Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the meantime, we define the indicator sequences vector. Using the orthogonal or row orthogonal transformations of the indicator sequences vector, we construct some sp...

This paper offers a new mathematical formulation that addresses the relationship between expected price-to-book ratio, dividend per share, dividend payout ratio, systematic and unsystematic risks. The sample includes the non-financial firms in the DJIA covering the period 1997-2006. The general results show that the expected price-to-book ratios are: (a) positively associated with the expected ...

1. Caffeine is widely used as an in vivo probe for CYP1A2; the distribution/activity of this enzyme is reported to be reflected by metabolic ratios. 2. Several metabolic ratios using different combinations of urinary metabolites have been used to measure CYP1A2, with varying conclusions on its distribution. 3. A mathematical comparison of five metabolic ratios claiming to reflect CYP1A2 activit...

− This article describes fundamentals of Global Advertising Strategies' MPT3 Continuum TM framework − a set of mathematical and visual models designed to optimize marketing campaigns in respect to P&L, ROI and price/performance ratios. Various non-linear optimization techniques were created and implemented for numerous niche − targeted marketing campaigns. Pre-and post-campaign surveys are cons...

The classical three-body problem { where is abstract mathematics, physical intuition, computational physics most powerful? We propose a simple oscillator model for the reduced three-body problem to understand the stability of orbits with small eccentricity of the light planet. It models the main short-time features for small mass ratios of the other bodies. These results are confronted with the...

In a corpus study we found that authors vary both mathematical form and precision1 when expressing numerical quantities. Indeed, within the same document, a quantity is often described vaguely in some places and more accurately in others. Vague descriptions tend to occur early in a document and to be expressed in simpler mathematical forms (e.g., fractions or ratios), whereas more accurate desc...