The probability that two elements commute in some 2-generator 2-groups of nilpotency class 2

Erdos and Turan have introduced the determination of the abelianness of a finite group for symmetric groups, finite groups and finite rings in 1968. Basic probability theory will be used in studying its connection with group theory. Some basic concepts related with P(G) , the probability a random pair of elements in a group commutes, will be presented. This research will focus on the 2-generator 2- groups of nilpotency class 2, based on the classification that have been done by Kappe et.al in 1999. Finally, some properties of P(G) for some 2-generator 2- groups of nilpotency class 2 will be determine

An algorithms for finding the cube roots in finite fields

Let Fq be a finite field with q elements. Quadratic residues in number theory and finite fields is an important theory that has many applications in various aspects. The main problem of quadratic residues is to find the solution of the equation x2 = a, given an element a. It is interesting to find the solutions of x3 = a in Fq. If the solutions exist for a we say that a is a cubic residue of Fq and x is a cube root of a in Fq. In this paper we examine the solubility of x3 = a in general finite fields. Here, we give some results about the cube roots of cubic residue, and we propose an algorithm to find the cube roots using primitive elements

Perceived oral hygiene habits amongst 16-year-old school children

This study was aimed at assessing dental habits among 16-year-old schoolchildren A total of 116 16-year-old schoolchildren took part in this survey, which was part of a larger study to assess dental fluorosis occurrence among the respondents. A questionnaire was given to each respondent prior to getting written consent from the parents. They were asked three categories of questions pertaining to habits of oral hygiene, firstly the number of tooth-brushings per day, then the quantity of toothpaste used per brushing, and lastly the number of visits to the dentist per year. From 116 respondents, 32 (27.6%) were males and 84 (72.4%) were females. On the first question, 100 respondents (86.2%) used fluoridated toothpastes while the remaining 16 (13.8%) used non-fluoridated toothpastes For the second question, 8 respondents (6.8%) brushed their teeth once per day, 59 (51.0%) twice per day, 35 (30.1%) three times per day and 14 (12.1%) 4 times per day About the question on quantity of toothpaste used for brushing (question 3), 25 respondents (21.5%) used ½ pea size, 66 (56.8%) used 1 pea-size, 24 (20.9%) used 2 pea-size and 1 (0.8%) used 3 pea-size. For the final question (question 4), 43 (37.1%) had never had any dental visits all their life, 33 (28.4%) had one dental visit per year, 30 (25.9%) had twice-a-year visit, 4 (3.4%) had 3 visit, 3 (2.6%) had 4 times-a-year visit and 3 (2.6%) had more than 4 times-a-year visit. This study concluded that more oral health education programs should be organized to improve the understanding of oral hygiene and the importance of dental visits in order to sustain a healthy oral life for a lifetime especially for the respondents

The representation of n-cutting site splicing languages for a single string with palindromic rule via de Bruijn graph

Yusof-Goode (Y-G) splicing system proposed by Yusof illustrates the deoxyribonucleic acid (DNA) splicing process in a luminous way, where the rule is written in a double triple notation. In the process of generating splicing languages, DNA molecules are cut and pasted, based on the reaction of the molecules with restriction enzyme and ligase. The resulting molecules, either in original or new molecules can be classified mathematically in the form of limit, adult or transient languages. Conducting a wet lab experiment to produce splicing languages is a huge investment, thus mathematical approach is one of the best options in predicting the outcome on splicing languages when n-cutting site exist in a splicing process. Besides the generation of splicing languages through splicing system, a meaningful representation of the languages can be portrayed in a graph. In this paper, the n-cutting site splicing languages generated from Y-G splicing system containing single string with 2-cutting site, with palindromic rule and palindromic crossing site is investigated. The features of left and right contexts of the rule are considered in the two cases discussed in this paper. Besides, two new definitions namely connectors and sub-connectors are given and are adopted in the generation of de Bruijn graph. With the constructed de Bruijn graph for the resulting splicing languages from both cases, a theorem is proposed

Clustering of rainfall data using k-means algorithm

Clustering algorithms in data mining is the method for extracting useful information for a given data. It can precisely analyze the volume of data produced by modern applications. The main goal of clustering is to categorize data into clusters according to similarities, traits and behavior. This study aims to describe regional cluster pattern of rainfall based on maximum daily rainfall in Johor, Malaysia. K-Means algorithm is used to obtain optimal rainfall clusters. This clustering is expected to serve as an analysis tool for a decision making to assist hydrologist in the water research problem

On the computations of some homological functors of 2-Engel groups of order at most 16

The homological functors including J (G) , ∇ (G) , exterior square, the Schur multiplier, Δ (G) , the symmetric square and J (G) of a group were originated in homotopy theory. The nonabelian tensor square which is a special case of the nonabelian tensor product is vital in the computations of the homological functors of a group. It was introduced by Brown and Loday in 1987. The nonabelian tensor square G⊗G of a group G is generated by the symbols g ⊗ h, for all g,h∈G subject to the relations gg′⊗h=(gg′⊗gh)(g⊗h) and g⊗hh′=(g⊗h)(hg⊗hh′), for all g,g′,h,h′ ∈G where g g′ = gg′g−1 . In this paper, the computations of nonabelian tensor squares and some homological functors of all 2-Engel groups of order at most 16 are done. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results

Persistency And Permanency of Two Stages DNA Splicing Languages with Respect to One Initial String and Two Rules Via Yusof-Goode (Y-G) Approach

The notion of Yusof-Goode (Y-G) splicing system was first schemed by Yusof to study the relationship between formal language theory and molecular biology. The splicing languages that are produced by splicing system have some important characteristics called persistent and permanent. In biological perspective, the recombinant DNA molecules can be manipulated by recombination action if they have persistent property. Thus, the persistency as well as permanency of splicing languages (recombinant DNA molecules) is considered to be an interesting topic in the field of DNA recombination, particularly when the recombination process is accomplished at second stage. Conducting a wet-lab experiment to show the mentioned properties of splicing languages are time consuming and expensive. Therefore, to overcome this problem, mathematical approach is chosen to investigate the persistency and permanency of splicing languages which will be then given as theorem and corollary. Thus, an initial string (with two recognition sites) and two rules are considered for introducing the above characteristics using Y-G approach

Automorphisms of finite cyclic 3-groups

A distinct compatible pair of actions will result in distinct nonabelian tensor products. This proves that the number of compatible pairs of action plays a huge role as the greatest variety nonabelian tensor product relies on it. However, the actions of finite cyclic group are defined by automorphisms, thus the number of automorphisms needs to be known before obtaining the number of actions that are compatible with one another. This paper focuses on determining the automorphism finite cyclic 3-groups. The general presentation of the automorphism of such groups is obtained with the help of Groups, Algorithm, and Programming (GAP) Software

Relationship of viewing Islamic based films with pro-social personality among teenaged audience

The viewing of Islamic based films or films that contain Islamic message is seen as a contribution towards positive actions. Therefore, this study aims to determine the relationship between the viewing of Islamic based films and the development of pro-social personality among teenaged audience. The social cognitive theory was used as the theoretical framework via the three constructs (observational learning, symbolic modeling through characters and self-efficacy) as the mediating variables. The research design employed was a cross-sectional survey where data were collected through the distribution of questionnaire by using the stratified random sampling as the sampling technique. 1028 students from 5 public universities in the Klang Valley were taken as the sample from the 3324 total of the population. The questionnaire was generated from Prosocial Personality Battery (PSB) (Penner et al., 1995; Penner, 2002) and General Self-Efficacy Scale (SGSE) (Sherer et al., 1982). The quantitative data were analyzed by using the SPSS 18 through the univariate and multivariate statistical inferential analysis

Relationship of viewing Islamic based films with pro-social personality among teenaged audience

The viewing of Islamic based films or films that contain Islamic message is seen as a contribution towards positive actions. Therefore, this study aims to determine the relationship between the viewing of Islamic based films and the development of pro-social personality among teenaged audience. The social cognitive theory was used as the theoretical framework via the three constructs (observational learning, symbolic modeling through characters and self-efficacy) as the mediating variables. The research design employed was a cross-sectional survey where data were collected through the distribution of questionnaire by using the stratified random sampling as the sampling technique. 1028 students from 5 public universities in the Klang Valley were taken as the sample from the 3324 total of the population. The questionnaire was generated from Prosocial Personality Battery (PSB) (Penner et al., 1995; Penner, 2002) and General Self-Efficacy Scale (SGSE) (Sherer et al., 1982). The quantitative data were analyzed by using the SPSS 18 through the univariate and multivariate statistical inferential analysis