Construction of the transcomplex numbers from the complex numbers

A geometrical construction of the transcomplex numbers was given elsewhere. Here we simplify the transcomplex plane and construct the set of transcomplex numbers from the set of complex numbers. Thus transcomplex numbers and their arithmetic arise as consequences of their construction, not by an axiomatic development. This simplifes transcom- plex arithmetic, compared to the previous treatment, but retains totality so that every arithmetical operation can be applied to any transcomplex number(s) such that the result is a transcomplex number. Our proof establishes the consistency of transcomplex and transreal arithmetic and establishes the expected containment relationships amongst transcomplex, complex, transreal and real numbers. We discuss some of the advantages the transarithmetics have over their partial counterparts.

Fish oil supplementation alters numbers of circulating endothelial progenitor cells and micro particles independent of eNOS genotype

Background Emerging cellular markers of endothelial damage and repair include endothelial microparticles (EMPs) and endothelial progenitor cells (EPCs) respectively. Effects of long chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) and influence of genetic background on these markers are not known. Objective This study investigated the effects of fish oil supplementation on both classical and novel markers of endothelial function in subjects prospectively genotyped for the Asp298 eNOS polymorphism and at moderate risk of CVD. Design 84 subjects with moderate risk of CVD (n=40 GG and n=44 GT/TT) completed a randomized, double-blind, placebo-controlled, 8-week cross-over trial of fish oil supplementation providing 1.5 g/d LC n-3 PUFA. Effects of genotype and fish oil supplementation on the blood lipid profile, inflammatory markers, vascular function (EndoPAT) and numbers of circulating EPCs and EMP (flow cytometry) were assessed. Results There was no significant effect of fish oil supplementation on blood pressure, plasma lipids or plasma glucose, although there was a trend (P = 0.069) towards a decrease in plasma TG concentration after FO supplementation compared to placebo. GT/TT subjects tended to have higher levels of total cholesterol and LDL-cholesterol, but vascular function was not affected by either treatment or eNOS genotype. Biochemical markers of endothelial function were also unaffected by treatment and eNOS genotype. In contrast, there was a significant effect of fish oil supplementation on cellular markers of endothelial function. Fish oil supplementation increased numbers of EPCs and reduced numbers of EMPs relative to the placebo, potentially favouring maintenance of endothelial integrity. There was no influence of genotype for any of the cellular markers of endothelial function, indicating that the effects of fish oil supplementation were independent of eNOS genotype. Conclusions Emerging cellular markers of endothelial damage, integrity and repair appear to be sensitive to potentially beneficial modification by dietary n-3 PUFA.

The multidimensional character of accounting numbers

This paper takes as its motivation debates surrounding the multiplicity of functions of accounting information. We are in particular interested in the existential function of accounting numbers and argue that numerical signs having discursive possibilities may acquire new meanings through reframing. Drawing on Goffman’s (1974) frame analysis and Vollmer’s (2007) work on three-dimensional character of numerical signs, we explore the ways in which numbers can go through instantaneous transformations and tell a new kind of story. In our analysis, we look at the main historical developments and current controversies surrounding accounting practice with a specific focus on scandals involving numerical signs as moments where our understandings and the discursive function of previously inoffensive signs shifts through a collective involvement. We map the purpose and usefulness of Vollmer’s three-dimensional framework in the analysis of selected financial accounting practices and scandals as examples of instances where numbers are reframed to suddenly perform a different existential function in context of their calculative and symptomatic dimensions.

Numbers in motion

We explore the debates surrounding the constructive and discursive capabilities of accounting information focusing in particular on the reception volatility of numbers once they are produced and ‘exposed’ to various communities of minds. Drawing on Goffman’s (1974) frame analysis and Vollmer’s (2007) work on the three-dimensional character of numerical signs, we explore how numbers can go through gradual or instantaneous transformations, get caught up in public debates and become ‘agents’ or ‘captives’ in creating social order and in some cases social drama. In our analysis we also relate to the work of Durkheim (1993, 2002) on the sociology of morality to illustrate how numbers can become indicators of moral transgression. The study explores both historical and contemporary examples of controversies and recent accounting scandals to demonstrate how preparers (of financial information) can lose control over numbers which then acquire new meanings through social context and collective (re)framing. The main contribution of the study is to illustrate how the narratives attached to numbers are malleable and fluid across both time and space.