Versal unfoldings for linear retarded functional differential equations

We consider parametrized families of linear retarded functional differential equations (RFDEs) projected onto finite-dimensional invariant manifolds, and address the question of versality of the resulting parametrized family of linear ordinary differential equations. A sufficient criterion for versality is given in terms of readily computable quantities. In the case where the unfolding is not versal, we show how to construct a perturbation of the original linear RFDE (in terms of delay differential operators) whose finite-dimensional projection generates a versal unfolding. We illustrate the theory with several examples, and comment on the applicability of these results to bifurcation analyses of nonlinear RFDEs

Keller--Osserman conditions for diffusion-type operators on Riemannian Manifolds

In this paper we obtain generalized Keller-Osserman conditions for wide classes of differential inequalities on weighted Riemannian manifolds of the form $L u\geq b(x) f(u) \ell(|\nabla u|)$ and $L u\geq b(x) f(u) \ell(|\nabla u|) - g(u) h(|\nabla u|)$, where $L$ is a non-linear diffusion-type operator. Prototypical examples of these operators are the $p$-Laplacian and the mean curvature operator. While we concentrate on non-existence results, in many instances the conditions we describe are in fact necessary for non-existence. The geometry of the underlying manifold does not affect the form of the Keller-Osserman conditions, but is reflected, via bounds for the modified Bakry-Emery Ricci curvature, by growth conditions for the functions $b$ and $\ell$. We also describe a weak maximum principle related to inequalities of the above form which extends and improves previous results valid for the \vp-Laplacian

Short article: When are moving images remembered better? Study–test congruence and the dynamic superiority effect

It has previously been shown that moving images are remembered better than static ones. In two experiments, we investigated the basis for this dynamic superiority effect. Participants studied scenes presented as a single static image, a sequence of still images, or a moving video clip, and 3 days later completed a recognition test in which familiar and novel scenes were presented in all three formats. We found a marked congruency effect: For a given study format, accuracy was highest when test items were shown in the same format. Neither the dynamic superiority effect nor the study–test congruency effect was affected by encoding (Experiment 1) or retrieval (Experiment 2) manipulations, suggesting that these effects are relatively impervious to strategic control. The results demonstrate that the spatio-temporal properties of complex, realistic scenes are preserved in long-term memory. </jats:p

Strategic maritime container transport design in oligopolistic markets

AbstractThis paper considers the maritime container assignment problem in a market setting with two competing firms. Given a series of known, exogenous demands for service between pairs of ports, each company is free to design a liner service network serving a subset of the ports and demand, subject to the size of their fleets and the potential for profit. The model is designed as a three-stage complete information game: in the first stage, the firms simultaneously invest in their fleet; in the second stage, they individually design their networks and solve the route assignment problem with respect to the transport demand they expect to serve, given the fleet determined in the first stage; in the final stage, the firms compete in terms of freight rates on each origin-destination movement. The game is solved by backward induction. Numerical solutions are provided to characterize the equilibria of the game

Scalar-tensor analysis of an exponential Lagrangian for the Gravitational Field

Within the scheme of modified gravity, an exponential Lagrangian density will be considered, and the corresponding scalar-tensor description will be addressed for both positive and negative values of the cosmological constant. For negative values of the cosmological term, the potential of the scalar field exhibits a minimum, around which scalar-field equations can be linearized. The study of the deSitter regime shows that a comparison with the modified-gravity description is possible in an off-shell region, i.e., in a region where the classical equivalence between the two formulations is not fulfilled. Furthermore, despite the negative cosmological constant, an accelerating deSitter phase is predicted in the region where the series expansion of the exponential term does not hold. For positive values of the cosmological constant, the quantum regime is analyzed within the framework of Loop Quantum Cosmology.Comment: 8 pages, 2 figures, to appear in the proceedings of'' 4th Italian-Sino Workshop on Relativistic Astrophysics'', AIP Conference Serie

Una metáfora esencial de Unamuno ("Como el crecer de las encinas")

Si Unamuno fue fundamentalmente un escritor, es decir, un creador a partir de la palabra, parece natural que sea a través de la palabra por donde pueda venirnos la posibilidad de su mejor entendimiento. Buscar a Unamuno a través de sus ideas es más complicado y más peligroso que buscarlo en sus palabras, sobre todo si se piensa que le interesaban más las palabras que las ideas, lo que explicaría su desconfianza de las ideas y su devoción por las palabras.If Unamuno was essentially a writer, that is, a creator of the word, it seems natural that were through the word where can come to us the possibility of better understanding. Search Unamuno through his ideas is more complicated and more dangerous that look into his words, especially if you think that is more interested in the words than ideas, which would explain his distrust of ideas and his devotion to the words

On the very long term evolutionary behavior of hydrogen-accreting Low-Mass CO white dwarfs

Hydrogen-rich matter has been added to a CO white dwarf of initial mass 0.516 \msun at the rates $10^{-8}$ and $2\times 10^{-8}$ \msun \yrm1, and results are compared with those for a white dwarf of the same initial mass which accretes pure helium at the same rates. For the chosen accretion rates, hydrogen burns in a series of recurrent mild flashes and the ashes of hydrogen burning build up a helium layer at the base of which a He flash eventually occurs. In previous studies involving accretion at higher rates and including initially more massive WDs, the diffusion of energy inward from the H shell-flashing region contributes to the increase in the temperature at the base of the helium layer, and the mass of the helium layer when the He flash begins is significantly smaller than in a comparison model accreting pure helium; the He shell flash is not strong enough to develop into a supernova explosion. In contrast, for the conditions adopted here, the temperature at the base of the He layer becomes gradually independent of the deposition of energy by H shell flashes, and the mass of the He layer when the He flash occurs is a function only of the accretion rate, independent of the hydrogen content of the accreted matter. When the He flash takes place, due to the high degeneracy at the base of the He layer, temperatures in the flashing zone will rise without a corresponding increase in pressure, nuclear burning will continue until nuclear statistical equilibrium is achieved; the model will become a supernova, but not of the classical type Ia variety.Comment: 14 pages and 3 Postscript figures, Accepted for publication on ApJ Letter