This study examined the different types of
mathematical tasks used in the classroom to explore the nature of mathematics
instruction of three sixth grade teachers in an elementary school. Case
studies, instructional observations,
and classroom artifacts were used to collect data. The results showed that the
three teachers used different types of mathematical tasks and implementation
methods. One teacher focused on high cognitive demand tasks, most of which
involved substantial group discussion and students working cooperatively. Even
though the other two also used many high cognitive demand tasks, these were
mainly presented via teacher-student dialogue. By examining the types of
mathematical tasks and their implementation, it was found that the group discussion tasks were generally
all high cognitive demand tasks, in which the students fully explained the
solution process. As for the tasks administered through teacher-student dialogue, due to the usage of large
amounts of closed-ended dialogue, the students used low cognition to solve the mathematical tasks and
did not have the opportunity to completely explain their thinking about the solutions. Thus, in order to
fully understand the nature of mathematics instruction by teachers, there should be simultaneous
consideration of the types of mathematical tasks used as well as how the tasks
were implemented.

Abstract:
This study probed into elementary school teachers’ use of instruction time in mathematics on the basis of a case study. Recording a teacher with 20 years’ teaching experience in his classroom and having interviews with him for six months, this study aims to understand the teacher’s use of mathematics instruction time and the influencing factors on this case. According to the results, the teacher in this case tends to divide his teaching activities into review and preview, new content development, interactions and discussions, and exercises and applications. In each class, he would carry out these activities. As the teaching of a module advanced, less instruction time is spent on new content development and more on interactions, discussions, exercises and applications. In terms of the factors influential on the instruction time use, the teacher in this case takes into account mainly the students’ learning initiatives in mathematics and their learning motives, and rarely considers other factors.

Abstract:
This study aims to probe into the teaching performance and the effects of implementation of culture-based mathematics instruction by two indigenous teachers. By case study, this study treats two Paiwan elementary school teachers as the subjects and collects data by the design of teaching plans, instructional observations, video recordings, and mathematical cognitive tests. The researcher thus explores their culture-based curriculum design, instructional implementation, and the effect on Grade 5 and Grade 6 Paiwan students’ learning performance of mathematics. The findings demonstrate that prior to implementation of culturebased mathematics instruction, mathematics learning performance of the students of the two teachers was behind those of other counties, cities, and schools. The two teachers adopt three types of instructional design, namely, Paiwan culture and festivals, stories and traditional art, and practice mathematics questions upon cultural situations by teacher demonstration, individual problem-solving, and group discussion. After the teachers practice 23 and 31 units of culture-based mathematics instruction, the researcher finds that the gap of learning performance between Paiwan students and those in other cities, counties, and schools is reduced, which demonstrates that culture-based mathematics instruction can enhance Paiwan students’ learning performance of mathematics.

Abstract:
In this study, the structural and nanomechanical properties of Cu 2O thin films are investigated by X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM) and nanoindentation techniques. The Cu 2O thin films are deposited on the glass substrates with the various growth temperatures of 150, 250 and 350 °C by using radio frequency magnetron sputtering. The XRD results show that Cu 2O thin films are predominant (111)-oriented, indicating a well ordered microstructure. In addition, the hardness and Young’s modulus of Cu 2O thin films are measured by using a Berkovich nanoindenter operated with the continuous contact stiffness measurements (CSM) option. Results indicated that the hardness and Young’s modulus of Cu 2O thin films decreased as the growth temperature increased from 150 to 350 °C. Furthermore, the relationship between the hardness and films grain size appears to closely follow the Hall-Petch equation.

Abstract:
In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.

Abstract:
The reactivity of the C12-21 alkene of some erythromycin A derivatives was studied. This double bond was easily oxidized to the corresponding epoxide with excellent stereoselectivity. A single crystal X-ray structure showed that the epoxide moiety was on the same side as the acetonide. When an erythromycin derivative containing a C12-21 alkene was treated with diazomethane a [3+2] cycloaddition affording a pyrazoline occurred. In the case of 6-O-allylated erythromycin derivatives the C12-21 alkene was selectively epoxidized in the presence of the 6-O-allyl moiety. These results show that the C12-21 alkene is an active reaction site, which can be used for useful further modification of erythromycin derivatives.

Abstract:
I suggest a new particle model to integrate the fermion flavor, the TeV scale Leptogenesis and cold dark matter. The model has a local gauge symmetry $U(1)_{B-L}$ at the TeV scale and a flavor family symmetry SO(3), in addition, it also contains the fourth generation fermions in which including a cold dark matter neutrino. The model can simultaneously account for the fermion masses and flavor mixings, and the baryon asymmetry and cold dark matter. It not only excellently fits all the current experimental data, but also predicts some new results which are promising to be test in future experiments.

Abstract:
I suggest a practical particle model as an extension to the standard model. The model has a TeV scale $U(1)_{B-L}$ symmetry and it contains the fourth generation fermions with the TeV scale masses, in which including a cold dark matter neutrino. The model can completely account for the fermion flavor puzzles, the cold dark matter, and the matter-antimatter asymmetry through the leptogenesis. In particular, it is quite feasible and promising to test the model in future experiments.

Abstract:
This paper has been withdrawn by the author. I suggest a new particle model to solve simultaneously the problems of fermion masses and flavor mixings, and baryon asymmetry and dark matter. The model extends the standard model by adding a local $U(1)_{B-L}$ gauge symmetry at the TeV scale, in addition, the fermion flavor structures are characterized by the original $S_{3}$ and residual $S_{2R}$ flavor family symmetries. The model can excellently fit all the current experimental data by the fewer parameters. The new results and predictions are promising to be test in future experiments.

Abstract:
In this paper the new concept of relative near PS-compactness in L-fuzzy topological spaces is introduced. The relative near PS-compactness is described with a-net , r-ps-cover, r-finite intersection property. The relationship between relative near PS-compactness and near PS-compactness is in vestigated. It is found that near PS-compactness implies relative near PS-compactness and every LF-set of near PS-compact space is relative near PS-compact. The relative near PS-compactness possess the following properties:the union of two arbirtrary relative near PS-compact sets is relative near PS-compact;the intersection of a family relative near PS-compact sets is also relative near PS-compact. Finally, it is proved that the relative near PS-compactness is invariant under the PS-continuous maps.This relative near PS-compactness is defined for arbitrary L-fuzzy subsets, and it preserves many good properties of compactness in general topological spaces.