Some new results on decidability for elementary algebra and geometry

We carry out a systematic study of decidability for theories of (a) real vector spaces, inner product spaces, and Hilbert spaces and (b) normed spaces, Banach spaces and metric spaces, all formalised using a 2-sorted first-order language. The theories for list (a) turn out to be decidable while the theories for list (b) are not even arithmetical: the theory of 2-dimensional Banach spaces, for example, has the same many-one degree as the set of truths of second-order arithmetic. We find that the purely universal and purely existential fragments of the theory of normed spaces are decidable, as is the AE fragment of the theory of metric spaces. These results are sharp of their type: reductions of Hilbert's 10th problem show that the EA fragments for metric and normed spaces and the AE fragment for normed spaces are all undecidable.Comment: 79 pages, 9 figures. v2: Numerous minor improvements; neater proofs of Theorems 8 and 29; v3: fixed subscripts in proof of Lemma 3

Domesticating Lebeckia ambigua: Solving the rhizobia issues.

Permanent dryland pastures are under-utilised in southern Australia (Angus and Peoples 2012), possibly due to the lack of well adapted perennial legume species that can fit into current farming systems. Lebeckia ambigua has been proposed as a candidate to fill this void with its adaptability to drought, acidic and infertile soils in low rainfall areas (Howieson et al. 2013). The research on L. ambigua has so far focussed on deep, sandy soils where cropping is problematic. Increasing the soil fertility in these previously low-profitable regions could provide mixed farming production with a comparative advantage over continuous cropping (Angus and Peoples 2012). However, the successful incorporation of L. ambigua into an agricultural system will require an understanding of its symbiont, Burkholderia species. Although L. ambigua and Burkholderia spp. have only recently been identified for domestication into agriculture (Howieson et al. 2013), researchers have had success with cultivating them throughout southern Western Australia (WA), except with inoculation. There is a challenge to keep the inoculant B. spp. alive, in a peat carrier, when coated onto L. ambigua seed for sowing in a drying environment. Clay granules, as an alternative carrier, have previously been shown to be unable to carry high numbers of cells of B. spp. (Howieson et al. 2013). Field experiments with amended clay granules carrying B. spp. produced nodules on L. ambigua, albeit not in large number. Attempts at quantifying the numbers of cells in the amended granules, by resuscitating B. spp. from them using antibiotic media and plant infection techniques, were unsuccessful. However, antibiotic profiling of B. spp. strains identified chloramphenicol (20μg/ml) in YMA as an excellent media to suppress contaminants in the clay to facilitate enumeration. Recently recovered strains of B. spp. were assessed alongside previous strains for tolerance to desiccation, which gave rise to a set of possible strains that could surpass the commonly used strain in this regard (WSM4204). Although clay granules were indicated to hold B. spp. cells sufficient for nodulation in the field, further studies must focus on the optimisation of a suitable inoculant technology for L. ambigua. The B. spp. and strain differences in tolerance to desiccation identified in this work may assist this target

Accommodating repair actions into gas turbine prognostics

Elements of gas turbine degradation, such as compressor fouling, are recoverable through maintenance actions like compressor washing. These actions increase the usable engine life and optimise the performance of the gas turbine. However, these maintenance actions are performed by a separate organization to those undertaking fleet management operations, leading to significant uncertainty in the maintenance state of the asset. The uncertainty surrounding maintenance actions impacts prognostic efficacy. In this paper, we adopt Bayesian on-line change point detection to detect the compressor washing events. Then, the event detection information is used as an input to a prognostic algorithm, advising an update to the estimation of remaining useful life. To illustrate the capability of the approach, we demonstrated our on-line Bayesian change detection algorithms on synthetic and real aircraft engine service data, in order to identify the compressor washing events for a gas turbine and thus provide demonstrably improved prognosis

The economic importance of agricultural production in selected rural persistent poverty counties in Tennessee

It has been suggested that the agricultural sector has little potential as an instrument for rural economic development in Tennessee. However, many persistent poverty counties in Tennessee have relatively large agricultural sectors. Therefore, agriculture may have a greater impact on the economies of rural persistent poverty counties than on the economies of other rural counties. This study estimated the indirect and induced income and employment effects generated by production of agricultural commodities in selected rural persistent poverty counties in Tennessee. These rural persistent poverty counties were grouped into relatively self-contained economic regions based on similarity of enterprise mix, spatial proximity, and transportational routes. Type I and Type III income and employment multipliers were estimated for each of these regions using the IMPLAN input/output model. Indirect and induced income and employment effects were derived from these multipliers. The Type I income multipliers ranged from a low of 1.47 in TPPR 6 to a high of 1.77 in TPPR 4 while Type III income multipliers ranged from 2.12 in TPPR 1 to 2.83 in TPPR 4. The Type I employment multipliers ranged from a low of 1.25 in TPPR 6 to a high of 1.46 in TPPR 1 while Type III employment multiplier ranged from 1.61 in TPPR 6 to 1.80 in TPPR\u27s 1 and 2. The results generated by this study indicate that rural persistent poverty counties which are proximate to major metropolitan areas do not generate as much indirect or induced income or employment from agricultural production as rural persistent poverty counties which have no neighboring major metropolitan areas. Contrary to hypotheses of the study, average farm size and amount of cash receipts were not found to be correlated with the Type I or Type III income and employment multipliers or the indirect or induced income or employment effects. The income and employment multipliers generated by this study represent the additions to income and employment that would accrue if demand for agricultural commodities produced in the study area were increased by one dollar. Additional information concerning the ability of persistent poverty counties to respond to increased agricultural demand is needed before economic development decisions can be made. Furthermore, the size of the multipliers generated by agricultural production relative to multipliers in other industrial sectors must be evaluated. Finally, the effects of governmental agricultural programs must be appraised when agricultural production is considered as an economic development option

Continuous Restricted Boltzmann Machines

Restricted Boltzmann machines are a generative neural network. They summarize their input data to build a probabilistic model that can then be used to reconstruct missing data or to classify new data. Unlike discrete Boltzmann machines, where the data are mapped to the space of integers or bitstrings, continuous Boltzmann machines directly use floating point numbers and therefore represent the data with higher fidelity. The primary limitation in using Boltzmann machines for big-data problems is the efficiency of the training algorithm. This paper describes an efficient deterministic algorithm for training continuous machines

One-dimensional, mixed-metal sulphides – structural and physical properties

New one-dimensional sulphides based on Ba2CoS3 have been synthesised and their structural and electronic properties investigated. The starting point was the one-dimensional sulphide Ba2CoS3, which shows one-dimensional anti-ferromagnetism, metallic-like behaviour and a small negative magnetoresistance. Cationic substitutions were carried out on both the barium and cobalt sites of Ba2CoS3. The substitution of zinc for cobalt into Ba2CoS3 resulted in the formation of the series Ba2Cox1−xZnxS3 (x = 0.0-1.0). Ba2Co1−xZnS3 compounds maintain the one-dimensional structure but become paramagnetic and show semiconducting properties. Interestingly significant values of magnetoresistance (up to −25%) are found in the series. The origin of the magnetoresistance is currently unknown although it is suspected that there is some extrinsic contribution. The compound Ba2Co0.75Fe0.25S3 has also been successfully synthesised although attempts to form compounds with higher iron content were not successful. A large number of compounds in the series Ba2Zn1–xMxS3 (M = Fe, Mn, Cr, Ni) have also been synthesised and initial investigations into the properties of these materials show that again they exhibit negative magnetoresistance. Finally Ba1.9K0.1CoS3 has been synthesised although no investigation into the properties has yet been carried out

A Survey of Human Intestinal Protozoa of Logan City and Vicinity

Surveys of human intestinal protozoa in the United States have been confined mostly to Eastern sections of the country and to the Pacific coast. There has been little work done concerning these parasites in western mountain states, and no previous surveys have been made of these organisms in the Intermountain West. It is important that the kinds oand numbers of these parasitic protozoa be determined for this locality; and it is only through surveys that the harmful, as well as the commensal, intestinal protozoa can be determined and treated. In 1933, teh city of Chicago experienced a general epidemic of amoebic dysentry, believed to be caused by a Endameba histolytica carrier. The seriousness of this epidmic led to the realization that the amoebic dysentary of the tropics could occur in tempearte regions. It is one of the purposes of surveys to recognized the incidence of pathogenic protozoa, with the purpose of averting possible epidemics of dysentary, diarrhea and other minor intestinal disturbances

AN ELECTROMAGNETIC FIELD MODEL FOR THE DESIGN OF RF REED RELAYS

A model of the electromechanical characteristics, electrostatic characteristics and coil eddy current losses of a reed relay was developed. These characteristics were returned from reed and coil dimensions. The model was intended as an aid to the design of reed relays for Radio Frequency (RF) and high voltage applications. An electromechanical model of a reed switch and coil was developed using a combination of an axisymmetric finite element model and analytical methods. The characteristics returned from this model were operate, release and differential amp turns, contact gap and contact force. Inclusion of results for contact resistance against contact force yielded the contact resistance characteristics. Electrostatic force between reed contacts was calculated and a criteria for contact arcing in a vacuum applied to allow prediction of breakdown voltage in an evacuated reed switch. The above elements were incorporated in a "Reed Switch Design Program" in which operating, contact resistance and breakdown voltage characteristics were calculated from reed and coil dimensions. Results were found to be in agreement with measured values for three reed switch types. Eddy current losses in relay coils were investigated through experimental measurement of losses occurring in coils mounted around a copper conductor carrying a high frequency current. The losses occurring in the coil were found to present an effective resistance to the current in the conductor. The influence of coil dimensions and the magnetic properties of the conductor on losses were observed. An analytical model of eddy current losses was derived from first principals results and were found concordant with those measured. An "RF Reed Relay Design Program" embodying the eddy current loss model and preceding work was created to demonstrate how relay performance (and efficiency) can be enhanced by tuning reed and coil dimensions. An example of its successful application to product development at Crydom Magnetics Ltd is presented. Proposals for future work are included.Crydom Magnetics Limite