Utilizing Free Augmented Reality App for Learning Geometry at Elementary School in Taiwan

From random interviews of mathematics teachers, the researchers are conscious that students have difficulties in solving problems regarding compound body volume measurement. The researchers found the main factor involved in the difficulties was incomplete spatial concepts. Augmented reality (AR), which is a kind of educational technology, has been widely applied in the educational field in recent years. AR provides two- or three-dimensional objects and/or information and interaction with them. These characteristics can compensate for the insufficient characterization of compound-body volume in traditional education environments. The paper studies evaluation in utilizing free augmented reality to learn volumetric measurement of compound bodies to complete spatial concepts as well as improve the students' learning performance. The finding suggests that the positive impact on visualization and interaction as well as attitude lead students to be more engaged in learning activities with less cognitive effort, resulting in better learning performance.

The Study on Accuracy Control System with the Three Datum Planes in Fixture Design

The fixture accuracy is controlled on the three datum planes with fixture or compound body used as design object, with structure of parts and the machine accuracy used as the target required, with cutting tool and the machine datum plane mounted fixture used as viewed body. The assistance datum plane is towards the machine locating planes mounted fixture, and it is parallel to the cutting speed of tools; the assistance datum plane (or line) is perpendicular to the assistance datum plane, and it is passing through center line of tool (or fixture);the assistance datum plane is through the single point of fixture , perpendicular to both two.

Experimental Study and Analysis of Different Air-Injecting Segment on the Separation Performance of Air-Injected De-Oiling Hydrocyclone

Developing state-of-the-art and separating principle of deoiling hydrocyclones are introduced. By theoretical analysis, the ways to enhance hydrocyclone’s separation efficiency are described. One way is to inject air into the hydrocyclones so as to combine with oil to form oil-gas compound body, and then increase de-oiling efficiency. By means of injecting air into large cone segment, or fine cone segment of the hydrocyclone, experiments were carried out. It is found that the best injecting part is fine cone segment. Further experimental studies were continued for confirming detail part in fine cone segment, which includes one-third segment and two-thirds segment for the sake of research. Results show that the best air-injecting part is the first one-third segment of fine cone segment. This conclusion would be useful for understanding of air-injected de-oiling hydrocyclone’s separating process, and for its design and applications.

On Mahler's compound bodies

Let 1 ≤ M ≤ N − 1 be integers and K be a convex, symmetric set in Euclidean N-space. Associated with K and M, Mahler identified the Mth compound body of K, (K)m, in Euclidean (MN)-space. The compound body (K)M is describable as the convex hull of a certain subset of the Grassmann manifold in Euclidean (MN)-space determined by K and M. The sets K and (K)M are related by a number of well-known inequalities due to Mahler.Here we generalize this theory to the geometry of numbers over the adèle ring of a number field and prove theorems which compare an adelic set with its adelic compound body. In addition, we include a comparison of the adelic compound body with the adelic polar body and prove an adelic general transfer principle which has implications to Diophantine approximation over number fields.