Measuring nonlinearity by means of static parameters in Bernoulli binary sequences distribution: A brief approach

This paper analyzes Bernoulli’s binary sequences in the representation of empirical nonlinear events, analyzing the distribution of natural resources, population sizes and other variables that influence the possible outcomes of resource’s usage. Consider the event as a nonlinear system and the metrics of analysis consisting of two dependent random variables 0 and 1, with memory and probabilities in maximum finite or infinite lengths, constant and equal to 1/2 for both variables (stationary process). The expressions of the possible trajectories of metric space represented by each binary parameter remain constant in sequences that are repeated alternating the presence or absence of one of the binary variables at each iteration (symmetric or asymmetric). It was observed that the binary variables [Formula: see text] and [Formula: see text] assume on time [Formula: see text] specific behaviors (geometric variable) that can be used as management tools in discrete and continuous nonlinear systems aiming at the optimization of resource’s usage, nonlinearity analysis and probabilistic distribution of trajectories occurring about random events. In this way, the paper presents a model of detecting fixed-point attractions and its probabilistic distributions at a given population-resource dynamic. This means that coupling oscillations in the event occur when the binary variables [Formula: see text] and [Formula: see text] are limited as a function of time [Formula: see text].

Evaluating the impact of binary parameter uncertainty on stellar population properties

ABSTRACT Binary stars have been shown to have a substantial impact on the integrated light of stellar populations, particularly at low metallicity and early ages – conditions prevalent in the distant Universe. But the fraction of stars in stellar multiples as a function of mass, their likely initial periods and distribution of mass ratios are all known empirically from observations only in the local Universe. Each has associated uncertainties. We explore the impact of these uncertainties in binary parameters on the properties of integrated stellar populations, considering which properties and time-scales are most susceptible to uncertainty introduced by binary fractions and whether observations of the integrated light might be sufficient to determine binary parameters. We conclude that the effects of uncertainty in the empirical binary parameter distributions are likely smaller than those introduced by metallicity and stellar population age uncertainties for observational data. We identify emission in the He ii 1640 Å emission line and continuum colour in the ultraviolet–optical as potential indicators of a high-mass binary presence, although poorly constrained metallicity, dust extinction, and degeneracies in plausible star formation history are likely to swamp any measurable signal.

The Addition of N-Butanol in Ethanol-Isooctane Mixture to Reduce Vapor Pressure of Oxygenated-Gasoline Blend

In this work, vapor pressure of binary systems for isooctane + ethanol, isooctane + n-butanol and ethanol + n-butanol and ternary system for isooctane + ethanol + n-butanol were measured in the temperature range from 313.15 to 318.15 K using the inclined ebulliometer. The experimental results showed that the existence of n-butanol in isooctane decreases the vapor pressure of mixture, while increasing n-butanol fraction in ternary isooctane-ethanol-n-butanol mixture decreased vapor pressure of mixture. Experimental data for binary systems studied were correlated with Wilson, NRTL and UNIQUAC models with average relative deviation (ARD) of 3.5%. The optimized binary parameter pairs obtained in this work were used to estimate the ternary system. The Wilson model gave the best performance for estimation of ternary system with ARD of 5.4%. All systems studied showed non-ideal solution with positive deviation from Raoult’s law.

An approximability-related parameter on graphs―-properties and applications

Graph Theory International audience We introduce a binary parameter on optimisation problems called separation. The parameter is used to relate the approximation ratios of different optimisation problems; in other words, we can convert approximability (and non-approximability) result for one problem into (non)-approximability results for other problems. Our main application is the problem (weighted) maximum H-colourable subgraph (Max H-Col), which is a restriction of the general maximum constraint satisfaction problem (Max CSP) to a single, binary, and symmetric relation. Using known approximation ratios for Max k-cut, we obtain general asymptotic approximability results for Max H-Col for an arbitrary graph H. For several classes of graphs, we provide near-optimal results under the unique games conjecture. We also investigate separation as a graph parameter. In this vein, we study its properties on circular complete graphs. Furthermore, we establish a close connection to work by Šámal on cubical colourings of graphs. This connection shows that our parameter is closely related to a special type of chromatic number. We believe that this insight may turn out to be crucial for understanding the behaviour of the parameter, and in the longer term, for understanding the approximability of optimisation problems such as Max H-Col.