPSR