Endomorphism Rings and Isogenies Classes for Drinfeld Modules of Rank 2 Over Finite Fields

Let $\Phi$ be a Drinfeld $\mathbf{F}_{q}[T]$-module of rank 2, over a finite field $L$, a finite extension of $n$ degrees of a finite field with $q$ elements $\mathbf{F}_{q}$. Let $m$ be the extension degrees of $L$ over the field $\mathbf{F}_{q}[T]/P$, $P$ is the $\mathbf{F}$-characteristic of $L$, and $d$ the degree of the polynomial $P$. We will discuss about a many analogies points with elliptic curves. We start by the endomorphism ring of a Drinfeld $\mathbf{F}_{q}[T]$-module of rank 2, End$_{L}\Phi$, and we specify the maximality conditions and non maximality conditions as a $\mathbf{F}_{q}[T]$-order in the ring of division End$_{L}\Phi \otimes _{\mathbf{F}_{q}[T]}$, in the next point we will interested to the characteristic polynomial of a Drinfeld module of rank 2 and used it to calculate the number of isogeny classes for such module, at last we will interested to the Characteristic of Euler-Poincare $\chi_{\Phi}$ and we will calculated the cardinal of this ideals.Comment: 1

Supply chain collaboration among Malaysian SME manufacturers

Malaysian 3rd Industrial Master Plan was developed to improve the country global competitiveness by positioning Malaysia as a major manufacturing hub and service provider in the global supply chain. To achieve this, it is suggested that Malaysian manufacturers especially SME should be involved in supply chain collaboration in their business operations. However, it is discovered that there are very few reported research on the supply chain collaboration activities among Malaysian SME manufacturers. The objective of this research is to uncover the supply chain collaboration activities among Malaysian SME manufacturers with their trading partners. This is to be done by determining the level of supply chain collaboration of Malaysian SME manufacturer and investigating the reason Malaysian SME manufacturers supply chain collaborations is at that level. In order to achieve the above objective, a mixed method of quantitative approach using survey method is employed to determine the level of supply chain collaboration and qualitative approach using personal interview method is employed to find out the reason for why Malaysian SME manufacturers’ supply chain collaboration is at that level. This research discovered that the supply chain collaboration of Malaysian SME manufactures with their trading partners is at minimal level. This is due to their current business relationship that they have with their trading partners do not required them to collaborate at higher level. On the other hand, Malaysian SME manufacturer are willing to have a high level of supply chain collaboration if long term business relationship could be established. Therefore, it is concluded that the type of business relationship or cooperation with trading partners can determine level of supply chain collaboration

A comparative study fourth order runge kutta-tvd Scheme and fluent software case of inlet flow problems

Inlet as part of aircraft engine plays important role in controlling the rate of airflow entering to the engine. The shape of inlet has to be designed in such away to make the rate of airflow does not change too much with angle of attack and also not much pressure losses at the time, the airflow entering to the compressor section. It is therefore understanding on the flow pattern inside the inlet is important. The present work presents on the use of the Fourth Order Runge Kutta – Harten Yee TVD scheme for the flow analysis inside inlet. The flow is assumed as an inviscid quasi two dimensional compressible flow. As an initial stage of computer code development, here uses three generic inlet models. The first inlet model to allow the problem in hand solved as the case of inlet with expansion wave case. The second inlet model will relate to the case of expansion compression wave. The last inlet model concerns with the inlet which produce series of weak shock wave and end up with a normal shock wave. The comparison result for the same test case with Fluent Software [1, 2] indicates that the developed computer code based on the Fourth Order Runge Kutta – Harten – Yee TVD scheme are very close to each other. However for complex inlet geometry, the problem is in the way how to provide an appropriate mesh model