Quantum -space

The prime and primitive spectra of , the multiparameter quantized coordinate ring of affine -space over an algebraically closed field , are shown to be topological quotients of the corresponding classical spectra, and , provided the multiplicative group generated by the entries of avoids .

     

An affine PI Hopf algebra not finite over a normal commutative Hopf subalgebra

In formulating a generalized framework to study certain noncommutative algebras naturally arising in representation theory, K. A. Brown asked if every finitely generated Hopf algebra satisfying a polynomial identity was finite over a normal commutative Hopf subalgebra. In this note we show that Radford's biproduct, applied to the enveloping algebra of the Lie superalgebra , provides a noetherian prime counterexample.

     

Derivations and nil ideals

IfR is a torsion free ring, then the nil radical ofR is stable relative to any derivation ofR. In this note, we show the same is true for the Levitzki radical ofR, which is the largest locally nilpotent ideal ofR.     

Monochromatic paths in random tournaments

We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices contains a monochromatic path of length . This resolves a conjecture of Ben‐Eliezer, Krivelevich, and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.     

3-Color bipartite Ramsey number of cycles and paths

The -color bipartite Ramsey number of a bipartite graph is the least integer for which every -edge-colored complete bipartite graph contains a monochromatic copy of . The study of bipartite Ramsey numbers was initiated, over 40 years ago, by Faudree and Schelp and, independently, by Gyárfás and Lehel, who determined the 2-color Ramsey number of paths. In this paper we determine asymptotically the 3-color bipartite Ramsey number of paths and (even) cycles.     

An experimental study of the effect of the axial heat flux distribution on the dryout conditions in a 3650-mm long annulus

Dryout measurements have been carried out for flow of boiling water in a 3650-mm long annulus. Eight different axial heat flux profiles, typical for BWRs, as well as one with uniform heat flux have been studied. It was found that for the present geometry the effect of the axial heat flux profile upon the total dryout power was rather small or in the range of ± 6 per cent.