Search

In this paper we prove the cube difference labeling of some special graphs such as arrow graphs (Ant), Double arrow graphs (DAnt), Pyramid Pyn, Hanging pyramid (HPyn), H-graph, Hn ⊙ Pm, Hn⊙K1,m¯ and Duplication of all edges of Hn are cube difference graphs.

Let E be an elliptic curve defined over F2m and T denotes the Frobenius endomorphism from the set E(F2m) to itself. The Koblitz curves are a special type of curves for which the T can be used for improving the performance of computing a scalar multiplication. In this paper, we give an alternative formula for Tm = rm + smT where rm and sm are integers. We used the triangular and pyramid numbers, Nicomachus’s theorem and Faulhaber’s formula to produce the formula for Tm. Through this approach, we improve the technique to express Tm.

The interaction between prey, secondary predator, and primary predator as a mathematical model of the one-prey and two-predator system with constant harvesting in prey population will be introduced in this article. Their interaction might describe as a food pyramid, with the preys is in the lowest level of the pyramid, secondary predators in the middle, and primary predators in the top of the pyramid. Human intervention to controlling prey population is needed and will be analyzed how this will effect on the existence of secondary predator and primary predator population. Equilibrium points and their existence criteria will be analyzed to find a threshold that will guarantee the coexistence of this system. Some numerical simulation will be given to illustrate the analytical results. We find that as long as harvesting rate in prey population is smaller than prey intrinsic growth rate, coexistence might achieve.

Geometry is the most difficult topic for majority of junior secondary school students. An endeavor to handle these students' difficulties, the teacher works collaboratively with mathematics educator in a lesson study setting. Learning materials for teaching the volume of pyramid was designed collaboratively. Prism and pyramid container were made for preparing the lesson. Prism and pyramid which have equal base area and height were designed. As many as 40 students of the eight grade were grouped into 8 cohorts of 5 students. Each cohort got one set of geometric containers and beach sand. Students learn the lesson in an open lesson setting. All cohorts work in cooperative group lesson to observe and find out the formula of pyramid compare to the formula of prism which was known previously. Students were manipulating the materials to relate the volume of both pyramid and prism and to compare between the volume of pyramid and the volume of prism by measuring out using the beach sand Learning process was set in lesson study context and was attended by the group of mathematics teachers for at least 30 teachers. In the apperception session, the teacher reminded the students for the formula of prism volume. After manipulating the learning materials which consisted of model of prism, model of pyramid, the beach sand, and worksheet, measuring the volume of pyramid and prism by using sand, comparing, and contrasting, then the students in each group discussed all information from their activity to find out and conclude the volume pyramid. The results are surprising; the students found that the volume of pyramid is one third of the base area times height of the pyramid. From the reflection session we can analyzed that such learning model of mathematics was expected by most mathematics teachers in Bandung. The teachers knew that this kind of teaching emphasized on students active learning, but the teachers need examples, or models for teaching which enable students to re-invent or discover mathematical concepts. This lesson study can be considered as a model to activate students learning mathematics.

An application of high energy physics instrumentation is to look for structure or different densities (materials) hidden in a matrix (tons) of material. By tracing muons produced by primary Cosmic Rays, it has been possible to generate a kind of radiographs which shows the inner structure of dense containers, monuments or mountains. In this paper I review the basics principles of such techniques with emphasis in the Sun Pyramid project, carried out by IFUNAM in collaboration with Instituto Nacioanal de Antropologia e Historia.

In this work a status report of a search for caves in the Sun pyramid in Teotihuacan, Mexico is presented. From an archeological perspective the main goal is to gather evidence to determine whether the pyramid was a state or a funerary temple. The general layout of the detector that is being built is an updated version of the one originally proposed by Alvarez et al..