Stress in dilute suspensions

Generally, two types of theory are used to describe the field equations for suspensions. The so-called postulated equations are based on the kinetic theory of mixtures, which logically should give reasonable equations for solutions. The basis for the use of such theory for suspensions is tenuous, though it at least gives a logical path for mathematical arguments. It has the disadvantage that it leads to a system of equations which is underdetermined, in a sense that can be made precise. On the other hand, the so-called averaging theory starts with a determined system, but the very process of averaging renders the resulting system underdetermined. A third type of theory is proposed in which the kinetic theory of gases is used to motivate continuum equations for the suspended particles. This entails an interpretation of the stress in the particles that is different from the usual one. Classical theory is used to describe the motion of the suspending medium. The result is a determined system for a dilute suspension. Extension of the theory to more concentrated systems is discussed

Morphic and principal-ideal group rings

We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For $R$ an artinian principal ideal ring and $G$ a group, we characterize when $RG$ is a principal ideal ring; for finite groups $G$, this characterizes when $RG$ is a left and right morphic ring. This extends work of Passman, Sehgal and Fisher in the case when $R$ is a field, and work of Chen, Li, and Zhou on morphic group rings.Comment: 21 page

It’s Not Brain Science… Or Is It? How Early Second Language Learning Can Impact Future Achievement

Capstone paper from 2015 spring MPA program. Instructed by Allen Zagoren.We live in a global economy, yet U.S. citizens lag far behind in the knowledge of other countries’ languages, cultures, customs, geographies and peoples. Equipping the next generation with foreign language skills as well as knowledge of other cultures and customs will not only provide increased career opportunities for individuals but also aid in the future success of the U.S. economy. The U.S. educational system does not stress the learning of language beyond English: K-12 curriculum is rigidly mandated, budgets are tight, class time and teacher training is limited, and language programs are often among the first to be cut during budget crises. There is a time period when a child’s brain is developing and most receptive to learning, and that is early childhood. If the seed were planted in a child before he/she enters kindergarten to learn the basics of a foreign language and culture, perhaps that knowledge could be nourished throughout the rest of their lives, preparing those children to embrace cultural differences, live and compete more successfully in an evolving and diverse world, and be better equipped for later education. Besides examining the current state of foreign language education in the U.S. and how learning occurs, the benefits of foreign language learning in relation to business and human relations are examined in this paper. Multiple solutions to solving the foreign language deficit are mentioned including a proposal for an early-learning language program

Computing the symmetric ring of quotients

AbstractWe discuss and compute the symmetric Martindale ring of quotients for various classes of prime rings. In particular, we consider free algebras and group algebras