Suitable normalization of time{homogeneous rotation{invariant random walks on unit spheres S d R d+1 for d > 2 leads to a central limit theorem with a Gaussian limit measure. This paper is devoted to an associated Edgeworth expansion with respect to the total variation norm. This strong type of convergence is diierent from the classical case. The proof is performed in the more general setting o...

We establish several results regarding dividing and forking in NTP2 theories. We show that dividing is the same as array-dividing. Combining it with existence of strictly invariant sequences we deduce that forking satisfies the chain condition over extension bases (namely, the forking ideal is S1, in Hrushovski’s terminology). Using it we prove an independence theorem over extension bases (whic...

We discuss the properties of strictly typed languages on the one hand and soft typing on the other one and identify disadvantages of these approaches to type checking in the context of powerful type languages. To overcome the problems we develop an approach that combines ideas of both strict and soft typing. This approach is based on the concept of complete typing that is guaranteed to accept e...

We classify, in a non-trivial amenable collection of functors, all 2-chains up to the relation of having the same 1-shell boundary. In particular, we prove that in a rosy theory, every 1-shell of a Lascar strong type is the boundary of some 2-chain, hence making the 1st homology group trivial. We also show that, unlike in simple theories, in rosy theories there is no upper bound on the minimal ...

Abstract. In this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.

We prove that in a rosy theory, the n-uniqueness of a strong type p implies the strong n-uniqueness of p. In addition we study some of the boundary properties of p. In [5], given a strong type p = tp(c/A) in a stable theory T , if T has (≤ n)-uniqueness while p does not have (n + 1)-uniqueness then, over an infinite Morley sequence of the type of some finite tuple c′ ∈ acl(cA) over A witnessing...

In this paper, we will obtain the strong type and weak type estimates for vector-valued analogs of intrinsic square functions in the generalized weighted Morrey spacesM w (l2). We study the boundedness of intrinsic square functions including the Lusin area integral, the Littlewood-Paley g-function and gλ -function, and their multilinear commutators on vector-valued generalized weighted Morrey s...

We discuss the properties of strictly typed languages on the one hand and soft typing of the other and identify disadvantages of these approaches to type checking in the context of powerful type languages. To overcome the problems we develop an approach that combines ideas of strict and soft typing. This approach is based on the concept of complete typing that is guaranteed to accept every well...

When using existing ACL2 datatype frameworks, many theorems require type hypotheses. These hypotheses slow down the theorem prover, are tedious to write, and are easy to forget. We describe a principled approach to types that provides strong type safety and execution efficiency while avoiding type hypotheses, and we present a library that automates this approach. Using this approach, types help...