Abstract We develop combinatorics of Fulton’s essential set particularly with a connection to Baxter permutations. For this purpose, we introduce a new idea: dual essential sets. Together with the original essential set, we reinterpret Eriksson-Linusson’s characterization of Baxter permutations in terms of colored diagrams on a square board. We also discuss a combinatorial structure on local mo...

It is well-known that any morphism between two p-compact groups will lift, nonuniquely, to an admissible morphism between the maximal tori. We identify here a class of pcompact group morphisms, the p-toric morphisms, which can be perceived as generalized rational isomorphisms, enjoying the stronger property of lifting uniquely to a morphism between the maximal torus normalizers. We investigate ...

We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

BACKGROUND AND AIMS  Non-lifting large laterally spreading colorectal lesions (LSLs) are challenging to resect endoscopically and often necessitate surgery. A safe, simple technique to treat non-lifting LSLs endoscopically with robust long-term outcomes has not been described. METHODS  In this single-center prospective observational study of consecutive patients referred for endoscopic mucosa...

We investigate the symmetry properties of hierarchies of non-linear Schrödinger equations, introduced in [1], which describe non-interacting systems in which tensor product wave-functions evolve by independent evolution of the factors (the separation property). We show that there are obstructions to lifting symmetries existing at a certain number of particles to higher numbers. Such obstruction...

Let F be a nearly holomorphic vector-valued Siegel modular form of weight ρ with respect to some congruence subgroup of Sp2n(Q). In this note, we prove that the function on Sp2n(R) obtained by lifting F has the moderate growth (or “slowly increasing”) property. This is a consequence of the following bound that we prove: ‖ρ(Y )F (Z)‖ ∏n i=1(μi(Y ) λ1/2 + μi(Y ) −λ1/2) where λ1 ≥ . . . ≥ λn is th...

In a paper of 1974, Brian Day employed a notion of factorization system in the context of enriched category theory, replacing the usual diagonal lifting property with a corresponding criterion phrased in terms of hom-objects. We set forth the basic theory of such enriched factorization systems. In particular, we establish stability properties for enriched prefactorization systems, we examine th...

Weak mixing is an important property for group extensions because its absence is the principal obstruction to lifting a large number of stronger mixing properties. Whether or not an extension is weakly mixing can be determined by studying the sub-extension corresponding to the quotient by the commutator subgroup. Several conditions equivalent to weak mixing are given. In particular, an extensio...

This zero-circulation property of source sheets has severe consequences for flow representation. Any aerodynamic model consisting only of a freestream and superimposed source sheets will have Γ = 0, and hence L = 0 as well. Hence, lifting flows cannot be represented by source sheets alone. This limitation is illustrated if we use source panels to model a flow expected to produce lift, such as t...