Local rings of bounded Cohen-Macaulay type

Let (R,m,k) be a local Cohen-Macaulay (CM) ring of dimension one. It is known that R has finite CM type if and only if R is reduced and has bounded CM type. Here we study the one-dimensional rings of bounded but infinite CM type. We will classify these rings up to analytic isomorphism (under the additional hypothesis that the ring contains an infinite field). In the first section we deal with the complete case, and in the second we show that bounded CM type ascends to and descends from the completion. In the third section we study ascent and descent in higher dimensions and prove a Brauer-Thrall theorem for excellent rings.Comment: 13 pages, revised and correcte

Hypersurfaces of bounded Cohen--Macaulay type

Let R = k[[x_0,...,x_d]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x_0,...,x_d]]. We investigate the question of which rings of this form have bounded Cohen--Macaulay type, that is, have a bound on the multiplicities of the indecomposable maximal Cohen--Macaulay modules. As with finite Cohen--Macaulay type, if the characteristic is different from two, the question reduces to the one-dimensional case: The ring R has bounded Cohen--Macaulay type if and only if R is isomorphic to k[[x_0,...,x_d]]/(g+x_2^2+...+x_d^2), where g is an element of k[[x_0,x_1]] and k[[x_0,x_1]]/(g) has bounded Cohen--Macaulay type. We determine which rings of the form k[[x_0,x_1]]/(g) have bounded Cohen--Macaulay type.Comment: 16 pages, referee's suggestions and correction

Inhomogeneity-induced variance of cosmological parameters

Modern cosmology relies on the assumption of large-scale isotropy and homogeneity of the Universe. However, locally the Universe is inhomogeneous and anisotropic. So, how can local measurements (at the 100 Mpc scale) be used to determine global cosmological parameters (defined at the 10 Gpc scale)? We use Buchert's averaging formalism and determine a set of locally averaged cosmological parameters in the context of the flat Lambda cold dark matter model. We calculate their ensemble means (i.e. their global values) and variances (i.e. their cosmic variances). We apply our results to typical survey geometries and focus on the study of the effects of local fluctuations of the curvature parameter. By this means we show, that in the linear regime cosmological backreaction and averaging can be reformulated as the issue of cosmic variance. The cosmic variance is found largest for the curvature parameter and discuss some of its consequences. We further propose to use the observed variance of cosmological parameters to measure the growth factor. [abbreviated]Comment: 12 pages, 10 figures, references added, estimate of lightcone effects added, matches version published in A&

Comparisons among a new soil index and other two- and four-dimensional vegetation indices

The 2-D difference vegetation index (DVI) and perpendicular vegetation index (PVI), and the 4-D green vegetation index (GVI) are compared in LANDSAT MSS data from grain sorghum (Sorghum bicolor, L. Moench) fields for the years 1973 to 1977. PVI and DVI were more closely related to LAI than was GVI. A new 2-D soil line index (SLI), the vector distance from the soil line origin to the point of intersection of PVI with the soil line, is defined and compared with the 4-D soil brightness index, SBI. SLI (based on MSS and MSS7) and SL16 (based on MSS 5 and MSS 6) were smaller in magnitude than SBI but contained similar information about the soil background. These findings indicate that vegetation and soil indices calculated from the single visible and reflective infrared band sensor systems, such as the AVHRR of the TIROS-N polar orbiting series of satellites, will be meaningful for synoptic monitoring of renewable vegetation

Ascent of module structures, vanishing of Ext, and extended modules

Let (R,\m) and (S,\n) be commutative Noetherian local rings, and let $\phi:R\to S$ be a flat local homomorphism such that \m S = \n and the induced map on residue fields R/\m \to S/\n is an isomorphism. Given a finitely generated $R$-module $M$, we show that $M$ has an $S$-module structure compatible with the given $R$-module structure if and only if \Ext^i_R(S,M)=0 for each $i\ge 1$. We say that an $S$-module $N$ is {\it extended} if there is a finitely generated $R$-module $M$ such that $N\cong S\otimes_RM$. Given a short exact sequence $0 \to N_1\to N \to N_2\to 0$ of finitely generated $S$-modules, with two of the three modules $N_1,N,N_2$ extended, we obtain conditions forcing the third module to be extended. We show that every finitely generated module over the Henselization of $R$ is a direct summand of an extended module, but that the analogous result fails for the \m-adic completion.Comment: 16 pages, AMS-TeX; final version to appear in Michigan Math. J.; corrected proof of Main Theorem and made minor editorial changes; v3 has dedication to Mel Hochste

Estimating total standing herbaceous biomass production with LANDSAT MSS digital data

Rangeland biomass data were correlated with spectral vegetation indices, derived from LANDSAT MSS data. LANDSAT data from five range and three other land use sites in Willacv and Cameron Counties were collected on October 17 and December 10, 1975, and on July 31 and September 23, 1976. The overall linear correlation of total standing herbaceous biomass with the LANDSAT derived perpendicular vegetation index was highly significant (r = 0.90**) for these four dates. The standard error of estimate was 722 kg/ha. Biomass data were recorded for two of these range sites for 8 months (March through October) during the 1976 growing season. Standing green biomass accounted for most of the increase in herbage, starting in June and ending about September and October. These results indicate that satellite data may be useful for the estimation of total standing herbaceous biomass production that could aid range managers in assessing range condition and animal carrying capacities of large and inaccessible range holdings

RascalC: A Jackknife Approach to Estimating Single and Multi-Tracer Galaxy Covariance Matrices

To make use of clustering statistics from large cosmological surveys, accurate and precise covariance matrices are needed. We present a new code to estimate large scale galaxy two-point correlation function (2PCF) covariances in arbitrary survey geometries that, due to new sampling techniques, runs $\sim 10^4$ times faster than previous codes, computing finely-binned covariance matrices with negligible noise in less than 100 CPU-hours. As in previous works, non-Gaussianity is approximated via a small rescaling of shot-noise in the theoretical model, calibrated by comparing jackknife survey covariances to an associated jackknife model. The flexible code, RascalC, has been publicly released, and automatically takes care of all necessary pre- and post-processing, requiring only a single input dataset (without a prior 2PCF model). Deviations between large scale model covariances from a mock survey and those from a large suite of mocks are found to be be indistinguishable from noise. In addition, the choice of input mock are shown to be irrelevant for desired noise levels below $\sim 10^5$ mocks. Coupled with its generalization to multi-tracer data-sets, this shows the algorithm to be an excellent tool for analysis, reducing the need for large numbers of mock simulations to be computed.Comment: 29 pages, 8 figures. Accepted by MNRAS. Code is available at http://github.com/oliverphilcox/RascalC with documentation at http://rascalc.readthedocs.io

How does the chain extension of poly (acrylic acid) scale in aqueous solution? A combined study with light scattering and computer simulation

This work adresses the question of the scaling behaviour of polyelectrolytes in solution for a realistic prototype: We show results of a combined experimental (light scattering) and theoretical (computer simulations) investigation of structural properties of poly (acrylic acid) (PAA). Experimentally, we determined the molecular weight (M_W) and the hydrodynamic radius (R_H) by static light scattering for six different PAA samples in aqueous NaCl-containing solution (0.1-1 mol/L) of polydispersity D_P between 1.5 and 1.8. On the computational side, three different variants of a newly developed mesoscopic force field for PAA were employed to determine R_H for monodisperse systems of the same M_W as in the experiments. The force field effectively incorporates atomistic information and one coarse-grained bead corresponds to one PAA monomer. We find that R_H matches with the experimental data for all investigated samples. The effective scaling exponent for R_H is found to be around 0.55, which is well below its asymptotic value for good solvents. Additionally, data for the radius of gyration (R_G) are presented.Comment: 17 pages, 3 figures, submitted to Macromolecule

Using Intelligent Agents to Manage Business Processes

This paper describes work undertaken in the ADEPT (Advanced Decision Environment for Process Tasks) project towards developing an agent-based infrastructure for managing business processes. We describe how the key technology of negotiating, service providing, autonomous agents was realised and demonstrate how this was applied to the BT business process of providing a customer quote for network services

Resistance weld monitoring Centaur tanks 55-0501-22, 55-0501-23 /AC-21, A-22/ Preliminary report

Resistance weld monitoring of Centaur tanks evaluated using ultrasonic and thermal expansion method