Neighborhood Complexes and Generating Functions for Affine Semigroups

Given a₁,a₂,...,a_n ∈ ℤ^d$, we examine the set, G, of all non-negative integer combinations of these a_i. In particular, we examine the generating function f(z) = ∑_{b ∈ G}z_b. We prove that one can write this generating function as a rational function using the neighborhood complex (sometimes called the complex of maximal lattice-free bodies or the Scarf complex) on a particular lattice in ℤ_n. In the generic case, this follows from algebraic results of Bayer and Sturmfels. Here we prove it geometrically in all cases, and we examine a generalization involving the neighborhood complex on an arbitrary lattice.     

An exponential lower bound to the size of bounded depth frege proofs of the pigeonhole principle

We prove lower bounds of the form exp(n^{ε d}), ε_d > 0, on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d, for any constant d. This is the largest lower bound for the strongest proof system, for which any superpolynomial lower bounds are known.     

Complete structure determination of the astrophysically important nucleus Na below the proton threshold

The fusion–evaporation reaction ¹⁰B(¹²C, 2n) was used to make the first observation of in-beam γ decays from the astrophysically important nucleus ²⁰Na, lying adjacent to the proton drip-line. All states below the proton threshold in ²⁰Na were populated and identified in the experiment. These include new levels, previously unresolved levels, and states located with improved energy precision. The level structure of ²⁰Na, and its γ transitions, are compared to the mirror partner ²⁰F measured simultaneously in this experiment. In particular, a high degree of energy stability is found for all negative parity states. These results are discussed in the context of the nuclear shell model.     

The influence of chain dynamics on the far-infrared spectrum of liquid methanol

Far-infrared-absorption spectroscopy is used to investigate the low-frequency (相似文献   

Use of the64Ni(36S,34,35Si)66,65Zn reactions to measure the masses of34Si and35Si

The ground-state masses of³⁵Si and³⁴Si have been measured using the reactions⁶⁴Ni(³⁶S,^35,34Si)^65,66Zn at a³⁶S beam energy of 198 MeV.^34,35Si¹⁴⁺ ions were analysed and identified in a QMG/2 magnetic spectrometer and gas-filled focal-plane detector. The experimental mass excess of³⁵Si was determined to be ?14.58± _0.12 ^0.07 MeV while that of³⁴Si was measured as ?19.961±0.034 MeV. A comparison is made with the results of mass model predictions.     

Solution dynamics and stability of lanthanide(III) (S)-2-(p-nitrobenzyl)DOTA complexes

Addition of a benzyl substituent to the macrocyclic ring of DOTA has a substantial impact on the conformational ring flipping motion of the macrocycle in the resulting LnDOTA complexes. The p-NO2-benzyl substituent in the Ln(p-NO2-Bn-DOTA)- complexes lies in an equatorial position and effectively "locks" the conformation of the ring into the deltadeltadeltadelta configuration. The presence of the p-NO2-benzyl group also increases the population of the square antiprismatic (SAP) coordination isomer for all Ln(p-NO2-Bn-DOTA)- complexes relative to that seen for the respective LnDOTA- complexes. Despite this increase in SAP isomer population, the rate of water exchange in these complexes remains comparatively fast. The kinetic and thermodynamic stabilities of the Ln(p-NO2-Bn-DOTA)- complexes are also slightly lower than the corresponding LnDOTA- complexes but appear to be sufficiently high for in vivo use.