In this paper, we introduce arithmetic Heilbronn characters that generalize the notion of the classical Heilbronn characters, and discuss several properties of these characters. This formalism has several arithmetic applications. For instance, we obtain the holomorphy of suitable quotients of L-functions attached to elliptic curves, which is predicted by the Birch–Swinnerton–Dyer conjecture, an...

Problems are considered in which an objective function expressible as a max of finitely many C2 functions, or more generally as the composition of a piecewise linear-quadratic function with a C2 mapping, is minimized subject to finitely many C2 constraints. The essential objective function in such a problem, which is the sum of the given objective and the indicator of the constraints, is shown ...

G. Rond has proved a Diophantine type inequality for the field of quotients of the convergent or formal power series ring in multivariables. We generalize his theorem to the field of the quotients of an excellent Henselian local domain whose reduced order function is expressed as the minimum of a finite set of good valuations in Rees’s sense. 2000 Mathematics Subject Classification Number: 13H1...

The importance for image processing of a good theory for morphological operators in complete lattices is now well understood. In this paper we introduce inverses and quotients of mappings between complete lattices which are analogous to inverses and quotients of positive numbers. These concepts are then used to create a convenient formalism for dilations and erosions as well as for cleistomorph...

We investigate homomorphisms of degree structures with various relations, functions and constants. Our main emphasis is on pseudolattices, i.e., partially ordered sets with a join operation and relations simulating the meet operation. We show that there are no 5nite quotients of the pseudolattice of degrees or of the pseudolattice of degrees 6 0′, but that many 5nite distributive lattices are p...

Hoping for a richer supply of phenomena, we should wonder about limits of two-dimensional things (surfaces). It was convenient that all the circles in the solenoids were uniformized compatibly, that is, were compatibly expressed as quotients of R. For ease of description, we choose to look at surfaces X which are quotients of the upper half-plane H in C, with quotient mappings H→ X that fit tog...

The classi cation of foliated surfaces, [McQ08], is applied to the study of curves on surfaces with big co-tangent bundle and varying moduli, be it purely in characteristic zero, or, more generally when the characteristic is mixed. Almost everything that one might naively imagine is true, but with one critical exception: rational curves on bi-disc quotients which aren't quotients of products of...

Oxygen recycling inside photosynthesizing leaves was found to amount to less than 0.3% of the oxygen consumed by photorespiration under natural conditions, provided the influence of buildup of oxygen released by photosynthesis into the external air was taken into consideration. When this is related to the amounts of photorespired CO(2), which had been previously found to be reabsorbed by photos...

We obtained data on the writing of 110 deaf or hard-of-hearing students attending public schools who completed the spontaneous writing portion of the Test of Written Language. The average written quotient for the sample was in the below-average range but within 1 standard deviation of the test mean. Forty-nine percent of the sample received written quotients within or above the average range. M...

It has long been known that every quasi-homogeneous normal complex surface singularity with Q–homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called “splice type singularities,” which generalize Brieskorn complete intersections....