Stress wave propagation when the elastic coefficients vary with depth

Of concern is the propagation of distortionless surface waves in a medium that may be nonuniform relative to depth. Distortionless wave propagation in inhomogeneous media was discussed by V. Burke, R. J. Duffin and D. Hazony, inQuart. Appl. Math., 183–194 (1976). Accordingly, the media could be modeled by a distributed electrical ladder network, nonuniform along the axis. We give a two-dimensional development based on Hooke's law and Newton's law which leads to the well-known case of Rayleigh waves in homogeneous media. It will be seen that the available pool of propagation modes greatly increases when high-pass propagation is included. The emphasis is on media where the elastic coefficients track one another as a function of depth. Special cases are studied in detail showing that as a disturbance travels along the surface, it may assume a broadband phase change, which translates into a shape distortion in the time domain, which is periodic with distance. Applications may be found in acousto-optics, in situ monitoring of elongated bodies, high-frequency SAW filters, microstrips, and any situations where surface waves are used in an environment of high precision or relatively large distances. Work supported, in part, by the ONR, C. K. Vasudevan contract monitor.     

Analytic Calculi for Product Logics

Product logic is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.     

Exactly solvable model for driven dissipative systems

We introduce a solvable stochastic model inspired by granular gases for driven dissipative systems. We characterize far from equilibrium steady states of such systems through the non-Boltzmann energy distribution and compare different measures of effective temperatures. As an example we demonstrate that fluctuation-dissipation relations hold, however, with an effective temperature differing from the effective temperature defined from the average energy.     

LIGHT-DRIVEN MOVEMENTS IN THE SOLAR TRACKING LEAF OF Lupinus palaestinus Boiss. (Fabaceae)

Abstract— The palmatcly-compound leaf lamina of Lupinus palaestinus Boiss. tracks the sun by independent diaphototropic movements of its individual leaflets, operated by the appropriate flexing of their pulvinules. The lamina also exhibits two additional, light-dependent nastic movements, that can operate concurrently with the diaphototropic response: (1) a nyctinastic response to light/dark transitions bv which all the leaflets fold down simultaneously and at equal rates, and which is reversed by a photonastic response to dark/light transitions by which all the leaflets unfold into a co-planar configuration; (2) a photonastic upward folding ("cupping"), which all the leaflets exhibit simultaneously and at equal rates in response to high irradiance. thereby modulating their diaphototropic response to reduce light interception and evade over-exposure. Although the individual leaflets can sense all these tight-signals and respond to them independently, they do so simultaneously, so that the entire lamina responds in a co-ordinated manner, as a unit. The photoreceptors for the two nastic responses are localized in the individual pulvinules and may or may not be the same. The photoreceptors for the diaphototropic perception are localized in the proximal segment of the lamina of the individual leaflets, adjacent to but outside the pulvinule. The separation of the sites of perception for the tropic and nastic responses allows these responses to operate concurrently. The capacity of the diaphototropic response to occur concurrently with one or the other of the two nastic responses may be accounted for by its inductive nature.     

A remark on an areally meanp-valent function

We bring an example which shows that in a theorem due to Cartwright, Spencer and Hayman concerning areally meanp-valent functions a multiplicative constant cannot be reduced to 1. (This is possible in the corresponding theorem for circumferentially meanp-valent functions).     

A socio-cognitive model of trust using argumentation theory

Trust is used to minimise the uncertainty in the interactions of the agents especially in case of conflicting information from different sources. Besides conflicts among information there can also be conflicts about the trust attributed to the information sources. In this paper, we discuss how to reason about trust using argumentation theory, so to express also the possibly conflicting motivations about trust and distrust. The methodology of meta-argumentation allows us to model both information and information sources as arguments and to argue about them. First, we present a model for representing evidence provided as motivation of the sources’ arguments to represent the need of a trusted source to believe the information, and we show how to model the information sources in a way that it can be argued whether they should be considered trustworthy or not. Second, we provide a focused representation of trust about the sources in which trust concerns not only the sources but also the information items and the relation with other information. Third, we introduce the feedback on the trustworthiness of the sources and the information items they propose, such that an attack to the trustworthiness of the items feeds back on the trustworthiness of the source. Finally, we distinguish two dimensions of trust, namely competence and sincerity, and we present a formal way to express those dimensions, only informally described in the socio-cognitive models of trust.