Experimenting with maple to obtain sums of bessel series

In the study of pulse-width modulation within electrical engineering many authors develop a series representation of the modulated wave using a double Fourier series based on properties of the carrier and reference waveforms

Sets of p-spectral synthesis

Let G be a Hausdorff locally compact Abelian group..

Positive definite and related functions on hypergroups

In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Lévy-Khinchin representation for negative definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely alternating functions. The techniques employed here also lead to considerable simplification of the proofs of known results on positive definite and negative definite functions on hypergroups

World War 1 appeal medals of Western Australia

Appeal medals were produced in Western Australia over the first four years of World War I in support of various worthy causes, including the Red Cross, Children’s Hospital and returned injured soldiers and widows of those who fought for Australia, the latter through the Ugly Men’s Voluntary Workers’ Association of Western Australia (Incorporated). There has been very little known about these medals, not even their manufacturer, but an analysis of the die characteristics together with an examination of newspapers of the day and other contemporary records leads us to their common manufacturer, Cumpston’s City Electric Engraving Works, then located in Hay Street, Perth

Isomorphisms of hypergroups

Let K1, K2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L1-algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces

The first Anzacs at Gallipoli - April 1915: Contemporary Australian commemorative medallions & their background

It is almost exactly 100 years since the first ANZAC force went ashore with other Allied forces on the Gallipoli Peninsula that overlooks the strategic Dardanelles Strait..

Pure mathematics in Australia

I.D. Macdonald argued in this journal in 1968 that there was an inadequate number of mathematicians teaching in Australian universities who were qualified by international standards to conduct honours courses and supervise research students..

Stationary Random Fields on the Unitary Dual of a Compact Group

We generalise the notion of wide-sense stationarity from sequences of complex-valued random variables indexed by the integers, to fields of random variables that are labelled by elements of the unitary dual of a compact group. The covariance is positive definite, and so it is the Fourier transform of a finite central measure (the spectral measure of the field) on the group. Analogues of the Cramer and Kolmogorov theorems are extended to this framework. White noise makes sense in this context and so, for some classes of group, we can construct time series and investigate their stationarity. Finally we indicate how these ideas fit into the general theory of stationary random fields on hypergroups

Sediment compaction rates and subsidence in deltaic plains : numerical constraints and stratigraphic influences

This paper is not subject to U.S. copyright. The definitive version was published in Basin Research 19 (2007): 19-31, doi:10.1111/j.1365-2117.2006.00310.x.Natural sediment compaction in deltaic plains influences subsidence rates and the evolution of deltaic morphology. Determining compaction rates requires detailed knowledge of subsurface geotechnical properties and depositional history, neither of which is often readily available. To overcome this lack of knowledge, we numerically forward model the incremental sedimentation and compaction of stochastically generated stratigraphies with geotechnical properties typical of modern depositional environments in the Mississippi River delta plain. Using a Monte Carlo approach, the range of probable compaction rates for stratigraphies with compacted thicknesses <150 m and accumulation times <20 kyr. varies, but maximum values rarely exceed a few mm yr-1. The fastest compacting stratigraphies are composed primarily of peat and bar sand, whereas the slowest compacting stratigraphies are composed of prodelta mud and natural levee deposits. These results suggest that compaction rates can significantly influence vertical and lateral stratigraphic trends during deltaic evolution

Putting theory oriented evaluation into practice

Evaluations of gaming simulations and business games as teaching devices are typically end-state driven. This emphasis fails to detect how the simulation being evaluated does or does not bring about its desired consequences. This paper advances the use of a logic model approach which possesses a holistic perspective that aims at including all elements associated with the situation created by a game. The use of the logic model approach is illustrated as applied to Simgame, a board game created for secondary school level business education in six European Union countries