We study the univariate moment problem of piecewise-constant density functions on interval [0,1] and its consequences for an inference in population genetics. show that, up to closure, any collection n moments is achieved by a step function with at most ? 1 breakpoints that this bound tight. use point th coalescence manifold genetics can be attained piecewise constant history 2 changes. Both co...

Let R be a reduced ring that is essentially of finite type over an excellent regular local ring of prime characteristic. Then it is shown that the test ideal of R commutes with localization and, if R is local, with completion, under the additional hypothesis that the tight closure of zero in the injective hull E of the residue field of every local ring of R is equal to the finitistic tight clos...

Tight closure test ideals have been central to the classification of singularities in rings characteristic p &gt; 0 p&gt;0</mml:annot...

Suppose that R is a two-dimensional normal standard-graded domain over a finite field. We prove that there exists a uniform Frobenius test exponent b for the class of homogeneous ideals in R generated by at most n elements. This means that for every ideal I in this class we have that f b ∈ I [p ] if and only if f ∈ I . This gives in particular a finite test for the Frobenius closure. On the oth...

The Briançon-Skoda theorem can be seen as an effective version of the Hilbert Nullstellensatz and gives a connection between size conditions on holomorphic functions and ideal membership. The size conditions are captured algebraically by the notion of integral closure of ideals. Many techniques have been applied to prove the Briançon-Skoda theorem and variations of it. The first proof by Brianç...

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing subor superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of 2O(n) on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size n. (2) We present a family of CFGs for which the minimal deterministic finite automata ...

SECTION 1 introduces a method for constructing a measure by inner approximation, starting from a set function defined on a lattice of sets. SECTION 2 defines a “tightness” property, which ensures that a set function has an extension to a finitely additive measure on a field determined by the class of approximating sets. SECTION 3 defines a “sigma-smoothness” property, which ensures that a tight...

This paper proves a sharp lower bound for Newton polygons of L-functions of exponential sums of one-variable rational functions. Let p be a prime and let Fp be the algebraic closure of the finite field of p elements. Let f(x) be any one-variable rational function over Fp with l poles of orders d1, . . . , dl. Suppose p is coprime to d1 · · · dl. We prove that there exists a tight lower bound wh...

‘Hermetic sealing’ is defined by the Shorter OED as “air-tight closure of a vessel by fusion, soldering or welding”. The term ‘hermetic package’ used in the electronics industry is however at best slightly misleading, in that the term is used to describe components where the die and associated bonds are sealed within a cavity in a hollow package (as distinct from being embedded in a resin), and...