A Significant ‘False Perception’ of Wittgenstein’s Draft on Mind’s Eye

If we read the Tractatus logico-philosophicus according to the decimal numbering of its propositions, we may understand, finally, the section about the self and the limits of language and world. Proposition 5.64 follows 5.63 (not 5.634); 5.634 follows 5.633 (not 5.6331); and so on. Thus, it becomes clear that the picture of the visual field (TLP 5.6331) cannot be what scholars have always quoted and discussed, i.e. a draft of an eye inside its field of sight. Actually, Wittgenstein’s original drafts depict (to criticise it) the ordinary way of representing the visual field. Following him, the field of vision is ‘without limits’; it does not have a form that implies the existence of an eye, as far as the phenomenological experience does not have a form that implies the existence of an ‘I’. As a result, the current reproductions of the 5.6331 image must be rectified, and all references to this similitude should be radically amended.     

Complex dynamics in an OLG model of neoclassical growth with endogenous retirement age and public pensions

This study analyses the dynamics of a general equilibrium, overlapping-generations (closed) economy with pay-as-you-go public pensions and tax-financed health investments that affect the retirement time when old. Life of the typical agent is divided between youth (firth period) and old age (second period). The latter period of life is, in turn, divided between work time and retirement time in a proportion contingent on an individual’s state of health. We show that: (i) a unique non-trivial steady state exists, and (ii) when the labour income tax rates used to finance health expenditure or public pensions are included in an intermediate range of values, complex dynamics occur when individuals have perfect foresight. This holds because the increase either in the fraction of time spent working when old or disability pensions reduces savings and capital accumulation. In addition, dynamic phenomena such as multiple bubbling structures related to the bifurcation diagram can be observed. Under some general assumptions, we show that the rise in health care expenditure and/or public pensions initially destabilises the steady-state equilibrium and causes complex dynamics but eventually acts as a stabilising device.     

Some Results about Dissipativity of Kolmogorov Operators

Given a Hilbert space H with a Borel probability measure , we prove the m-dissipativity in L ¹(H, ) of a Kolmogorov operator K that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.     

Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field

In this paper we consider the issue of sliding motion in Filippov systems on the intersection of two or more surfaces. To this end, we propose an extension of the Filippov sliding vector field on manifolds of co-dimension p, with p ≥ 2. Our model passes through the use of a multivalued sign function reformulation. To justify our proposal, we will restrict to cases where the sliding manifold is attractive. For the case of co-dimension p = 2, we will distinguish between two types of attractive sliding manifold: “node-like” and “spiral-like”. The case of node-like attractive manifold will be further extended to the case of p ≥ 3. Finally, we compare our model to other existing methodologies on some examples.     

Estimating VAR models for the term structure of interest rates

In this paper we follow the work of Evans and Marshall and propose new approaches for modelling the joint development of macro variables and the returns of government bond yields of several maturities. The models are estimated and compared with other forecasting schemes previously proposed in the literature, especially those relying on univariate, VAR and error correction methods. The models are then used to judge the hypothesis that the information content of macro variables and the term structure of interest rates as a whole help improving forecasting performance. Our main conclusion is quite simple: if one is interested in computing short-term forecasts, then there is no significant improvement in incorporating information other than the one already present in past observations of the yield at hand; however, if one worries about long-term forecasts (which is frequently the case with pension insurance companies), then the information content of macro variables and the term structure can improve forecasting performance.     

Self-adjointness of some infinite-dimensional elliptic operators and application to stochastic quantization

We consider an operator K˚ϕ = Lϕ−: <CDU(x), Dϕ> in a Hilbert space H, where L is an Ornstein–Uhlenbeck operator, U∈W ^1,4(H, μ) and μ is the invariant measure associated with L. We show that K˚ is essentially self-adjoint in the space L ²(H, ν) where ν is the “Gibbs” measure ν(dx) = Z ^−:1 e ^−:2U(x) dx. An application to Stochastic quantization is given. Received: 13 August 1998 / Revised version: 20 September 1999 / Published online: 8 August 2000     

Flame surface modification of polyethylene sheets

High density polyethylene sheets 2 mm thick were flame treated to modify the surface properties. Sheets treated using a flame with air to gas (methane) ratio ∼ 10:1 at different distances between the inner cone tip of the flame and the polymer surface were investigated. Grafting of selected monomers as maleic anhydride, acrylamide and glycidyl methacrylate was attempted by flame treatment of sheets covered with a monomer layer. Good grafting results were obtained with acrylamide and maleic anhydride. The surface temperature-time dependence during the flame treatment was measured with a high resolution thermocouple. Scanning Electron Microscopy (SEM) allowed evidencing a modified thickness of about 120 μ. The chemical surface modification was studied by X ray Photoelectron Spectroscopy (XPS) and Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFT). The hydroxyl, carbonyl and carboxyl content was measured after derivatization with reagents containing an elemental tag to facilitate XPS analysis of surface functional groups. In comparison to the untreated polyethylene, wetting tension and contact angle of the flamed materials showed a strong variation. This variation was almost independent of the distance between the flame and the polymer surface. Adhesion between treated polyethylene and a polyurethane adhesive was determined using T-peel test measurements. High adhesion levels were found with flame treated polyethylene at 5 mm distance. XPS results indicate that when adhesion is high, the hydroxyl is in excess compared to the other measured functions, i.e. carbonyl and carboxyl species.     

Molecular dynamics simulation of semirigid polymers

The chain rigidity of poly(p-hydroxybenzoate) was estimated through the theoretical evaluation of its persistence length (L_p). A non-Brownian molecular dynamics (MD) simulation of an isolated chain with 20 monomeric units was performed. The sampled conformational population was analyzed and the orientational correlation function between monomeric units along the chain was calculated. An algorithm based on the worm-like chain model was applied to evaluate the persistence length. The results were compared with those obtained from equilibrium models like the freely-rotating-chain and the rotational-matrix method with fluctuations. Equilibrium models give different results depending on the degree of accuracy used in describing the monomeric unit. The inclusion of thermal fluctuations is crucial to obtain realistic results. These coincide with those given by MD simulation when only nearest-neighbour orientational correlations are taken into account: inclusion of higher-order correlation terms leads to lower values of the persistence length. The origin of this discrepancy was investigated. The MD simulation results are characterized by an overrepresentation of conformations with a short end-to-end distance resulting from an anomalous energy concentration in the first bending mode of the chain. In analogy with previous simulation results from systems characterized by a week coupling amoung their degrees of freedom, failure in the energy equipartition is proposed as a likely explanation of the anomalous dynamical behaviour.