We show that each direct summand of the associated graded module test filtration τ(M,fλ)λ≥0 admits a natural Cartier structure. If λ is an F-jumping number, then this structure nilpotent on τ(M,fλ−ε)/τ(M,fλ) if and only denominator divisible by p. also these structures coincide with certain are obtained considering D-modules to M were used construct Bernstein-Sato polynomials. Moreover, we poin...

Let L be a free Lie algebra of finite rank r over a field . For each positive integer n, denote the degree n homogeneous component of L by L. The group of graded algebra automorphisms of L may be identified with GLr; ‘ in such a way that L1 becomes the natural module, and then the L are referred to as the Lie powers of this module. Understanding the GLr; ‘-module structure of the L may be tho...

Controlled K-theory is used to show that algebraic K-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The part coming from infinite subgroups is called the Farrell-Jones summand. This is shown to split from the finite-isotropy part; is parameterized by the rational projective space of the group; and a reduced version i...

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...

in [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.also, we exhibited the topic of limit summability of real functions in [2,3]. inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. finally, we pose an unsolved problem aboutthem.

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...

The large deviation problem for sums of i.i.d. random vectors is considered. It is assumed that the underlying distribution is absolutely continuous and its density is of regular variation. An asymptotic expression for the probability of large deviations is established in the case of a non-normal stable limit law. The role of the maximal summand is also emphasized. AMS Subject Classification: P...

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs discretely with finite multiplicity (admissible restrictions). Basic theory and new perspectives of admissible restrictions are presented from both analytic and alge...