Previously, we constructed the transfinite Goodwillie spectral sequence (TGSS), whose signature is roughly E t,J(S ) = πtS ⇒ πtS. This spectral sequence computes unstable homotopy from stable data. Over the next couple of talks, we’ll discuss the differentials in this spectral sequence, but for today, let’s just focus on understanding the relationship between the E page and the E∞ page at a hig...

Although transfinite iteration functionals have been used in the past to construct ever-larger initial segments of the ordinals ([5],[1]), there appears to be little investigation into the nature of the functionals themselves. In this note, we investigate the relationship between (countable) transfinite iteration and ordinal arithmetic. While there is a nice connection between finite iteration ...

latticed columns are frequently used in industrial steel structures. in some countries these built-up columns might be even used in other types of steel structures such as residential and commercial buildings. besides, latticed columns are parts of skeletons of many historic buildings all around the world. to analyze a steel structure with latticed columns a more accurate numerical model for su...

The thesis aims to solve partial differential equations numerically using mimetic spectral element method. The method rewrites the PDEs with differential forms so the resulting equations are able to preserve geometrical characteristics in physics. The equation we focus is the Poisson equation, which can be utilized for potential flow problems. The physical domain to be tested is a typical flow ...

Reinhardt’s conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and transfinite induction up to a smaller ordinal.

This contribution extends the notions of roots and periodicity to strings of transfinite lengths. It shows that given a transfinite string, either it possesses a unique root or the set of its roots are equivalent in a strong way. Mathematics Subject Classification. 68R15.

The aim of this paper is to investigate geometrically nonlinear static analysis of axially functionally graded cantilever beam subjected to transversal non follower load. The considered problem is solved by finite element method with total Lagrangian kinematic approach. The material properties of the beam vary along the longitudinal direction according to the power law function. The finite elem...