Open Access Short Research Article

Open Access Original Research Article

Path Connectedness over Soft Rough Topological Space

Li Fu, XiaoAn Shi

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2019/v31i530122

In this paper, we mainly discuss the path connectedness of the soft rough topological space. We study the properties of connected soft rough real space, give the denition of path between soft points, and discuss the property of path connectedness in the soft rough topological space, and the relation between connected soft rough topological space and path local connected soft rough topological space.

Open Access Original Research Article

Face Recognition Using 2D-FLDA Based on Approximate SVD Obtained with Kronecker Products with One Training Sample

Ümit Çiğdem Turhal

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/jamcs/2019/v31i530123

Aims: In a face recognition task, it is a challenging problem to find lots of images for a person. Even, sometimes there can be only one image, available for a person. In these cases many of the methods are exposed to serious performance drops even some of these fail to work. Recently this problem has become remarkable for researchers. In some of these studies the database is extended using a synthesized image which is constructed from the singular value decomposition (SVD) of the single training image. In this paper, for such a method, SVD based 2 Dimensional Fisher Linear Discriminant Analysis (2D-FLDA), it is proposed a new approach to find the SVD of the image matrix with the aim of to increase the recognition performance.

Study Design: In this paper, in a face recognition task with 2D-FLDA, in one training sample case, instead of original SVD of the image matrix, the approximate SVD of its based on multiple kronecker product sums is used. In order to obtain it, image matrix is first reshaped thus it is to be lower dimensional matrices and, then the sum of multiple kronecker products (MKPS) is applied in this lower dimensional space.

Methodology: Experiments are performed on two known databases Ar-Face and ORL face databases. The performance of the proposed method is evaluated when there are facial expression, lightning conditions and pose variations.

Results: In each experiment, the approximate SVD approach based on multiple kronecker product sum gets approximately 3% better results when compared with the original SVD.

Conclusion: Experimental results verify that the proposed method achieves better recognition performance over the traditional one. The reason for this is the proposed approximate SVD has the advantages of simplicity, and also as the kronecker factors possess additional linear structure, kronecker product can capture potential self-similarity.

Open Access Original Research Article

Scrutiny of Steganalysis for Flipping Steganography Method

Aqsa Rashid, Muhammad Khurrum Rahim

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/jamcs/2019/v31i530124

Steganography is the skill of hiding data inside other information in such a way that it is hard or even impossible to tell that it is there. There are many different carriers for steganography but the most popular is digital images. In recent times, there it has been supposed that terrorist cells are using steganography to hide their clandestine policies, and consequently it is fetching increasingly significant to notice the images that contain steganography such that we can decrease criminal action. This counter-technique is known as steganalysis. In comparison to the importance of papers that examine either steganography or steganalysis methods, this paper presents in-depth metaphors of steganalysis.

Open Access Original Research Article

New Criterion that Guarantees Sufficient Conditions for Globally Asymptotically Stable Periodic Solutions of Non-Linear Differential Equations with Delay

Ebiendele Peter

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2019/v31i530126

The objective of this paper is to investigate and give sufficient conditions that we guarantees globally asymptotically stable periodic solutions, of non-linear differential Equations with Delay of the form (1.1). The Razumikhin’s technique was improve upon to enhance better result’s hence equation (1.2), was studied along side with equation (1.1). Equation (1.2) is an integro-differential equations with delay kernel. Since the coefficients of (1.2) are periodic, it is re-written as equation (3.1), where a ,b, and c ≥ 0, and ω- periodic continuious function on R. G ≥ 0, is a normalized kernel from equation (1.2), which enable us to defined equation (3.1) as a fixed point. Since the defined operator B, for equation (3.1) are not empty, claim1 -1V enable us to used the fixed point theorem to investigate and established our defined properties. See, (Theorem 3.1, Lemma 3.1 and Theorem 3.2) and the Liapunov’s direct (second) method to prove our main results. See, (Theorem3.3, 3.4, and 3.5) which established the objective of this study.