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.

The numbers of sample design for evaluation of the soil fertility

The determination of the amount of sample units that will compose the sample express the optimization of the workforce, and reduce errors inherent in the report of recommendation and evaluation of soil fertility. This study aimed to determine in three systems use and soil management, the numbers of units samples design, needed to form the composed sample, for evaluation of soil fertility. It was concluded that the number of sample units needed to compose the composed sample to determination the attributes of organic matter, pH, P, K, Ca, Mg, Al and H+Al and base saturation of soil vary by use and soil management and error acceptable to the mean estimate. For the same depth of collected, increasing the number of sample units, reduced the percentage error in estimating the average, allowing the recommendation of 14, 14 and 11 sample in management with native vegetation, pasture cultivation and corn, respectively, for a error 20% on the mean estimate.

On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

Calculating Flash Point Numbers from Molecular Structure: An Improved Method for Predicting the Flash Points of Acyclic Alkanes

We report a novel method for calculating flash points of acyclic alkanes from flash point numbers, N(FP), which can be calculated from experimental or calculated boiling point numbers (Y(BP)) with the equation N(FP) = 1.020Y(BP) - 1.083 Flash points (FP) are then determined from the relationship FP(K) = 23.369N(FP)(2/3) + 20.010N(FP)(1/3) + 31.901 For it data set of 102 linear and branched alkanes, the correlation of literature and predicted flash points has R(2) = 0.985 and an average absolute deviation of 3.38 K. N(FP) values can also be estimated directly from molecular structure to produce an even closer correspondence of literature and predicted FP values. Furthermore, N(FP) values provide a new method to evaluate the reliability of literature flash point data.

Uncertainty Characterization Of A Conceptual Rainfall-Runoff Model By Using Grey Numbers

A procedure for characterizing global uncertainty of a rainfall-runoff simulation model based on using grey numbers is presented. By using the grey numbers technique the uncertainty is characterized by an interval; once the parameters of the rainfall-runoff model have been properly defined as grey numbers, by using the grey mathematics and functions it is possible to obtain simulated discharges in the form of grey numbers whose envelope defines a band which represents the vagueness/uncertainty associated with the simulated variable. The grey numbers representing the model parameters are estimated in such a way that the band obtained from the envelope of simulated grey discharges includes an assigned percentage of observed discharge values and is at the same time as narrow as possible. The approach is applied to a real case study highlighting that a rigorous application of the procedure for direct simulation through the rainfall-runoff model with grey parameters involves long computational times. However, these times can be significantly reduced using a simplified computing procedure with minimal approximations in the quantification of the grey numbers representing the simulated discharges. Relying on this simplified procedure, the conceptual rainfall-runoff grey model is thus calibrated and the uncertainty bands obtained both downstream of the calibration process and downstream of the validation process are compared with those obtained by using a well-established approach, like the GLUE approach, for characterizing uncertainty. The results of the comparison show that the proposed approach may represent a valid tool for characterizing the global uncertainty associable with the output of a rainfall-runoff simulation model.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.