##### The Cocycle for the Non-autonomous Stochastic Damped Wave Equations with White Noises

Hongyan Li

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/jamcs/2019/v33i130165

This paper is devoted to the cocycle of solutions of the non-autonomous stochastic damped wave equations with multiplicative white noises defined on unbounded domains. And we obtain the existence of a pullback absorbing set of the cocycle in a certain parameter region.

##### Fixed Points of Contractive Type Maps in Cone Metric Space over Banach Algebra

Ashfaque Ur Rahman, Geeta Modi, K. Qureshi, Manoj Ughade

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/jamcs/2019/v33i130166

Our goal in this paper is to prove some fixed point and common fixed theorems for contractive type maps in a CMS over Banach algebra, which unify, extend and generalize most of the existing relevant fixed point theorems from Shaoyuan Xu and Stojan Radenovic [1]. We provide illustrative example to verify our results.

##### Cramér-Rao Bound of Direction Finding Using Uniform Arc Arrays

Veronicah Nyokabi, Dominic Makaa Kitavi, Cyrus Gitonga Ngari

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2019/v33i130168

Direction-of-Arrival estimation accuracy using arc array geometry is considered in this paper.
There is a scanty use of Uniform Arc Array (UAA) in conjunction with Cramer-Rao bound (CRB)
for Direction-of-Arrival estimation. This paper proposed to use Uniform Arc Array formed from a considered Uniform Circular Array (UCA) in conjunction with CRB for Direction-of-Arrival estimation. This Uniform Arc Array is obtained by squeezing all sensors on the Uniform Circular Array circumference uniformly onto the Arc Array. Cramer-Rao bounds for the Uniform Arc Array and that of the Uniform Circular Array are derived. Comparison of performance of the Uniform Circular Array and Uniform Arc Array is done. It was observed that Uniform Arc Array has better estimation accuracy as compared to Uniform Circular Array when number of sensors equals four and ve and azimuth angle ranging between $$\frac{\pi}{9}~ and ~\frac{7}{18}\pi~ and~ also ~\frac{10}{9}\pi ~and ~\frac{25}{18}\pi$$. However, UCA and UAA have equal performance when the number of sensors equals three and the azimuth angle ranging between 0 and 2π. UCA has better estimation accuracy as compared to UAA when the number of sensors equals four and ve and the azimuth angle ranging between

$$\frac{\pi}{2} ~and~ \pi ~and ~also~ \frac{3}{2}\pi ~and~ 2\pi$$

##### Cell Arrangement Method for Solving Systems of Linear Equations in Three Unknown

A. Adu-Sackey, G. O. Lartey, F. T. Oduro, Stephen Eduafo

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/jamcs/2019/v33i130170

In this paper, we develop an approach for finding the cofactor, ad joint, determinant and inverse of a three by three matrix under the Cell Arrangements method using the coefficient matrix of a given systems of linear equation in three unknowns. The method takes out completely the seemingly daunting task in evaluating such matrices associated to the standard matrix method in solving simultaneous equation in three variable. Unlike the standard matrix method that goes through a lengthy process to obtain separately all the matrices necessary for the determination of the unknowns, the structural frame of the Cell Arrangement method comes in handy and are consistent with the results from systems that have unique solutions. This alternative approach provides all the vital hybrid matrices of the coefficient matrix needed in the determination of the unknowns of the system of equations in three variables. It is our view that by far, the Cell arrangement method is easy to work with and less prone to errors that are often connected with other known methods.

##### Revisiting Feller Diffusion: Derivation and Simulation

Ranjiva Munasinghe, Leslie Kanthan, Pathum Kossinna

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2019/v33i130169

We propose a simpler derivation of the probability density function of Feller Diffusion by using the Fourier Transform on the associated Fokker-Planck equation and then solving the resulting equation via the Method of Characteristics. We use the derived probability density to formulate an exact simulation algorithm whereby a sample path increment is drawn directly from the density. We then proceed to use the simulation to verify key statistical properties of the process such as the moments and the martingale property. The simulation is also used to confirm properties related to hitting time probabilities. We also mention potential applications of the simulation in the setting of quantitative finance.