Pearson’s statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtos...

Abstract We obtain limit theorems (Stable Laws and Central Limit Theorems, both standard non-standard) thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function is studied in an abstract functional analytic framework, which may be applicable to other classes flows.

Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p. Then we show that B satisfies Brauer’s k(B)-Conjecture (i. e. k(B) ≤ |D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.

We prove large deviation results for Minkowski sums Sn of iid random compact sets where we assume that the summands have a regularly varying distribution and finite expectation. The main focus is on random convex compact sets. The results confirm the heavy-tailed large deviation heuristics: “large” values of the sum are essentially due to the “largest” summand. These results extend those in [8]...

We present a general algorithmic framework that allows not only to deal with summation problems over summands being rational expressions in indefinite nested sums and products (Karr 1981), but also over ∂-finite and holonomic summand expressions that are given by a linear recurrence. This approach implies new computer algebra tools implemented in Sigma to solve multi-summation problems efficien...

Suppose a connected reductive complex algebraic group G acts linearly on a complex projective variety X. We prove that if 1→ N → G→ H → 1 is a short exact sequence of connected reductive groups and X the open set of semistable points for the action of N on X then IH H (X/N) is a direct summand of IH G (X). The inclusion is provided by the decomposition theorem and certain resolutions of the act...

Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the nth syzygy module of the residue class field of R has a non-trivial direct summand of finite Gdimension for some n. It is proved that if n is at most two then it is true, and moreover, the structure of the ring R is determined essentially uniquely.