Parallel matrix inversion techniques

In this paper, we present techniques for inverting sparse, symmetric and positive definite matrices on parallel and distributed computers. We propose two algorithms, one for SIMD implementation and the other for MIMD implementation. These algorithms are modified versions of Gaussian elimination and they take into account the sparseness of the matrix. Our algorithms perform better than the general parallel Gaussian elimination algorithm. In order to demonstrate the usefulness of our technique, we implemented the snake problem using our sparse matrix algorithm. Our studies reveal that the proposed sparse matrix inversion algorithm significantly reduces the time taken for obtaining the solution of the snake problem. In this paper, we present the results of our experimental work.

High volume versus low volume balance training on postural sway in adults with previous ankle inversion injury

Balance training is commonly used in the rehabilitation process of ankle injuries; however, the exercise prescription guidelines for prescribing balance training are poorly understood. The aim of the present study was to determine if high or low volume balance training is more effective in improving postural sway after an 8 week balance training program utilising the same exercises. Seventeen subjects (14 male, 3 female) with a mean age of 24.06 ± 5.6 years were randomly allocated into a control group (CG), low volume training (LVT) or high volume training (HVT). All subjects had sustained at least two inversion ankle injuries within the last 18 months. Subjects completed 8 weeks of balance training of up to 30 mins duration, 3 times per week. LVT consisted of 40 repetitions for week 1, progressing to 90 repetitions by week 8. HVT consisted of 60 repetitions for week 1, progressing to 130 repetitions by week 8. The maximum centre of pressure (COP) excursion was obtained from the porce plate in the medial-lateral (ML) direction and subsequently used for pre-test and post-test analysis. After the 8 week training intervention, there was a significant (P<0.001) difference in postural sway between pre and post testing for both the LVT (pre = 88.69mm ± 25.08mm, post = 72.17mm ± 27.53mm) and HVT (pre = 77.47mm ±10.57mm, post = 58.54mm ± 7.01mm) groups. There was no significant (P>0.01) difference detected for improvements between the LVT and HVT, however reported effect sizes (ES) showed large effect size chances in the high volume training (ES = 1.7) whereas low volume training showed medium effect sizes changes (ES = 0.6). This preliminary study demonstrates the importance of training volume in the rehabilitation of ankle injuries, with the HVT being superior to LVT.

Applications of symbolic computing for symmetry analysis of differential equations

 This thesis presents a number of applications of symbolic computing to the study of differential equations. In particular, three packages have been produced for the computer algebra system MAPLE and used to find a variety of symmetries (and corresponding invariant solutions) for a range of differential systems.

Phase inversion of ionomer-stabilized emulsions to form high internal phase emulsions (HIPEs)

Herein, we report the phase inversion of ionomer-stabilized emulsions to form high internal phase emulsions (HIPEs) induced by salt concentration and pH changes. The ionomers are sulfonated polystyrenes (SPSs) with different sulfonation degrees. The emulsion types were determined by conductivity measurements, confocal microscopy and optical microscopy, and the formation of HIPE organogels was verified by the tube-inversion method and rheological measurements. SPSs with high sulfonation degrees (water-soluble) and low sulfonation degrees (water-insoluble) can stabilize oil-in-water emulsions; these emulsions were transformed into water-in-oil HIPEs by varying salt concentrations and/or changing the pH. SPS, with a sulfonation degree of 11.6%, is the most efficient, and as low as 0.2 (w/v)% of the organic phase is enough to stabilize the HIPEs. Phase inversion of the oil-in-water emulsions occurred to form water-in-oil HIPEs by increasing the salt concentration in the aqueous phase. Two phase inversion points from oil-in-water emulsions to water-in-oil HIPEs were observed at pH 1 and 13. Moreover, synergetic effects between the salt concentration and pH changes occurred upon the inversion of the emulsion type. The organic phase can be a variety of organic solvents, including toluene, xylene, chloroform, dichloroethane, dichloromethane and anisole, as well as monomers such as styrene, butyl acrylate, methyl methacrylate and ethylene glycol dimethacrylate. Poly(HIPEs) were successfully prepared by the polymerization of monomers as the continuous phase in the ionomer-stabilized HIPEs.