The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

"Anteroposterior Patterning: How the Hox Genes Help Us Tell Our Heads from Our ***es"

The fundamental problem of developmental biology is how a single cell- a fertilized egg- is able to produce an entire organism in all its complexity. One essential aspect of this process is spatial patterning-in essence, instructing cells as to their location in developing body so that they can exhibit characteristics appropriate to their functions. he Hox genes, first discovered in mutant fruit fly "hopeful monsters" with extra pairs of wings or legs growing out of their heads, confer spatial information along the anteroposterior axis in animals from worms to humans. Prof Marin's research focuses on the roles of specific Hox genes in sculpting the developing entral nervous system of the fruit fly and how the same gene can direct a neuron to die, survive, or send its axon in search of different connections, depending on cellular context.

The Dual Ownership Structure: a Model to Connect the Cooperative Model With Financial Markets

In business literature, the conflicts among workers, shareholders and the management have been studied mostly in the frame of stakeholder theory. The stakeholder theory recognizes this issue as an agency problem, and tries to solve the problem by establishing a contractual relationship between the agent and principals. However, as Marcoux pointed out, the appropriateness of the contract as a medium to reduce the agency problem should be questioned. As an alternative, the cooperative model minimizes the agency costs by integrating the concept of workers, owners and management. Mondragon Corporation is a successful example of the cooperative model which grew into the sixth largest corporation in Spain. However, the cooperative model has long been ignored in discussions of corporate governance, mainly because the success of the cooperative model is extremely difficult to duplicate in reality. This thesis hopes to revitalize the scholarly examination of cooperatives by developing a new model that overcomes the fundamental problem in the cooperative model: the limited access to capital markets. By dividing the ownership interest into financial and control interest, the dual ownership structure allows cooperatives to issue stock in the capital market by making a financial product out of financial interest.