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.

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 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.

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.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Chromosome numbers of some Brazilian species of diplopods (Diplopoda, Arthropoda)

The present paper presents the chromosome numbers of five brazilian species of diplopods: Plusioporus setiger (2n = 10 and 2n= 10+ lB, the distinction of the sexual pair was not possible), Pseudonannolene ophiulus (2n=12, XY), Pseudonannolene halophila (2n=16, XY), Rhinocricus sp. (2n=28, XY) and Rhinocricus padbergi (2n=20, the distinction of the sexual pair was not possible).

Critical numbers of attractive Bose-Einstein condensed atoms in asymmetric traps

A quantitative analysis of the critical number of attractive Bose-Einstein condensed atoms in asymmetric traps was studied. The Gross-Pitaevskii (GP) formalism for an atomic system with arbitrary nonspherically symmetric harmonic trap was also discussed. Characteristic limits were obtained for reductions from three to two and one dimensions from three to two and one dimensions, in perfect cylindrical symmetries as well as in deformed ones.

Border detection in digital images: An approach by fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in gray shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the gray shades making up the image, and thus calculate the appropriateness of the pixels in relation to an homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. © 2007 IEEE.

Edge detection in digital images using fuzzy numbers

The purpose of this paper is to introduce a new approach for edge detection in grey shaded images. The proposed approach is based on the fuzzy number theory. The idea is to deal with the uncertainties concerning the grey shades making up the image and, thus, calculate the appropriateness of the pixels in relation to a homogeneous region around them. The pixels not belonging to the region are then classified as border pixels. The results have shown that the technique is simple, computationally efficient and with good results when compared with both the traditional border detectors and the fuzzy edge detectors. Copyright © 2009, Inderscience Publishers.

Influence of anatomical location on CT numbers in cone beam computed tomography

Objective: To assess the influence of anatomical location on computed tomography (CT) numbers in mid- and full field of view (FOV) cone beam computed tomography (CBCT) scans. Study Design: Polypropylene tubes with varying concentrations of dipotassium hydrogen phosphate (K2HPO4) solutions (50-1200 mg/mL) were imaged within the incisor, premolar, and molar dental sockets of a human skull phantom. CBCT scans were acquired using the NewTom 3G and NewTom 5G units. The CT numbers of the K2HPO 4 phantoms were measured, and the relationship between CT numbers and K2HPO4 concentration was examined. The measured CT numbers of the K2HPO4 phantoms were compared between anatomical sites. Results: At all six anatomical locations, there was a strong linear relationship between CT numbers and K2HPO4 concentration (R 2 > 0.93). However, the absolute CT numbers varied considerably with the anatomical location. Conclusion: The relationship between CT numbers and object density is not uniform through the dental arch on CBCT scans. © 2013 Elsevier Inc.