##### Existence of the Rotational Subsonic Stationary Solution for a Two-Dimensional Bipolar Euler-Poisson Equation

Fang Liu, Yeping Li

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/jamcs/2019/v34i230209

In this paper, we study a two-dimensional bipolar Euler-Poisson equation (hydrodynamic model), which arises in mathematical modeling for semiconductors and plasmas. We are interested in the existence of the rotational subsonic stationary solution. Under the proper boundary conditions, we show the existence of rotational subsonic stationary solutions for the two-dimensional bipolar Euler-Poisson equation. This result is the first result about the rotational subsonic stationary solution for the multi-dimensional bipolar isentropic Euler-Poisson equation. The proof is completed by delicate energy estimate and fixed point principle.

##### Primaries Oblateness Effects on the Collinear Libration Points in the Restricted-three Body Problem

M. N. Ismail, A. H. Ibrahim, G. H. F. Mohamadin, W. A. Okasha

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/jamcs/2019/v34i230210

In this work, the canonical Hamiltonian form of the restricted three- body problem including the effects of primaries oblateness is presented. Moreover, the collinear libration points are obtained. In addition to this, the relation between position of libration points and variation in (mass ration , oblateness coefficients A1 and A2) is studied. The results obtained are a good agreement with Perdios [1] & Singh [2].  The Poincare surface section PSS is used to illustrate the stability of motion around each of the collinear libration points. A numerical application on the real system Earth-Moon is presented.

##### Testing the Fairness of a Coin by Akaike's Information Criterion

Kunio Takezawa

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/jamcs/2019/v34i230212

In this paper, AIC (Akaike's Information Criterion) is used to judge whether a coin is biased or not using the sequence of heads and tails produced by tossing the coin several times. It is well known that AIC·(−0:5) is an efficient estimator of the expected log-likelihood when the true distribution is contained in a specified parametric model. In the coin tossing problem, however, AIC·(−0:5) works as an efficient estimator even if the true distribution is not contained in a specied parametric model. Moreover, the judgement of fairness of coin using AIC is equivalent to a statistical test using the Bernoulli distribution with a signicance level ranging from 11% to 18%. This indicates that the judgement of the fairness of coin based on AIC leads to a higher probability of type I errors than that given by a statistical test with a signicance level of 5%. These findings show that we judge the fairness of a coin based on AIC when we do not have any prior knowledge about its fairness and we want to judge it from the standpoint of prediction. In contrast, a statistical test with a significance level of 5% is adopted when we have prior knowledge that the coin is probably unbiased. Moreover, a statistical test with a 5% significance level allows us to conclude that the coin is biased if we obtain sufficient evidence that permits us to disbelieve the prior knowledge.

##### On T1 T2-g-Open Sets in Bitopological Spaces

K. Vithyasangaran, P. Elango, S. Sathaananthan, J. Sriranganesan, P. Paramadevan

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/jamcs/2019/v34i230216

In this paper, we introduced and studied a new kind of generalized open set called τ1τ2-g-open set in a bitopological space (X, τ1, τ2). The properties of this τ1τ2-g-open set are studied and compared with some of the corresponding generalized open sets in general topological spaces and bitopological spaces. We also dened the τ1τ2-g-continuous function and studied some its properties.