A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.

Bioaccessibility of trace elements in soils in Northern Ireland

Assessment of elevated concentrations of potentially toxic elements (PTE) in soils and the association with specific soil parent material have been the focus of research for a number of years. Risk-based assessment of potential exposure scenarios to identified elevated PTE concentrations has led to the derivation of site- and contaminant-specific soil guideline values (SGVs), which represent generic assessment criteria (GACs) to identify exceeded levels that may reflect an unacceptable risk to human health. A better understanding of the ‘bioavailable’ or ‘bioaccessible’ contaminant concentrations offers an opportunity to better refine contaminant exposure assessments. Utilizing a comprehensive soil geochemical dataset for Northern Ireland provided by the Tellus Survey (GSNI) in conjunction with supplementary bioaccessibility testing of selected soil samples following the Unified BARGE Method, this paper uses exploratory data analysis and geostatistical analysis to investigate the spatial variability of pseudo-total and bioaccessible concentrations of As, Cd, Co, Cr. Cu, Ni, Pb, U, V and Zn. The paper investigates variations in individual element concentrations as well as cross-element correlations and observed lithological/pedological associations. The analysis of PTE concentrations highlighted exceeded levels of GAC values for V and Cr and exceeded SGV/GAC values for Cd, Cu, Ni, Pb, and Zn. UBM testing showed that for some soil parent materials associated with elevated PTE concentrations e.g. the Antrim Lava Group with high Ni concentrations, the measured oral bioaccessible fraction was relatively low. For other soil parent materials with relatively moderate PTE concentrations, measured oral bioaccessible fraction was relatively high (e.g. the Gala Sandstone Group of the Southern Uplands-Down Longford Terrain). These findings have implications for regional human health risk assessments for specific PTEs.

Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence

Belief revision characterizes the process of revising an agent’s beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation
is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster
rule of combination, just like revision in the sense of Alchourron, Gardenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey’s rule of updating, Dempster rule of conditioning and a form of AGM revision.

Theory of the Kinetics of Chemical Potentials in Heterogeneous Catalysis

Simple and powerful: The reaction kinetics at surfaces of heterogeneous catalysts is reformulated in terms of the involved chemical potentials. Based on this formulism, an approach of searching for good catalysts is proposed without recourse to extensive calculations of reaction barriers and detailed kinetic analyses. (see picture; R=reactant, I=surface intermediate, P=product, and =standard chemical potential).

Theory of pixel lensing toward M31. II. The velocity anisotropy and flattening of the MACHO distribution

The POINT-AGAPE collaboration is currently searching for massive compact halo objects (MACHOs) toward the Andromeda galaxy (M31). The survey aims to exploit the high inclination of the M31 disk, which causes an asymmetry in the spatial distribution of M31 MACHOs. Here, we investigate the effects of halo velocity anisotropy and flattening on the asymmetry signal using simple halo models. For a spherically symmetric and isotropic halo, we find that the underlying pixel lensing rate in far-disk M31 MACHOs is more than 5 times the rate of near-disk events. We find that the asymmetry is further increased by about 30% if the MACHOs occupy radial orbits rather than tangential orbits, but it is substantially reduced if the MACHOs lie in a flattened halo. However, even for halos with a minor- to major-axis ratio of q = 0.3, the number of M31 MACHOs in the far side outnumber those in the near side by a factor of similar to2. There is also a distance asymmetry, in that the events on the far side are typically farther from the major axis. We show that, if this positional information is exploited in addition to number counts, then the number of candidate events required to confirm asymmetry for a range of flattened and anisotropic halo models is achievable, even with significant contamination by variable stars and foreground microlensing events. For pixel lensing surveys that probe a representative portion of the M31 disk, a sample of around 50 candidates is likely to be sufficient to detect asymmetry within spherical halos, even if half the sample is contaminated, or to detect asymmetry in halos as flat as q = 0.3, provided less than a third of the sample comprises contaminants. We also argue that, provided its mass-to-light ratio is less than 100, the recently observed stellar stream around M31 is not problematic for the detection of asymmetry.

Theory of pixel lensing towards M31 - I. The density contribution and mass of MACHOs

POINT-AGAPE is an Angle-French collaboration which is employing the Isaac Newton Telescope (INT) to conduct a pixel-lensing survey towards M31. Pixel lensing is a technique which permits the detection of microlensing against unresolved stellar fields. The survey aims to constrain the stellar population in M31, and also the distribution and nature of massive compact halo objects (MACHOs) in both M31 and the Galaxy.

Pull-out behaviour of axially loaded basalt fibre reinforced polymer (BFRP) rods bonded parallel to the grain of glulam elements

Synopsis: Bonded-in rod timber joints off er several advantages over conventional types of joint, including high local force transfer, very stiff connections, and improved ?re and aesthetic properties since the connection is completely hidden in the insulating timber members. More recently, the use of ?bre reinforced polymer (FRP) as a connecting rod, alternative to steel rods, in bonded-in rod connections for timber structures has been investigated. However, the investigation into the behaviour of such joints is limited, in particular, connections involving basalt ?bre reinforced polymers (BFRP) bars - which is the primary focus of this research. This paper presents an experimental programme conducted to investigate the behaviour of bonded-in BFRP bars loaded parallel to the grain of glulam members. Tensile pull-out tests were conducted to examine the effect of bonded length and bond stress-slip on the structural capacity of the connection. An analytical design expression for predicting pull-out capacity is proposed and the results have been compared with some established design equations. It was found that pull-out load increased approximately linearly with the bonded length, up to maximum which occurred at a bonded length of 15 times the hole diameter, and did not increase beyond this bonded length. The most signi?cant failure modes were failure at the timber/adhesive interface followed by pullout of the BFRP rod. Increased bonded lengths resulted in higher bond slip values compared to lower equivalent bonded lengths. The proposed design model gave the best predictions of pull-out capacity compared with other existing models.

R-matrix Floquet theory of multiphoton processes:XIII. Resonances in H multiphoton detachment

The results of calculations investigating the effects of autodetaching resonances on the multiphoton detachment spectra of H are presented. The R-matrix Floquet method is used, in which the coupling of the ion with the laser field is described non-perturbatively. The laser field is fixed at an intensity of 10 W cm, while frequency ranges are chosen such that the lowest autodetaching states of the ion are excited through a two- or three-photon transition from the ground state. Detachment rates are compared, where possible, to previous results obtained using perturbation theory. An illustration of how non-lowest-order processes, involving autodetaching states, can lead to light-induced continuum structures is also presented. Finally, it is demonstrated that by using a frequency connecting the 1s and 2s states, the probability of exciting the residual hydrogen atom is significantly enhanced.