Applications of shuffle product to restricted decomposition formulas for multiple zeta values

In this paper we obtain a recursive formula for the shuffle product and apply it to derive two restricted decomposition formulas for multiple zeta values (MZVs). The first formula generalizes the decomposition formula of Euler and is similar to the restricted formula of Eie and Wei for MZVs with one strings of 1's. The second formula generalizes the previous results to the product of two MZVs with one and two strings of 1's respectively.Comment: 11 page

Influence of University Students' Demographics and Their Learning Styles: A Study of UUM's Students in Bank Rakyat Residential College

This paper investigates the relationship between students' demographics factors and the learning style preferences of students. By linking Kolb' model of learning style preferences to the students demographics differences of individual learners the researcher develop a study by data collected from 100 students from different nation backgrounds enrolled in different courses at university in Utara Malaysia. The finding show that learning style preferences differ across nationalities, gender, race, educational background and that these preferences are affected by a number of cultural values. We also find important differences in the learning styles of male and female students and between local and exchange students. The results are of importance to teachers and managers active in the education and development of individuals from different academic background and for researcher's influences in the influences of academic improvements on learning style preferences

Vertical absorption edge and universal onset conductance in semi-hydrogenated graphene

We show that for graphene with any finite difference in the on-site energy between the two sub-lattices ($\Delta$), The optical absorption edge is determined by the $\Delta$. The universal conductance will be broken and the conductance near the band edge varies with frequency as $1/\omega^2$. Moreover, we have identified another universal conductance for such systems without inversion symmetry, i.e., the onset conductance at the band edge is $\sigma_c=2\sigma_0=\pi e^2/2h$, independent of the size of the band gap. The total integrated optical response is nearly conserved despite of the opening of the band gap.Comment: 4 pages, 4 figure

Counterpart Theory and Its Applications

Inspired by the many-worlds interpretation in quantum theory, I present the concepts of “nousor” and the theory of counterpart, by which I make a metaphysical argument that the existence of other parallel worlds could be brought to light by dreams, and that counterparts in different worlds can exchange information through the nousor containing information packets to ensure the oneness of counterparts. Many worlds and all lives there follow the rules which are permanent and can not be violated. Based on the counterpart theory, I propose a new view on the origin and meaning of déjà vu, Planck’s problem, and actual dreams, to offer a novel way of thinking and a problem-solving paradigm. Governments should collect citizen’s dreams and use group dreams as a critical indicator to predicate catastrophes

Cross-cultural MOOCs: designing MOOCs for Chinese students

Advocates of Massive Open Online Courses (MOOCs), a cross-cultural phenomenon that has attracted public attention throughout the world, portray them as an equalizing force in international higher education; but researchers have noted discrepancies in how learners from different countries have engaged with them. The number of MOOC learners in China is growing rapidly, and Chinese learners are enthusiastic about the unprecedented freedom they now have in selecting courses and accessing resources from the best international universities. However, they have a significantly low completion rate and may experience unique challenges about which little is known. This study took into account the diversity of MOOC learners and proposed changes to its course design to make it more inclusive for Chinese students. I used a mixed method—including document analysis, surveys, and interviews—to investigate the Chinese experience of taking Western MOOCs and also to explore the educational theories and design principles of MOOCs that have been discussed in the Western and Chinese literature. My analysis of the literature revealed issues of contextualization that may play a critical role in improving the MOOC experience for Chinese students. Drawing on theoretical educational frameworks—including motivation, community of inquiry, self-regulated learning, and social identity—my analysis of surveys and interviews identified common themes in the Chinese experience of Western MOOCs. In accordance with the results of my analysis, and also in line with interaction equivalency and situational principles, this study provided suggestions for adapting MOOCs to Chinese learners, such as enhancing content quality, improving learner–learner and learner–instructor interactions, providing social support, and collaborating with local universities and agencies in providing technical and credentialing support

What Is the Philosophy of Problem?

The philosophy of problem is a logical view, putting the problem at the core of logic, promoting the development of thinking. The philosophy of problem is a view of life, revealing not only the skills and interests of survival but also the significance and value of life. The philosophy of problem is an ethical view, regarding the development of morality and ethics as the result of questioning in its most profound sense. Philosophy of problem is a scientific view, putting the problem at the core of the philosophy of science, exploring the law of the generation and evolution of scientific knowledge from the proposition, expression, structure, presupposition, evaluation, solution and evolution of questions. The philosophy of problem is a philosophical view, regarding answer as its goal and question as its service