Frobenius Solution for Legendre's Equation, Rodrigue's Formula and Normalization

The Frobenius solution to Legendre/s equation is developed in detail as is Rodrigue's formula, which is employed to normalize Legendre polynomials.

A Universal Formula for Continuous Utility

A single formula assigns a continuous utility function to every representable preference relation.

Ms. Praed. 31 - Formula novitiorum, p. III

Vorbesitzer: Dominikanerkloster Frankfurt am Main

Publishing Linked Data - There is no One-Size-Fits-All Formula

Publishing Linked Data is a process that involves several design decisions and technologies. Although some initial guidelines have been already provided by Linked Data publishers, these are still far from covering all the steps that are necessary (from data source selection to publication) or giving enough details about all these steps, technologies, intermediate products, etc. Furthermore, given the variety of data sources from which Linked Data can be generated, we believe that it is possible to have a single and uni�ed method for publishing Linked Data, but we should rely on di�erent techniques, technologies and tools for particular datasets of a given domain. In this paper we present a general method for publishing Linked Data and the application of the method to cover di�erent sources from di�erent domains.

A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

INSTRUCCIO y formula per a la bona execucio de la pragmatica dels processos de absencia [Texto impreso]

Port. con esc. real xil

Tunnel magnetoresistance in GaMnAs: going beyond Jullière formula

The relation between tunnel magnetoresistance (TMR) and spin polarization is explored for GaMnAs∕GaAlAs∕GaMnAs structures where the carriers experience strong spin–orbit interactions. TMR is calculated using the Landauer approach. The materials are described in the 6 band k⋅p model which includes spin–orbit interaction. Ferromagnetism is described in the virtual crystal mean field approximations. Our results indicate that TMR is a function of spin polarization and barrier thickness. As a result of the stong spin–orbit interactions, TMR also depends on the the angle between current flow direction and the electrode magnetization. These results compromise the validity of Julliere formula.

Measuring color differences in automotive samples with lightness flop: a test of the AUDI2000 color-difference formula

From a set of gonioapparent automotive samples from different manufacturers we selected 28 low-chroma color pairs with relatively small color differences predominantly in lightness. These color pairs were visually assessed with a gray scale at six different viewing angles by a panel of 10 observers. Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas. From a weighted STRESS index accounting for the uncertainty in visual assessments, the best prediction of our whole experiment was achieved using AUDI2000, CAM02-SCD, CAM02-UCS and OSA-GP-Euclidean color-difference formulas, which were no statistically significant different among them. A two-step optimization of the original AUDI2000 color-difference formula resulted in a modified AUDI2000 formula which performed both, significantly better than the original formula and below the experimental inter-observer variability. Nevertheless the proposal of a new revised AUDI2000 color-difference formula requires additional experimental data.

A partial success of trade cooperation within the ‘16+1’ formula: the case of food exports to China. OSW COMMENTARY #189, 2015-10-29

When in 2012 China approached the countries of Central and Eastern Europe (CEE) with a proposal of cooperation in the ‘16+1’ formula, it declared it was willing to meet the needs of CEE countries. Beijing had been aware of the political importance of the problem of trade deficit (which has been ongoing for years) and launched cooperation with the governments of 16 CEE countries to boost imports from these states. The years 2011–2014 brought an improvement in the balance of trade between China and: Hungary, Latvia, the Czech Republic, Romania, Bulgaria and Croatia. The remaining ten CEE countries recorded an increase in their trade deficits. Changes in CEE countries’ balance of trade with China resulted only slightly from political actions. Instead, they were due to the macroeconomic situation and to a deterioration of the debt crisis in the EU which, for example, caused a decline in the import of Chinese goods in some of these countries. Multilateral trade cooperation was successfully developed in the entire region only in the agricultural and food production sector – the area of greatest interest to China. The pace of bilateral cooperation with specific countries varied, with the fastest being Poland, Latvia, Romania, Hungary and Bulgaria. Actions by governments of CEE countries resulted in Chinese market opening up to hundreds of local companies which, in turn, translated into an increase in the volume of foodstuffs sold by ‘the 16’ to China from US$ 137 million in 2011 to US$ 400 million in 2014. The success achieved in the agricultural and food production sector has demonstrated the effectiveness of trade cooperation in the ‘16+1’ formula. It is, however, insufficient to generate a significant improvement of the trade balance. At present, the sector’s share in the total volume of goods sold to China by CEE states is a mere 3.7%, and any reduction of the trade deficit would require long-term and more comprehensive solutions still to be implemented by the governments of individual CEE states.