We study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...

Alas, the motivating examples of algebraically compact categories are not algebraically compact, and the enriched setting does not directly support the theory of algebraic compactness. We show that the structural setting, the same setting developed independently for models of linear logic, directly supports the theory of algebraic cocompleteness. We extend the structural setting to a bistructur...

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)

We call a nitely complete category algebraically coherent if the change-ofbase functors of its bration of points are coherent, which means that they preserve nite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdor algebras over a ...

Morse inequalities for diffeomorphisms of a compact manifold were first proved by Smale [21] under the assumption that the nonwandering set is finite. We call these the integral Morse inequalities. They were generalized by Zeeman in an unpublished work cited in [25] to diffeomorphisms with a hyperbolic chain recurrent set that is axiom-A-diffeomorphisms which satisfy the no cycle condition. For...

group Aut(M). Stability and Diophantine Geometry A structure M is said to be unstable if it interprets a bipartite graph (P,Q,R) with the feature that for each n there are ai ∈ P and bi ∈ Q for i = 1, . . . , n such that R(ai, bj ) if and only if i < j. A complete theory is unstable if some (any) model is unstable. If M is unstable (witnessed by (P,Q,R) ) and saturated, then there are ai and bi...

In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions  for a weighted Lebesgue space  $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$.  Among the other things, we also show that if $K$ is a locally compact hyper...