A map on a group is not necessarily an automorphism on the group. In this paper we determined the necessary and sufficient conditions of a map on a split metacyclic p-group to be an automorphism, where we only considered p as an odd prime number. The metacyclic group can be defined by a presentation and it will be beneficial to have a direct relation between the parameters in the presentation and an automorphism of the group. We considered the action of an automorphism on the generators of the group mentioned. Since any element of a metacyclic group will be mapped to an element of the group by an automorphism, we can conveniently represent the automorphism in a matrix notation. We then used the relations and the regularity of the split metacyclic p-group to find conditions on each entry of the matrix in terms of the parameters in its presentation so that such a matrix does indeed represent an automorphism.
Improvements over embedded diagonally implicit Runge-Kutta pair of order four in five are presented. Method of higher stage order with a zero first row and the last row of the coefficient matrix is identical to the vector output is given. The stability aspect of it is also looked into and a standard test problems are solved using the method. Numerical results are tabulated and compared with the existing method.
Recently, there is strong interest on the subject of outlier problem in circular data. In this paper, we focus on detecting outliers in a circular regression model proposed by Down and Mardia. The basic properties of the model are available including the exact form of covariance matrix of the parameters. Hence, we intend to identify outliers in the model by looking at the effect of the outliers on the covariance matrix. The method resembles closely the COVRATIO statistic for the case of linear regression problem. The corresponding critical values and the performance of the outlier detection procedure are studied via simulations. For illustration, we apply the procedure on the wind data set.
Kesan penggunaan kitosan terhadap nanozarah kuprum (Cu) yang disintesis menggunakan sinaran gama sebagai sumber agen penurunan telah dijalankan dalam sistem akues. Dos sinaran terserap yang digunakan adalah 50 kGy manakala penambahan isopropanol adalah penting sebagai penggarut kepada radikal pengoksidaan serta meningkatkan peranan agen penurun yang terhasil daripada proses radiolisis. Analisis serapan optik-uv telah mencirikan sifat optik larutan nanozarah Cu yang disintesis. Ketulenan fasa kristal nanozarah Cu yang terbentuk dalam matrix kitosan telah dibuktikan dengan pembelauan sinar-X (xRD). Berdasarkan imej mikroskop imbasan elektron (TEM), nanozarah Cu yang terhasil adalah berbentuk sfera dengan julat saiz 6-10 nm kecuali nanozarah Cu yang disintesis dalam kepekatan kitosan 03% wlv yang menunjukkan taburan bentuk yang tidak sekata. Analisis spektrofotometer transformasi Fourier inframerah (FHR) yang dijalankan telah mengesahkan kehadiran sebatian kitosan dalam sampel nanozarah Cu dengan kepekatan kitosan 0.1 dan 0.3% wlv. Kajian ini mendapati penggunaan kitosan dapat melindungi nanozarah Cu daripada pengoksidaan oleh persekitaran. Saiz nanozarah juga didapati meningkat seiring dengan peningkatan kepekatan kitosan yang digunakan.
In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integro-differential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms the equation and its conditions into matrix equations which comply with a system of linear algebraic equations with unknown Dickson coefficients, via collocation points in a finite interval. While solving the matrix equation, the Dickson coefficients and the polynomial approximation are obtained. Besides, the residual error analysis for our method is presented and illustrative examples are given to demonstrate the validity and applicability of the method.
The conversion of hexavalent molybdenum (Mo (VI)) to Mo-blue is a bioremediation technique
which reduces the toxicity of molybdenum to a less toxic form by bacteria. The aim of this study
is to determine the optimum conditions of significant parameters or variables that affect the
reduction of Mo (VI) to Mo-blue by the local isolate identified as Serratia sp. strain MIE2.
Response Surface Methodology (RSM) was used in this study to optimize the reduction process
using Central Composite Design (CCD) as an optimization matrix. The optimum conditions
predicted by RSM using the desirability function for the reduction process were 20 mM
molybdate concentration, 3.95 mM phosphate, 6.25 pH and 25 g/L glucose and Mo-blue
production occurred at the absorbance value of 20.5 at 865 nm. The validation of the predicted
optimum points showed the Mo-blue production occurred at the absorbance value of 21.85 with
a deviation around 6.6 % from the RSM predicted value.
Advanced oxidation processes (AOPs) are of special interest in treating landfill leachate as they are the most promising procedures to degrade recalcitrant compounds and improve the biodegradability of wastewater. This paper aims to refresh the information base of AOPs and to discover the research gaps of AOPs in landfill leachate treatment. A brief overview of mechanisms involving in AOPs including ozone-based AOPs, hydrogen peroxide-based AOPs and persulfate-based AOPs are presented, and the parameters affecting AOPs are elaborated. Particularly, the advancement of AOPs in landfill leachate treatment is compared and discussed. Landfill leachate characterization prior to method selection and method optimization prior to treatment are necessary, as the performance and practicability of AOPs are influenced by leachate matrixes and treatment cost. More studies concerning the scavenging effects of leachate matrixes towards AOPs, as well as the persulfate-based AOPs in landfill leachate treatment, are necessary in the future.