Nitrogen Dispersion

A mathematical model of free surface is presented for the study of the nitrogen injection of the gas cap for maintain of pressure, we used one model dispersion a flow in well zone. Nitrogen injected into the cap has a density greater than the original gas which has rushed to the gas-oil contact goc. Since the goc on the border there is a lot of nitrogen gas, it will spread and disperse into the oil. 

In the goc around a well about to be invaded by gas coning phenomena occur; therefore the model to interpret the output of the well must include the phenomenon of free surface. This paper proposes a method to measure the degree of contamination of the oil zone. This compositional data based on a production well before being invaded in producing interval by the gas cap. The most contaminated area of oil is close to the goc, as nitrogen is expected to exit the current production from the well just before being overcome by gas.

A Meeting of Great Minds, Sophus Lie and John Nash throughout their Works

It is well known that Marius Sophus Lie (1842-1899) and John Forbes Nash (1928-2015) are great mathematicians. Sophus Lie comes from Norway and John Nash from United States of America. Their stories have certain resemblances and remarkable relations. This editorial would emphasize some of them. When they have started their university studies, their respective first interests were not mathematics.

That is to say, Lie has been in Astronomy and Nash in Chemical Engineering. Whereas,when they worked on mathematics, the first had Lobatchevski award in 1897 and the second, Nobel prize 1994 and Abel award 2015 (Niels Abel is the uncle of the wife of Sophus Lie: Anna Birch). In addition, their contributions in geometry are considerable, particularly in differential equations. Lie worked on transformation groups relative to partial differential equations, in other words, on Lie groups and on special non-associative algebras named Lie algebras.

Advances in Logic, Operations and Computational Mathematics

Journal of Applied & Computational Mathematics Volume 5, Issue 2 comprised of 7 research articles and 4 opinion articles and is focused on the innovation of polygon, Euler, linear and non-linear equations.

EL-Kholy et al., in their research article discussed about balanced folding over a polygon and Euler numbers. The study proved that for a balanced folding of a simply connected surface M, there is a subgroup of the group which is called all homeomorphisms of M that will acts 1- transitively on the 2-cells of M.

Gil et al., in their research have reported about the exponentially stabile non-linear, non-autonomous multi variable discrete systems. Based on the recent estimates on matrix equations, the findings suggest that a class of non-autonomous discrete-time systems is governed by semi-linear vector difference equations along with slowly varying linear parts.

Models of damped oscillators in quantum mechanics

We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schr¨odinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. 

The factorization technique is applied to the case of a shifted harmonic oscillator. The time evolution of the expectation values of the energy-related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator.

On the Use of P-Values in Genome Wide Disease Association Mapping

In hypothesis testing, p-value is routinely used as a measure of statistical evidence against the null hypothesis, where a smaller p-value indicates stronger evidence substantiating the alternative hypothesis. P-value is the probability of type-I error made in a hypothesis testing, namely, the chance that one falsely reject the null hypothesis when the null holds true. In a disease genome wide association study (GWAS), p-value potentially tells us how likely a putative disease associated variant is due to random chance. For a long time p-values have been taken seriously by the GWAS community as a safeguard against false positives. 

Every disease-associated mutation reported in a GWAS must reach a stringent p-value cut off (e.g., 10-8) in order to survive the multiple testing corrections. This is reasonable because after testing millions of variants in the genome, some random variants ought to yield small p-values purely by chance. Despite of p-value’s theoretical justification, however, it has become increasingly evident that statistical p-values are not nearly as reliable as it was believed.