Chaotic quasi-collision trajectories in the 3-centre problem

We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see Bolotin and Negrini, J. Diff. Eq. 190 (2003), 539--558): this result has been obtained by the use of the Poincar\'e-Melnikov theory. Here we change the assumption on the third centre: we do not make any hypothesis on its position, and we obtain a perturbation of the 2-centre problem by assuming its intensity to be very small. Then, for a dense subset of possible positions of the perturbing centre on the real plane, we prove the existence of uniformly hyperbolic invariant sets of periodic and chaotic almost collision orbits by the use of a general result of Bolotin and MacKay (see Cel. Mech. & Dyn. Astr. 77 (2000), 49--75). To apply it, we must preliminarily construct chains of collision arcs in a proper way. We succeed in doing that by the classical regularisation of the 2-centre problem and the use of the periodic orbits of the regularised problem passing through the third centre.Comment: 22 pages, 6 figure

An international overview of assessment issues in technology education : disentangling the influences, confusion and complexities

Set in the context of wider research, this review of international literature describes some of the issues that contribute towards the prevailing confusion regarding the 'what', 'when' and 'why' of assessment. It explores the complexities embedded within assessment of, for and as learning and the difficulties arising in Technology Education. It discusses what comprises the goals and purposes, and precise nature of 'content' and how this impacts on what is considered as important to measure in terms of attainment, performance and achievement in Technology Education. The paper examines the influence of external assessment, the influence of the teacher and the influence of the various approaches and instruments of assessment on pedagogy, achievement and learner performance and motivation. The dimensions and discriminators of performance and progression in Technology Education are complex. The key issues need to be disentangled to provide some clarity and inform practice. Greater creativity is needed to help devise multi-dimension, multi-expression assessment strategies which celebrate the complexity and influence pedagogy appropriate for learning in the 21st century

The impact of weight classification on safety: timing steps to adapt to external constraints

OBJECTIVES: The purpose of the current study was to evaluate how weight classification influences safety by examining adults' ability to meet a timing constraint: walking to the pace of an audio metronome. METHODS: With a cross-sectional design, walking parameters were collected as 55 adults with normal (n=30) and overweight (n=25) body mass index scores walked to slow, normal, and fast audio metronome paces. RESULTS: Between group comparisons showed that at the fast pace, those with overweight body mass index (BMI) had longer double limb support and stance times and slower cadences than the normal weight group (all ps<0.05). Examinations of participants' ability to meet the metronome paces revealed that participants who were overweight had higher cadences at the slow and fast paces (all ps<0.05). CONCLUSIONS: Findings suggest that those with overweight BMI alter their gait to maintain biomechanical stability. Understanding how excess weight influences gait adaptation can inform interventions to improve safety for individuals with obesity

Differential equations over octonions

Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is used. Such technique is applied to linear and non-linear partial differential equations in real variables. Possible areas of applications of these results are outlined.Comment: 50 page

Mediation Patterns for Message Exchange Protocols

Systems interact with their environment (e.g., other systems) by ex-changing messages in a particular order. Interoperability problems arise when systems do not understand each other’s messages or follow incompatible message exchange protocols. In this paper we identify mismatches in message ex-change protocols (involving two systems) and we propose solution patterns to compensate these mismatches

The principle of symmetry of kinetic coefficients for media with ferrite inclusions and its application to nonreciprocal BI-ANISOTROPIC composites

The principle of the symmetry of kinetic coefficients (the Onsager-Casimir principle) is formulated for bi-anisotropic media containing dissipative ferrite inclusions and metal strip elements. Electrodynamic description of bi-anisotropic particles on the base of strip-line-coupled magnetostatic wave resonators is developed and analytical closed-form expressions for the tensor polarizabilities are obtained for an arbitrary direction of the bias magnetic field and an arbitrary resonator shape. The results open a pos-sibility to theoretically predict properties of novel nonreciprocal electrically controllable bi-anisotropic composites with exotic electromagnetic properties

Identification of a system required for the functional surface localization of sugar binding proteins with class III signal peptides in Sulfolobus solfataricus

The hyperthermophilic archaeon Sulfolobus solfataricus contains an unusual large number of sugar binding proteins that are synthesized as precursors with a class III signal peptide. Such signal peptides are commonly used to direct archaeal flagellin subunits or bacterial (pseudo)pilins into extracellular macromolecular surface appendages. Likewise, S. solfataricus binding proteins have been suggested to assemble in higher ordered surface structures as well, tentatively termed the bindosome. Here we show that S. solfataricus contains a specific system that is needed for the functional surface localization of sugar binding proteins. This system, encoded by the bas (bindosome assembly system) operon, is composed of five proteins: basABC, three homologues of so-called bacterial (pseudo)pilins; BasE, a cytoplasmic ATPase; and BasF, an integral membrane protein. Deletion of either the three (pseudo)pilin genes or the basEF genes resulted in a severe defect of the cells to grow on substrates which are transported by sugar binding proteins containing class III signal peptides, while growth on glucose and maltose was restored when the corresponding genes were reintroduced in these cells. Concomitantly, ΔbasABC and ΔbasEF cells were severely impaired in glucose uptake even though the sugar binding proteins were normally secreted across the cytoplasmic membrane. These data underline the hypothesis that the bas operon is involved in the functional localization of sugar binding proteins at the cell surface of S. solfataricus. In contrast to surface structure assembly systems of Gram-negative bacteria, the bas operon seems to resemble an ancestral simplified form of these machineries.

A permeability prediction for (un)sheared non-crimp fabrics

A permeability prediction model for relaxed and sheared Non-Crimp Fabrics is proposed. The model is based on geometrical features of the fabric. The stitches penetrating the uni-directional plies of the NCF induce distortions of the fibres in the plane of the fabric. These Stitch Yarn induced fibre Distortions (SYD) form flow channels, which determine the permeability of the NCF. The channels are connected to each other in overlap regions, allowing the fluid to flow from one channel to another and finally to impregnate the entire preform. A network of SYD flow channels is created to account for the statistical variations in the dimensions of the SYDs. The system of flow resistances is solved analogously to the solution of the effective resistance of an electrical circuit with parallel and serial resistances. The flow in each of the SYD domains is calculated employing an energy minimisation method. Analysis of different networks, with varying spatial distribution of the dimensions of the flow channels, allows the prediction of the variation in the permeability of an NC

Replica symmetry breaking related to a general ultrametric space II: RSB solutions and the n\to0 limit

Replica symmetry breaking solutions for the new replica anzats, related to general ultrametric spaces, are investigated. A variant of analysis on trees is developed and applied to the computation of the n\to0 limit in the new replica anzats.Comment: 22 page