Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

Equal access to the opportunities available? Equity and diversity laws and policies in Australia

Australia has been populated for more than 40,000 years with Indigenous Australians joined by European settlers only 230 years ago. The first settlers consisted of convicts from more than 28 countries and members of the British army who arrived in 1788 to establish a British penal colony. Mass migration in the nineteenth century with one and a half million immigrants from Europe, principally from the United Kingdom and Ireland (Haines and Shlomowitz, 1992), established the continent as an Anglo society in the Pacific. In the twentieth century immigrants came from many European countries and in the latter decades from many parts of Asia and the Middle East (Collins, 1991, pp.10-13). In the 21st century Australia has an ethnically and culturally diverse population. The original Indigenous population of Australia accounts for approximately 460,000 or 2.5 per cent of the total population (ABS, 2006a). Estimates are that around 4.5m. persons in the population (close to 20 per cent), were born outside Australia with the majority of these arriving from Europe, principally the United Kingdom, and New Zealand (ABS, 2006b). Like many other countries, Australia has a legacy of discrimination and inequality in employment. Propelled by racist ideologies and the male breadwinner ideology, Indigenous Australians, and non-European immigrants, and women were barred from certain jobs and paid less for their work than any white male counterpart. These conditions were legally sanctioned through the industrial relations system and other laws in the nineteenth and first half of the twentieth century. Since the 1960s a dramatic change has occurred in social policy and national legislation and Australia today has an extensive array of laws which forbid employment discrimination on race, ethnicity, gender and many other characteristics, and other approaches which promote proactive organizational plans and actions to achieve equity in employment. This chapter outlines these developments.

Organizational probes : exploring playful interactions in work environment

Playfulness, with non-intrusive elements, can be considered a useful resource for enhancing social awareness and community building within work organizations. Taking inspirations from the cultural probes approach, we developed organizational probes as a set of investigation tools that could provide useful information about employees’ everyday playful experiences within their work organizations. In an academic work environment, we applied our organizational probes over a period of three weeks. Based on the collected data we developed two design concepts for playful technologies in work environments.