Mathematics

ABSTRACT We present new global stability results of neural networks with delay and show that these results generalize recently published stability results. In particular, several different stability conditions in the literature which were proved using different Lyapunov functionals are generalized and unified by proving them using the same Lyapunov functional. We also show that under certain conditions, reversing the directions of the coupling between neurons preserves the global asymptotical stability of the neural network.

ABSTRACT We present some new global stability results of neural networks with delay and show that these results generalize recently published stability results. In particular, several different stability conditions in the literature which were proved using different Lyapunov functionals are generalized and unified by proving them using the same Lyapunov functional. We also show that under certain conditions, reversing the directions of the coupling between neurons preserves the global asymptotical stability of the neural network.

Medication errors are the second most frequently reported hospital incident in Australia and are a global concern. A "Medication Calculation and Administration" workshop followed by a "hurdle" assessment (compulsory task mandating a minimum level of performance as a condition of passing the course) was introduced into Year 2 of the James Cook University medical curriculum to decrease dosage calculation and administration errors among graduates. This study evaluates the effectiveness of this educational activity as a long-term strategy to teach medical students' essential skills in calculating and administering medications. This longitudinal study used a pre- and post-test design to determine whether medical students retained their calculation and administration skills over a period of 4 years. The ability to apply basic mathematical skills to medication dose calculation, principles of safe administration (Part 1), and ability to access reference materials to ...

Given a compact Riemannian manifold M, we consider a warped prod-uct ¯M = I ×h M where I is an open interval in R. We suppose that the mean curvature of the fibers do not change sign. Given a positive differen-tiable function ψ in ¯M, we find a closed hypersurface Σ ...

We have studied the effects of the duration of severe hypothyroidism (thyroidectomy) and aging on the pituitary TSH response to exogenous TRH and the TSH MCR in female rats. Rats were thyroidectomized (THYREX) or sham operated (SHAM) 4, 14, or 68 days before experimentation. All rats were prepared with chronic intraatrial catheters through which TRH (0, 250, or 1000 ng/100 g BW) or [125I]TSH was administered, and sequential blood samples were obtained. The MCR of TSH was determined in each group from the plasma disappearance curves of injected [125I]iodo-TSH and were found to be decreased in 4-day-THYREX [0.23 +/- 0.01 (+/- SE) vs. 0.27 +/- 0.01 ml/min X 100 g; P less than 0.05], but not in 14-day-THYREX or 68-day-THYREX rats compared with age-matched SHAM controls. In addition, the TSH MCR was found to be decreased in 68-day-SHAM compared to 4- or 14-day-SHAM rats (0.15 +/- 0.01 vs. 0.27 +/- 0.01 ml/min X 100 g; P less than 0.05). The amount of TSH secreted (MCR X area under delta plasma TSH curve X BW) in response to each dose of TRH was calculated and was found to be decreased in 4-day-THYREX rats (4.5 +/- 1.5 vs. 30.0 +/- 4.5 micrograms; P less than 0.05), but not different in 14-day- or 68-day-THYREX rats compared with age-matched SHAM controls. The amount of TSH secreted in response to TRH was also reduced in 68-day-SHAM compared with 4- or 14-day-SHAM rats (16.0 +/- 1.0 vs. 30.0 +/- 4.5 micrograms; P less than 0.05). These results indicate that 1) the MCR of TSH is decreased by aging, but not by severe hypothyroidism in the rat; 2) the pituitary TSH response of the rat to exogenous TRH is decreased by aging, and 3) during severe hypothyroidism, the pituitary TSH response of the rat to a midrange or maximal dose of TRH is decreased (4-day-THYREX) or not different (14- and 68-day-THYREX) compared with that of age-matched euthyroid rats.

Mathematics of music and sound production brings to bear the physical and practical application of Mathematics in the field of Music. The composition of songs involves the principle of key scaling, their respective interval as calculated with the aid of an appropriate key division which suites the generality of songs composed in different keys with the keyboard. Melodies, harmonies and rhythms produced in the stage of rendition is characterized by transposition and inversion of key to suite each song. With the aid of keyboard, elements of Symmetric group are used to compose songs.

The use of dynamic, three-dimensional software with virtual reality offers new possibilities for the teaching and learning of geometry. We explore the effects of introducing the immersive virtual reality software NeoTrie VR in real classes. Within a Design Research framework, we present qualitative observational data to report how the collaboration among a software development company, university researchers, and schools produces improvements in the design and updating of the software; the geometrical content, representations, and mathematical activity that students have access to as well as the way teachers conceive and manage the teaching of geometry.

... Janine M. Lehane); (5) "Concept Development and Learning" (Linda D. Avery and Catherine A. Little); (6) "Adapting Language Arts Curricula for High-Ability Learners" (Catherine A. Little); (7) "Adapting Mathematics Curricula for High-Ability Learners" (Dana T. Johnson); (8 ...

We show that if p:F→E is a covering of directed graphs, then the Cuntz–Krieger algebra C*(F) of F can be viewed as a crossed product of C*(E) by a coaction of a homogeneous space for the fundamental group π1(E). Combining this result with information about Cuntz–Krieger algebras gives some interesting corollaries which suggest conjectures about crossed products by coactions of homogeneous spaces of discrete groups. We then prove these conjectures.

Let G be a second countable locally compact group and A a separable continuous trace C*-algebra. To each pointwise unitary coaction δ of G on A one can associate a proper G-bundle [Formula: see text], π × μ → π. We show that two pointwise unitary coactions δ and ∊ of G on A are exterior equivalent if and only if the proper G-bundles [Formula: see text] and [Formula: see text] are isomorphic. Thus, if A is stable, there exists a bijection between the isomorphism classes of proper G-bundles over [Formula: see text] and the exterior equivalence classes of pointwise unitary coactions of G on A. Moreover, when G is abelian we recover a theorem of Olesen and Raeburn.