##### Explicit Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices with the Pell-Lucas Numbers

Jinjiang Yao, Jixiu Sun

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2018/38768

In this paper, we consider the skew circulant and skew left circulant matrices with the Pell-Lucas numbers. We discuss the invertibility of the skew circulant and skew left circulant matrices and present the determinant and the inverse matrix of them by constructing the transformation matrices.

##### Relations between Various Magnitudes Which Serve as Signs of a Right-angled Triangle

Moshe Stupel, Avi Sigler

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/JAMCS/2018/38654

We present a proven scheme of 15 relations between the sides of a triangle, the radii of incircles and excircles of the triangle, the area and half the perimeter of the triangle, which serve as signs of a right-angled triangle, together with the 16th relation which is the Pythagorean Theorem. The relations are investigated dynamically using the computerized software.

##### There is No Standard Model of ZFC and ZFC2

Jaykov Foukzon, Elena Men'kova

Journal of Advances in Mathematics and Computer Science, Page 1-20
DOI: 10.9734/JAMCS/2018/38773

In this paper we view the rst order set theory ZFC under the canonical rst order semantics and the second order set theory ZFC2 under the Henkin semantics. Main results are: (i) Let MZFCst be a standard model of ZFC, then ¬Con(ZFC +∃MZFCst ).
(ii) Let MZFC2st be a standard model of ZFC2 with Henkin semantics, then ¬Con(ZFC2 +∃MZFC2st ).
(iii) Let k be inaccessible cardinal then ¬Con(ZFC + ∃κ).In order to obtain the statements (i) and (ii) examples of the inconsistent countable set in a settheory ZFC + ∃MZFCst and in a set theory ZFC2 + ∃MZFC2st were derived.
It is widely believed that ZFC + ∃MZFCst and ZFC2 + ∃MZFC2st are inconsistent, i.e. ZFC andZFC2 have a standard models. Unfortunately this belief is wrong.

##### The (P-A-L) Modified Weibull Distribution

Mahmoud R. Mahmoud, Rasha M. Mandouh, Marwa M. Hamada

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2018/39023

This paper presented The (P-A-L) Modified Weibull Distribution. We can compute several properties of this distribution. The maximum likelihood estimators are obtained. Using simulation study, mean, relative bias, root and scaled mean square error for maximum likelihood estimators are obtained. And also, Confidence intervals for unknown two parameters are calculated.

##### E-Bayesian Estimation of Two-Component Mixture of Inverse Lomax Distribution Based on Type-I Censoring Scheme

Hesham M. Reyad, Soha A. Othman

Journal of Advances in Mathematics and Computer Science, Page 1-22
DOI: 10.9734/JAMCS/2018/39087

This study is concerned with comparing the E-Bayesian and Bayesian methods for estimating the shape parameters of two-component mixture of inverse Lomax distribution based on type-i censored data. Based on the squared error loss (SELF), minimum expected loss (MELF), Degroot loss (DLF), precautionary loss (PLF), LINEX loss (LLF) and entropy loss (ELF) functions, formulas of E-Bayesian and Bayesian estimations are given. These estimates are derived based on a conjugate gamma prior and uniform hyperprior distributions. Comparisons among all estimates are performed in terms of absolute bias (ABias) and mean square error (MSE) via Monte Carlo simulation. Numerical computations showed that E-Bayesian estimates are more efficient than the corresponding Bayesian estimates.