We study the asymptotics of the heat trace Tr{fPe 2 } where P is an operator of Dirac type, where f is an auxiliary smooth smearing function which is used to localize the problem, and where we impose spectral boundary conditions. Using functorial techniques and special case calculations, the boundary part of the leading coefficients in the asymptotic expansion is found.

The effects of Phx-3 on changes in intracellular pH (pHi) in the MKN45 and MKN74 human gastric cancer cell lines were evaluated in order to determine the mechanism for the proapoptotic effects of 2-aminophenoxazine-3-one (Phx-3) on these cells. Phx-3 (100 μM) reduced pHi in MKN45 from 7.45 to 5.8, and in MKN74 from 7.5 to 6.2 within 1 min of engagement with these cells. Such a decrease of pHi w...

We give explicit, polynomial–time computable formulas for the number of integer points in any two– dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of our formulas are Dedekind–Rademacher sums, which are polynomial–time computable finite Fourier series. As a by–product we rederive a reciprocity law for these...

Motivation: Our textbook discusses and even proves many properties of R, the field of real numbers; but it doesn’t define it. I felt that it would be rather awkward to discuss real numbers without knowing what they were and I decided to write some notes on the construction of R. The approach I am following is called ‘Dedekind cut’, discovered by a German mathematician, Richard Dedekind (1831-19...

— We give an explicit upper bound for the residue at s = 1 of the Dedekind zeta function of a totally real number field K for which ζK(s)/ζ(s) is entire. Notice that this is conjecturally always the case, and that it holds true if K/Q is normal or if K is cubic. Résumé (Bornes supérieures explicites pour les résidus en s = 1 des fonctions zêta de Dedekind de corps de nombres totalement réels) N...

We give explicit, polynomial–time computable formulas for the number of integer points in any two– dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of our formulas are Dedekind–Rademacher sums, which are polynomial–time computable finite Fourier series. As a by–product we rederive a reciprocity law for these...

Five bacteriophages infecting only Saccharopolyspora erythraea (formerly Streptomyces erythreus) among 43 Streptomyces spp. tested were classified into two groups by phage-host relationships, restriction enzyme mapping, cohesive-end determinations, and Southern hybridizations. phi SE6, the most frequently isolated phage, produced clear plaques on all hosts tested, while phi SE45, phi SE57, phi ...

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.