There is no McLaughlin geometry

Is there a McLaughlin geometry?

It has long been an open problem whether or not there exists a partial geometry with parameters (s, t, α) = (4, 27, 2). Such a partial geometry, which we call a McLaughlin geometry, would have the McLaughlin graph as point graph. In this note we use tools from computational group theory and computational graph theory to show that a McLaughlin geometry cannot have certain automorphisms, nor can ...

Critical Points When There Is No Saddle Point Geometry

We show how mountain pass methods can be used even when there is no mountain pass or saddle point geometry. The functional can grow on linking subsets. Applications are given.

There is no lexicon!

0. Introduction Within generative linguistics, underlying representations have been a sine qua non. Such representations have been thought to encode what is unpredictable or not governed by rules. Within Optimality Theory (henceforth OT), even though the rules are virtually gone, this view continues. The function GEN and EVAL pair an underlying representation with an optimal output. I argue aga...

There is no Parkinson disease.

The term Parkinson disease defines a specific clinical condition characterized by a typical history and characteristic signs. This review examines the historical evolution of the concept of Parkinson disease and how the misunderstanding of Parkinson disease may be hindering clinical research trials. It is proposed that this syndrome be called Parkinson diseases or parkinsonism type 1 through in...

There Is No Dividing Line