## Academic Journal of Applied Mathematical Sciences

**Online ISSN**:

**2415-2188**

**Print ISSN**:

**2415-5225**

Quarterly Published (4 Issues Per Year)

# Archives

### Volume 2 Number 9 September 2016

#### Interval-Valued Intuitionistic L-Fuzzy Strong B -Filters On B -Algebras

**Authors:**D. Ramesh ; B. Satyanarayana

**Pages:**

*135-139*

Abstract

In 2002, J. Neggers and H. S. Kim introduced the notion of β-algebra. The theory of fuzzy sets proposed by L. A. Zadeh in 1965 is generalized in 1986 by K. T. Atanassov an intuitionistic fuzzy sets. The notion of β -filters was introduced by Henri Cartan in 1937. In 1991, C.S. Hoo introduced the concept of the β -filters in BCI-algebras and Satyanarayana, et al. [2], introduced interval-valued intuitionistic fuzzy ideals in BF-algebras. In this paper, we define the notion of an Interval-valued intuitionistic L-fuzzy strong β –filters on β-algebra and investigate some of their properties.

#### Graphs with Appended End Vertices: Laplacian Spectra, Laplacian Energy, and Laplacian Eigen-Bi-Balance

**Authors:**Paul August Winter ; Carol Lynne Jessop

**Pages:**

*109-134*

Abstract

In this paper, we determine the Laplacian spectra of graphs obtained by appending end vertex to all vertices of a defined class of graphs called the base graph. The end vertices allow for a quick solution to the eigen-vector equations of the Laplacian matrix satisfying the characteristic equation, and the solutions to the eigenvalues of the Laplacian matrix of the base graph arise. We determine the relationship between the eigenvalues of the Laplacian matrix of the base graph and the eigenvalues of the Laplacian matrix of the new graph as constructed above, and determine that if is an eigenvalue of the Laplacian matrix of the base graph, then is an eigenvalue of the Laplacian matrix of the constructed graph.

We then determine the Laplacian spectra for such graphs where the base graph is one of the well-known classes of graphs, namely the complete, complete split-bipartite, cycle, path, wheel and star graphs. We then use the Laplacian spectra to determine the Laplacian energy of the graph, constructed from the base graphs, for each of the above classes of graphs. We then analyse the case where only one end vertex is appended to each vertex in the base graph, and determine the Laplacian energy for large values of , the total number of vertices in the constructed graph.In the last section, we investigate the eigen-bi-balance of the graphs using the eigenvalues of the Laplacian matrix for graphs with appended end vertices, and consider the example of the star sun graph.

#### Steady-State Analysis of a Two Dimensional Model for Tumor Angiogenesis in the Absence of Endothelial Cell Proliferation

**Authors:**Serdal Pamuk ; Bushra Bajjah

**Pages:**

*102-108*

Abstract

This paper is an extension of the work done in [S. Pamuk, Qualitative Analysis of a Mathematical Model for Capillary Formation in Tumor Angiogenesis, Math. Models Methods Appl. Sci. 13 (1) (2003) 19-33] to a further 2D-mathematical analysis of a model for tumor angiogenesis in the absence of endothelial cell proliferation term. We actually obtain the long time dynamics of endothelial cells in the extra cellular matrix under some assumptions and using the results of a 1D-mathematical analysis. Also, the stability of the steady-state solution is studied. Some figures obtained from the numerical results are presented.