REGULARITIES OF NUMBERS IN THE FIBONACHI TRIANGLE CONSTRUCTED ON THE DEGREE TRANSFORMATIONS OF A SQUARE THREE MEMBERS

In this paper, it is shown that the Fibonacci triangle is formed from the elements of power transformations of a quadratic trinomial. It is binary structured by domains of rows of equal lengths, in which the sum of numbers forms a sequence of certain numbers. This sequence coincides with the transformed bisection of the classical sequence of Fibonacci numbers. The paper substantiates Pascal's rule for calculating elements in the lines of a Fibonacci triangle. The general relations of two forgings of numbers in lines of a triangle of Fibonacci for arbitrary values are received

The Usefulness of the Two-Step Normality Transformation in Retesting Existing Theories

The Two-Step normality transformation has been shown to reliably transform continuous variables toward normality. The procedure offers researchers a capable alternative to more prominent methods, such as winsorization, ranking, and power transformations. We demonstrate its utility in the context of the Productivity Paradox literature stream, which is renowned for inconsistent results. This paper demonstrates that the Two-Step normality transformation, which has not been used in Productivity Paradox research, may produce greater goodness-of-fit and affect theoretical understandings on the topic. We use a classic Productivity Paradox dataset to show that compared to the prominent normality transformations, the Two-Step produces unique findings, including 1) regression coefficients more closely resembling the original data, 2) different effect sizes and significance levels, and 3) strengthening evidence for fundamental theories in Productivity Paradox literature. We demonstrate results that challenge uncertainties about the relationship between IT investment and firm performance. Our results imply that the Two-Step procedure should be considered a viable transformation option in future information systems research.

A comparison between traditional ordinary least-squares regression and three methods for enforcing additivity in biomass equations using a sample of Pinus radiata trees

Background: Additivity has long been recognised as a desirable property of systems of equations to predict the biomass of components and the whole tree. However, most tree biomass studies report biomass equations fitted using traditional ordinary least-squares regression. Therefore, we aimed to develop models to estimate components, subtotals and above-ground total biomass for a Pinus radiata D.Don biomass dataset using traditional linear and nonlinear ordinary leastsquares regressions, and to contrast these equations with the additive procedures of biomass estimation.Methods: A total of 24 ten-year-old trees were felled to assess above-ground biomass. Two broad procedures were implemented for biomass modelling: (a) independent; and (b) additive. For the independent procedure, traditional linear models (LINOLS) with scaled power transformations and y-intercepts and nonlinear power models (NLINOLS) without y-intercepts were compared. The best linear (transformed) models from the independent procedure were further tested in three different additive structures (LINADD1, LINADD2, and LINADD3). All models were evaluated using goodness-of-fit statistics, standard errors of estimates, and residual plots.Results: The LINOLS with scaled power transformations and y-intercepts performed better for all components, subtotals and total above-ground biomass in contrast to NLINOLS that lacked y-intercepts. The additive model (LINADD3) in a joint generalised linear least-squares regression, also called seemingly unrelated regression (SUR), provided the best goodness-of-fit statistics and residual plots for four out of six components (stem, branch, new foliage and old foliage), two out of three subtotals (foliage and crown), and above-ground total biomass compared to other methods. However, bark, cone and bole biomass were better predicted by the LINOLS method.Conclusions: SUR was the best method to predict biomass for the 24-tree dataset because it provided the best goodness-of-fit statistics with unbiased estimates for 7 out of 10 biomass components. This study may assist silviculturists and forest managers to overcome one of the main problems when using biomass equations fitted independently for each tree component, which is that the sum of the biomasses of the predicted tree components does not necessarily add to the total biomass, as the additive biomass models do.

Application of Power Geometry and Normal Form Methods to the Study of Nonlinear ODEs

This paper describes power transformations of degenerate autonomous polynomial systems of ordinary differential equations which reduce such systems to a non-degenerative form. Example of creating exact first integrals of motion of some planar degenerate system in a closed form is given.

Gendered power transformations in India’s Northeast: Peace politics in Nagaland

As the middle space for ‘post ceasefire-cold peace’ politics expanded in Nagaland in India’s Northeast, the Naga women’s question has emerged as symbolic of the intense social churning in traditional hierarchies around three sites of inequality: decision-making in the public sphere, patriarchal customary laws and property rights. The article tracks the shift in Naga women’s peace politics, from motherhood politics to asserting more equal modes of citizenship, and explores the emancipatory potential of Naga women’s emergence in the public sphere as key stakeholders in the peace process within a context of growing tensions in the relationship between gender and ethnicity.