Open Access Original Research Article

A New Iterative Algorithm for Zeros of Generalized Phi-strongly Monotone and Bounded Maps with Application

C. E. Chidume, O. M. Romanus, U. V. Nnyaba

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2016/25884

Let E be a uniformly smooth and uniformly convex real Banach space and A : E → E* be a generalized Φ-strongly monotone and bounded map with A-1(0) ≠ θ. A new iterative process is constructed and proved to converge strongly to the unique solution of the equation Au = 0. An application to convex minimization problem is given. Furthermore, the technique of proof is of independent interest.

Open Access Original Research Article

On Solving Comrade Linear Systems Via Transformations

A. A. Karawia, S. S. Askar

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2016/27679

Recently, a new symbolic algorithm for solving comrade linear systems is given by Karawia [A. A. Karawia, Symbolic algorithm for solving comrade linear systems based on a modi fied Stair-Diagonal Approach, Appl. Math. Lett. 2013; 26:913-918.]. This paper introduces different numerical and symbolic algorithms for solving comrade linear systems via transformations. Our symbolic algorithm removes the cases where the numerical algorithms fail. The computational cost of these algorithms is given. It gives better absolute error than the other methods. The algorithm is implementable to the Computer Algebra System (CAS) such as MAPLE and MATLAB. Some illustrative examples are presented for the sake of illustration.

Open Access Original Research Article

The nth Power Transformation of the Error Component of the Multiplicative Time Series Model

A. O. Dike, E. L. Otuonye, D. C. Chikezie

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/BJMCS/2016/27246

In this paper the author(s) present derivations for the mean and variance of the nth power transformation of the error component of the multiplicative time series model. as a general rule to any power transformation. Some of the published transformations like the square root and the inverse were used to validate the results obtained. The results showed that they conformed to the general rule.

Open Access Original Research Article

A Rapid Quantization-based Image Retrieval Algorithm

Tingjia Shan, Qiang Ling, Kaikai Song, Binbin Du, Feng Li, Song Wang

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2016/27865

Fast image retrieval has been a fundamental problem in the area of image processing for a long time. This paper proposes a rapid image retrieval algorithm by improving the conventional nearest neighbor search through the implementation of vector product quantization and inverted indexing structure. Vector product quantization can efficiently accomplish the fast nearest neighbor search task, and has many great advantages in terms of storage requirements, retrieval speed and accuracy. In order to further reduce the search time, an approximate threshold-based distance estimation technique is introduced into the retrieval algorithm. Moreover, the quick sort method is implemented to reorder the image search results, which can significantly improve the performance of our retrieval algorithm.

Open Access Original Research Article

An Example of the Application of Provability Logic to Unsolved Problems in Number Theory: The Cullen Numbers and Conway’s Supposition

Alexander Bolotin

Journal of Advances in Mathematics and Computer Science, Page 1-5
DOI: 10.9734/BJMCS/2016/27581

This short paper offers an example of possibly fruitful interactions between modal logic and number theory. In the paper, Conway's remark that and p.2+ 1  can both be prime numbers is formulated as a formula of modal logic and then analyzed for its decidability.

Open Access Original Research Article

Permeable Rings and Their Extensions

M. A. Zalukh, S. K. Nauman

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2016/27803

Let us call a ring R to be right permeable if for any α ∈ R  = 0, then αR = 0. Left permeable and permeable rings are defined analogously. These rings are generalized reversible rings with a privileging role that permeability inherited in its several extensions where reversibility seized to be inherited. It will be proved that full matrix ring, polynomial ring, Laurent polynomial ring, Dorroh extension, group ring and Ore extensions of a right (left) permeable ring are right (left) permeable rings. Moreover, the same holds for Barnett matrix rings with their extensions in different quotient polynomials and matrix forms.

Open Access Review Article

Numerical Solution of First Order Fuzzy Differential Equations by Simpson’s Rule

S. Sindu Devi, K. Ganesan

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/BJMCS/2016/26060

The concept of fuzzy versions of Simpson’s rule and Runge-Kutta method of order four are introduced. In this paper, the solution of fuzzy ordinary differential equation of the first order by Simpson’s rule and Runge-Kutta method of order four is presented without converting them to crisp form. The results from these two methods are proved identical by complete error analysis. The accuracy and efficiency of the proposed methods are illustrated by an example with a trapezoidal fuzzy number and triangular fuzzy number.