Aurifeuillian factorization

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we can partially factor 24k+2+1. In 1962 Schinzel gave a list of such identities that have proved useful in the Cunningham project; we believe that Schinzel identified all numbers that can be factored by such identities and we prove this if one accepts our definition of what “such an identity” is. We then develop our theme to similarly factor f(bn) for any given polynomial f, using deep results of Faltings from algebraic geometry and Fried from the classification of finite simple groups.

Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions

Solvation. pressure due to adsorption of fluids in porous materials is the cause of elastic deformation of an adsorbent, which is accessible to direct experimental measurements. Such a deformation contributes to the Helmholtz free energy of the whole adsorbent-adsorbate system due to accumulation of compression or tension energy by the solid. It means that in the general case the solid has to be considered as not solely a source of the external potential field for the fluid confined in the pore volume, but also as thermodynamically nonmert component of the solid-fluid system. We present analysis of nitrogen adsorption isotherms and heat of adsorption in slit graphitic pores accounting for the adsorption deformation by means of nonlocal density functional theory. (c) 2006 Elsevier Ltd. All rights reserved.

Strong electronic correlations in superconducting organic charge transfer salts

We review the role of strong electronic correlations in quasi-two-dimensional organic charge transfer salts such as (BEDT-TTF)(2)X, (BETS)(2)Y, and beta'-[Pd(dmit)(2)](2)Z. We begin by defining minimal models for these materials. It is necessary to identify two classes of material: the first class is strongly dimerized and is described by a half-filled Hubbard model; the second class is not strongly dimerized and is described by a quarter-filled extended Hubbard model. We argue that these models capture the essential physics of these materials. We explore the phase diagram of the half-filled quasi-two-dimensional organic charge transfer salts, focusing on the metallic and superconducting phases. We review work showing that the metallic phase, which has both Fermi liquid and 'bad metal' regimes, is described both quantitatively and qualitatively by dynamical mean field theory (DMFT). The phenomenology of the superconducting state is still a matter of contention. We critically review the experimental situation, focusing on the key experimental results that may distinguish between rival theories of superconductivity, particularly probes of the pairing symmetry and measurements of the superfluid stiffness. We then discuss some strongly correlated theories of superconductivity, in particular the resonating valence bond (RVB) theory of superconductivity. We conclude by discussing some of the major challenges currently facing the field. These include parameterizing minimal models, the evidence for a pseudogap from nuclear magnetic resonance (NMR) experiments, superconductors with low critical temperatures and extremely small superfluid stiffnesses, the possible spin- liquid states in kappa-(ET)(2)Cu-2(CN)(3) and beta'-[Pd(dmit)(2)](2)Z, and the need for high quality large single crystals.

Economic incentives for farmers in the Philippine uplands to adopt hedgerow intercropping

Land degradation in the Philippine uplands is severe and widespread. Most upland areas are steep, and intense rainfall on soils disturbed by intensive agriculture can produce high rates of soil loss. This has serious implications for the economic welfare of a growing upland population with few feasible livelihood alternatives. Hedgerow intercropping can greatly reduce soil loss from annual cropping systems and has been considered an appropriate technology for soil conservation research and extension in the Philippine uplands. However; adoption of hedgerow intercropping has been sporadic and transient, rarely continuing once external support has been withdrawn. The objective of this paper is to investigate the economic incentives for farmers in the Philippine uplands to adopt hedgerow intercropping relative to traditional open-field maize farming. Cost-benefit analysis is used to compare the economic viability of hedgerow intercropping, as it has been promoted to upland farmers, with the viability of traditional methods of open-field farming. The APSIM and SCUAF models were used to predict the effect of soil erosion on maize yields from open-field farming and hedgerow intercropping. The results indicate that there have been strong economic incentives for farmers with limited planning horizons to reject hedgerow intercropping because the benefits of sustained yields are not realized rapidly enough to compensate for high establishment costs. Alternative forms of hedgerow intercropping such as natural vegetation and grass strips reduce establishment and maintenance costs and are therefore more economically attractive to farmers than hedgerow intercropping with shrub legumes. The long-term economic viability of hedgerow intercropping depends on the economic setting and the potential for hedgerow intercropping to sustain maize production relative to traditional open-field farming. (C) 1998 Academic Press.

Erosion/productivity modelling of maize farming in the Philippine uplands part III: Economic analysis of alternative farming methods

Two previous papers in this series (Nelson et al., this issue) described the use of the Agricultural Production Systems Simulator (APSIM) to simulate the effect of erosion on maize yields from open-field farming and hedgerow intercropping in the Philippine uplands. In this paper, maize yields simulated with APSIM are used to compare the economic viability of intercropping maize between leguminous shrub hedgerows with that of continuous and fallow open-field farming of maize. The analysis focuses on the economic incentives of upland farmers to adopt hedgerow intercropping, discussing farmers' planning horizons, access to credit and security of land tenure, as well as maize pricing in the Philippines. Insecure land tenure has limited the planning horizons of upland farmers, and high establishment costs reduce the economic viability of hedgerow intercropping relative to continuous and fallow open-field farming in the short term, In the long term, high discount rates and share-tenancy arrangements in which landlords do not contribute to establishment costs reduce the economic viability of hedgerow intercropping relative to fallow open-field farming, (C) 1998 Elsevier Science Ltd. All rights reserved.

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

Stimulus competition in affective and relational learning

Evaluative learning theory states that affective learning, the acquisition of likes and dislikes, is qualitatively different from relational learning, the learning of predictive relationships among stimuli. Three experiments tested the prediction derived from evaluative learning theory that relational learning, but not affective learning, is affected by stimulus competition by comparing performance during two conditional stimuli, one trained in a superconditioning procedure and the other in a blocking procedure. Ratings of unconditional stimulus expectancy and electrodermal responses indicated stimulus competition in relational learning. Evidence for stimulus competition in affective learning was provided by verbal ratings of conditional stimulus pleasantness and by measures of blink startle modulation. Taken together, the present experiments demonstrate stimulus competition in relational and affective learning, a result inconsistent with evaluative learning theory. (C) 2001 Academic Press.

Developing a meta model for the Bunge-Wand-Weber ontological constructs

At the core of the analysis task in the development process is information systems requirements modelling, Modelling of requirements has been occurring for many years and the techniques used have progressed from flowcharting through data flow diagrams and entity-relationship diagrams to object-oriented schemas today. Unfortunately, researchers have been able to give little theoretical guidance only to practitioners on which techniques to use and when. In an attempt to address this situation, Wand and Weber have developed a series of models based on the ontological theory of Mario Bunge-the Bunge-Wand-Weber (BWW) models. Two particular criticisms of the models have persisted however-the understandability of the constructs in the BWW models and the difficulty in applying the models to a modelling technique. This paper addresses these issues by presenting a meta model of the BWW constructs using a meta language that is familiar to many IS professionals, more specific than plain English text, but easier to understand than the set-theoretic language of the original BWW models. Such a meta model also facilitates the application of the BWW theory to other modelling techniques that have similar meta models defined. Moreover, this approach supports the identification of patterns of constructs that might be common across meta models for modelling techniques. Such findings are useful in extending and refining the BWW theory. (C) 2002 Elsevier Science Ltd. All rights reserved.

Rumors and stable-cause attribution in prediction and behavior

Two stock-market simulation experiments investigated the notion that rumors that invoke stable-cause attributions spawn illusory associations and less regressive predictions and behavior. In Study 1, illusory perceptions of association and stable causation (rumors caused price changes on the day after they appeared) existed despite rigorous conditions of nonassociation (price changes were unrelated to rumors). Predictions (recent price trends will continue) and trading behavior (departures from a strong buy-low-sell-high strategy) were both anti-regressive. In Study 2, stability of attribution was manipulated via a computerized tutorial. Participants taught to view price-changes as caused by stable forces predicted less regressively and departed more from buy-low-sell-high trading patterns than those taught to perceive changes as caused by unstable forces. Results inform a social cognitive and decision theoretic understanding of rumor by integrating it with causal attribution, covariation detection, and prediction theory. (C) 2002 Elsevier Science (USA). All rights reserved.