On a space with affine connection which has no closed path

On Proving that a Graph has no Large Clique: A Connection with Ramsey Theory

An Analytic Closed Space Curve Which Bounds No Orientable Surface of Finite Area.

The author has recently given several different examples of contours in space which bound no surface of finite area. One of these (found in collaboration with Ph. Franklin) was a skew polygon of a denumerable infinity of sides.' Another was constructed by winding a thread more and more times about the successive tori of a certain infinite sequence. shrinking to a point as limit.2 When one inqui...

Binomial options pricing has no closed-form solution

We set a lower bound on the complexity of options pricing formulae in the lattice metric by proving that no general explicit or closed form (hypergeometric) expression for pricing vanilla European call and put options exists when employing the binomial lattice approach. Our proof follows from Gosper’s algorithm. The binomial model as heralded by Cox et al. (1979), has become a well-known approa...

Spaces with Non-symmetric Affine Connection

The beginning of the study of non-symmetric affine connection spaces is especially in relation with the works of A. Einstein on United Field Theory (UFT). The paper is a short survey of the development of the theory of these spaces. AMS Mathematics Subject Classification (2000): 53C25, 53A45, 53B05

Deviation equations in spaces with affine connection

Connections between Lie derivatives and the deviation equation has been investigated in spaces Ln with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivatives with respect to the tangential vector of the basic trajectory. B. Z. Ili...