Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Economics of robots and automation in field crop production

This study reviewed research published after 1990 on the economics of agricultural mechatronic automation and robotics, and identified research gaps. A systematic search was conducted from the following databases: ScienceDirect, Business Source Complete, Wiley, Emerald, CAB Abstract, Greenfile, Food Science Source and AgEcon Search. This identified 4817 documents. The screening of abstracts narrowed the range to a dataset of 119 full text documents. After eligibility assessment, 18 studies were subjected to a qualitative analysis, with ten focused on automation of specific horticultural operations and eight related to autonomous agricultural equipment. All of the studies found some scenarios in which automation and robotic technologies were profitable. Most studies employed partial budgeting considering only costs and revenues directly changed by the introduction of automation or robotics and assuming everything else constant. None examined cropping system changes, or regional and national impacts on markets, trade and labour demand. The review identified a need for in-depth research on the economic implications of the technology. Most of the studies reviewed estimated economic implications assuming that technology design parameters were achieved and/or based on data from prototypes. Data are needed on the benefits and problems with using automation and robotics on farm. All of the studies reviewed were in the context of agriculture in developed countries, but many of the world’s most pressing agricultural problems are in the developing world. Economic and social research is needed to understand those developing country problems, and guide the engineers and scientists creating automation and robotic solutions

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes

A list decoding algorithm for matrix-product codes is provided when $C_1,..., C_s$ are nested linear codes and $A$ is a non-singular by columns matrix. We estimate the probability of getting more than one codeword as output when the constituent codes are Reed-Solomon codes. We extend this list decoding algorithm for matrix-product codes with polynomial units, which are quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for matrix-product codes with polynomial units

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools

A Memetic Analysis of a Phrase by Beethoven: Calvinian Perspectives on Similarity and Lexicon-Abstraction

This article discusses some general issues arising from the study of similarity in music, both human-conducted and computer-aided, and then progresses to a consideration of similarity relationships between patterns in a phrase by Beethoven, from the first movement of the Piano Sonata in A flat major op. 110 (1821), and various potential memetic precursors. This analysis is followed by a consideration of how the kinds of similarity identified in the Beethoven phrase might be understood in psychological/conceptual and then neurobiological terms, the latter by means of William Calvin’s Hexagonal Cloning Theory. This theory offers a mechanism for the operation of David Cope’s concept of the lexicon, conceived here as a museme allele-class. I conclude by attempting to correlate and map the various spaces within which memetic replication occurs

Poor maternal nutrition programmes a pro-atherosclerotic phenotype in ApoE-/- mice.

Numerous animal studies have consistently shown that early life exposure to LP (low-protein) diet programmes risk factors for CVD (cardiovascular disease) such as dyslipidaemia, high BP (blood pressure) and cardiac dysfunction in the offspring. However, studies on the effect of maternal under-nutrition on offspring development of atherosclerosis are scarce. Applying our LP model to the ApoE(-/-) atherosclerosis-prone mouse model, we investigated the development of atherosclerotic lesions in the aortic root of 6-month-old offspring. In addition, markers of plaque progression including SMA (smooth muscle actin) and Mac3 (macrophage marker 3) were studied. Pregnant dams were fed on a control (20% protein) or on an isocaloric LP diet (8% protein) throughout pregnancy and lactation. After weaning, male offspring were maintained on 20% normal laboratory chow. At 6 months of age, LP offspring showed a significantly greater plaque area (P<0.05) with increased cholesterol clefts and significantly higher indices of DNA damage compared with controls (P<0.05). The expression of HMG-CoA reductase (3-hydroxy-3-methyl-glutaryl-CoA reductase) (P<0.05) and LDL (low-density lipoprotein) receptor in the liver of LP offspring were increased. Furthermore, LP offspring had higher LDL-cholesterol levels (P<0.05) and a trend towards elevated insulin. There were no differences in other lipid measurements and fasting glucose between groups. These observations suggest that early exposure to an LP diet accelerates the development and increases the progression of atherosclerotic lesions in young adult offspring. Future studies are needed to elucidate the specific mechanisms linking in utero exposure to a diet low in protein to the development of atherosclerosis.This work was supported by the British Heart Foundation [grant numbers FS/09/029/27902, FS/09/050], the Biotechnology and Biological Sciences Research Council and the Cambridge Commonwealth Trust

The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach

A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces