International Journal of Mathematics And its Applications

9-18

Authors: Vedanti Bhargava

Accurate and efficient model development in the field of evolutionary biology is becoming increasingly important to study phylogenetic relationships. Studying these phylogenetic relationships can provide greater insight into areas such as drug development, analyzing disease transmission, and studying the host-pathogen evolutionary relationship. This study uses the idea of a transition matrix to predict how long ago two species shared a common ancestor. Using this concept and various linear algebraic ideas, a mathematical model that simulated amino acid mutations was developed, and it was implemented in Python to perform trials. The main result of the development of the model was a matrix containing the expected values for the number of years ago two amino acids were the same. Simulations of the model can be run in Python multiple times and the average of the values obtained gives an estimate of how many years ago two amino acids were the same. These represent the number of years ago the species shared a common ancestor. The result varies based on the species data analyzed. This model provides a foundation for development of more complex models that enhance phylogenetic tree development. As stated previously, this can have substantial impacts on biotechnology and biomedical sciences, which often rely on analyzing these evolutionary relationships.

27-33

Authors: Mitesh J. Patel and G. V. Ghodasara

An injective function $f:V(G)\rightarrow{}\{1,2,\ldots,|V(G)|\}$ is said to be permutation labeling if each edge $uv$ is assigned with label $\Perm{f(u)}{f(v)}= \ \frac{(f(u))!}{| f(u)-f(v)|! } \ (f(u)>f(v))$ are all distinct. A graph which admits permutation labeling is called permutation graph. In this paper we prove that wheel graph, restricted square and degree splitting graph of bistar graph are permutation graphs. We also proved that arbitrary super subdivision of path graph, star graph and cycle graph are permutation graphs.

41-50

Authors: F. F. Ngwane

Test information function (TIF) plays an important role in designing a test. The TIF does not only depend on the logistic model such as the 1PL, 2PL and 3PL logistic models, but it also on the parameter distributions of the model. In this study we conducted simulations using the R statistical software on different examinee sizes and different exam length, and we compare the results when using uniform parameter distribution and normal parameter distribution. The findings of this study illustrate the following: First, when using item parameters that are all uniformly distributed the obtained test information function is significantly small compared to the test information function obtained when we use item parameters that all follow a normal distribution. Second, the test information function increases as the length of the exam increases when we use item parameters that are all normally distributed. Third, this study also suggest great flexibility in writing an exam as we can choose the item parameter distribution depending on the goals of the test.

63-65

Authors: V. Durai Murugan, R. Seethalakshmi and P. Namasivayam

In this paper, we verify the complementedness in the subgroup lattices of the group of $2 \times 2$ matrices over $Z_{11}$.

73-82

Authors: Annela R. Kelly

In combinatorial game theory, multi-player games expands on the research of two-person games and are widely applicable to computer science and business. The given paper studies the mis\`{e}re version of the subtraction game (Nim with one pile of counters) for two alliances extending the results of Kelly in \cite{2,3}; Liu and Zhao in \cite{5}, Liu and Wang in \cite{6} and Suetsugu in \cite{7}. The main result of the current paper determines the optimal distribution of the players among two alliances that minimizes $N$, the smallest number of counters such that the larger alliance has a winning strategy for all the games with more than $N$ counters.

95-104

Authors: V. Mohan Babu and C. Pandurangappa

An analysis is made to study a three-dimensional boundary-layer flow of non-newtonian fluid over a porous media. The governing partial differential equations of momentum are transformed into self-similar non-linear ordinary differential equations by using new form of suitable similarity transformations. The obtain equations are then should by using shooting method. The flow phenomena is characterized by the power-law index `n', permeability of porous media `$\omega $' porosity parameter `$\phi $' effective viscosity `$\lambda $', three-dimensionality parameters `$\alpha $'. The numerical results of the velocity profiles are obtained and displayed graphically.

113-117

Authors: Meera Meghpara, H. M. Karavadiya and V. J. Kaneria

In this paper, we have derived a new graph named spade graph. We have proved two copies of spade graph joined by an arbitrary path is $\alpha-$graceful, $n$ copies of spade graph joined by any vertex is $\alpha-$graceful, path union of $n$ copies of spade graph is $\alpha-$graceful and open star of finite copies of spade graph is also $\alpha-$graceful.