Ideals and Centralizing Mappings in Prime Rings

Let H be a prime ring and U be a nonzero ideal of R. If T is a nontrivial automorphism or derivation of Ft such that uuT — uTu is in the center of R and uT is in U for every u in U, then R is commutative. If R does not have characteristic equal to two, then U need only be a nonzero Jordan ideal

Flexible Algebras of Degree Two

All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra. We then investigate the multiplicative structure of those algebras which are partially stable over an algebraically closed field of characteristic p A 2, 3, 5. The results obtained are then used to develop conditions under which such algebras must be commutative

High-order volterra model predictive control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but the existing design and implementation methods are restricted to linear process models. A chemical process involves, however, severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC), and also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design which relieves practising engineers from the need for first deriving a physical-principles based model. An on-line realisation technique for implementing the NMPC is also developed. The NMPC is then applied to a Mitsubishi Chemicals polymerisation reaction process. The results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the approach developed lie not only in control performance superior to existing NMPC methods, but also in relieving practising engineers from the need for deriving an analytical model and then converting it to a Volterra model through which the model can only be obtained up to the second order

Mixed-reality learning environments in teacher education: An analysis of TeachLivE™ research

TeachLivE™, a mixed-reality simulated classroom technology, has been used in initial teacher education programs to provide repeatable experiential learning opportunities for students now for more than a decade and in more than 80 universities worldwide. However, no broad scale investigation has been conducted into how the platform has been used or what research has been generated as a result. The aim of this study is to provide insight into the types of TeachLivE™ research carried out since its inception and to identify trends and potential gaps in this research. Peer-reviewed academic primary research publications—journal articles (23), conference proceedings (12), and thesis dissertations (20)—were reviewed for participants, research methods, analysis, research design, data collection tools, and design approaches. Of the 102 articles identified as relevant, “instructional skills development” and “integration of TeachLivE™ in teacher education” were the most commonly researched topics. Findings indicate that preservice teachers were the most commonly studied group of participants, research methods were predominately qualitative, single-subject experimental research design was employed most often, and the most used data collection tools were surveys and observation. These findings highlight that the range of topics is increasing, with studies on in-service teachers in school-based contexts beginning to emerge as a new area of interest. This systematic review has implications for researchers and the developers of TeachLivE™. It provides valuable insight and recommendations for future studies in this emerging teacher education field, where technology is not simply used “in the classroom” but rather “as the classroom.

Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature

We study the statistical properties of the sum $S_t=\int_{0}^{t}dt' \sigma_{t'}$, that is the difference of time spent positive or negative by the spin $\sigma_{t}$, located at a given site of a $D$-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of $S_{t}$ and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ($T>T_{c}$), criticality ($T=T_c$), and low temperature ($T<T_{c}$). We discuss in particular the question of the temperature dependence of the persistence exponent $\theta$, as well as that of the spectrum of exponents $\theta(x)$, in the low temperature phase. The probability that the temporal mean $S_t/t$ was always larger than the equilibrium magnetization is found to decay as $t^{-\theta-\frac12}$. This yields a numerical determination of the persistence exponent $\theta$ in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model.Comment: 21 pages, 11 PostScript figures included (1 color figure

Effect of anisotropy and destructuration on behavior of Haarajoki test embankment

This paper investigates the influence of anisotropy and destructuration on the behavior of Haarajoki test embankment, which was built by the Finnish National Road Administration as a noise barrier in 1997 on a soft clay deposit. Half of the embankment is constructed on an area improved with prefabricated vertical drains, while the other half is constructed on the natural deposit without any ground improvement. The construction and consolidation of the embankment is analyzed with the finite-element method using three different constitutive models to represent the soft clay. Two recently proposed constitutive models, namely S-CLAY1 which accounts for initial and plastic strain induced anisotropy, and its extension, called S-CLAY1S which accounts, additionally, for interparticle bonding and degradation of bonds, were used in the analysis. For comparison, the problem is also analyzed with the isotropic modified cam clay model. The results of the numerical analyses are compared with the field measurements. The simulations reveal the influence that anisotropy and destructuration have on the behavior of an embankment on soft clay

Cellular automata modelling of slime mould actin network signalling

© 2016, The Author(s). Actin is a cytoskeletal protein which forms dense, highly interconnected networks within eukaryotic cells. A growing body of evidence suggests that actin-mediated intra- and extracellular signalling is instrumental in facilitating organism-level emergent behaviour patterns which, crucially, may be characterised as natural expressions of computation. We use excitable cellular automata modelling to simulate signal transmission through cell arrays whose topology was extracted from images of Watershed transformation-derived actin network reconstructions; the actin networks sampled were from laboratory experimental observations of a model organism, slime mould Physarum polycephalum. Our results indicate that actin networks support directional transmission of generalised energetic phenomena, the amplification and trans-network speed of which of which is proportional to network density (whose primary determinant is the anatomical location of the network sampled). Furthermore, this model also suggests the ability of such networks for supporting signal-signal interactions which may be characterised as Boolean logical operations, thus indicating that a cell’s actin network may function as a nanoscale data transmission and processing network. We conclude by discussing the role of the cytoskeleton in facilitating intracellular computing, how computation can be implemented in such a network and practical considerations for designing ‘useful’ actin circuitry