Discrete Mathematics

A dynamic graphical display among the set of independent variables (partial regression plot), tolerance value, variance inflation factor (VIF) and pair wise correlation matrix among the set of predictors offers a variety of measures for assessing the problem of collinearity and multicollinearity in a multiple regression analysis. Multicollinearity is a violation of one of the assumption of regression analysis. Many diagnostics measures have been proposed for detecting multicollinearity. A tolerance value of less than 0.10 or 0.20 which is equivalent to a VIF of 5 or 10, p value>0.05 and the pair-wise correlation showing a linear dependence of 0.90 and above. A transformation is carried out to remove the problem of multicollinearity and the removal will help to improve on the model (yi = ?0 +? 1X1 + ?2X2 +……+ ?kXk, improve coefficient of determination (r2) and validate any of the assumption of regression analysis of homocesdasticity, linearity, normality and independence of the observations. Examples using stimulated small data sets illustrate this approach

In this paper, we present a design and implementation of a calculator software which applies the Microsoft visual studio and C-sharp (C#) for effective performance of some operations like polynomial solver of degree 10, simultaneous equation solver up to five systems of equations and evaluating the numerical integrations of some selected functions. It is expected that this application will help students and teaching staff in their daily doing of some mathematics related tasks.

In this paper we developed new matrices (angle matrix ,connection matrix and connection angle matrix) in addition to a set of matrices (adjacent matrix, incidence matrix) that previously used to introduce the mathematical representation of high-resolution protein structures an accurate representatin that facilitate analysis of its structures.

In this paper ,We introduced a novel method DS-CDMA based watermarking scheme on the basis of orthogonal pseudorandom sequence subspace projection, In this paper a new idea to eliminate the correlation between the code sequences and the host images in the watermark extraction phase, and in watermarking scheme improve the hiding capacity of message sequence. In our proposed scheme implements the steps and performance checking under different attacks by a series of experiments. The results observe the Host image under different attacks and show the higher robustness and achieve the high capacity to hide the data. In our proposed scheme implements the steps and performance testing under different attack conditions by a series of experiments. The experimental results observe the Host image under different attacks and show the higher robustness and increase the message capacity and achieve the high capacity to hide the data.

In this paper we derive new formulas for the number of spanning trees, of some product graphs such as cartesian product, tensor product, composition product, normal product, and strong sum using linear algebra, Chebyshev polynomials and matrix theory techniques.

The extent of departure of a set of data from the fundamental assumptions required by a test is often very important in the determination of the appropriate statistical test to be applied. Some test statistics are more robust to the departure from certain underlying assumptions than others. Hence, the study was aimed at examining the robustness or non-robustness of the F-test statistic in the two-way Interactive Balanced Design. The data used for the study were tested against the three basic assumptions of analysis of variance which include normality, independence and homogeneity of variance assumptions. The results show that even when the normality and homogeneity of variance assumptions were violated, the F-test still yields good results. Hence, it was concluded that the F-test is robust to the normality and homogeneity of variance assumptions. Based on the results of the study, it was recommended that large sample size should always be used in carrying out any experiment involving the applications of analysis of variance. It was also recommended that the rank transformation is a step in the right direction whenever our data fail to conform with the assumptions of ANOVA prior to the conventional ANOVA test since it yields result in test which are more robust to the non-normal and resistance to outliers and non-homogeneity of variance.

A cube divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1,2,...,|v|} such that an edge e=uv is assigned the label 1 if [ f(u) ]^3 |f(v) or [ f(v) ]^3 |f(u) and the label 0 otherwise, then |ef(0)- ef(1)| ?1 . A graph which admits a cube divisor cordial labeling is called a cube divisor cordial graph. In this paper we prove that barycentric subdivision of the star K1,n , switching of a vertex in cycle Cn , degree splitting graphs of Bn,n and Pn, n?5 admit cube divisor cordial labeling.

In this paper we introduced the concepts of fuzzy generalized super continuous mappings and explore some of its basic properties in fuzzy topological spaces.