A note on drastic product logic

The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. This $t$-norm is not left-continuous, and hence it does not admit a residuum. So, there are no drastic product $t$-norm based many-valued logics, in the sense of [EG01]. However, if we renounce standard completeness, we can study the logic whose semantics is provided by those MTL chains whose monoidal operation is the drastic product. This logic is called ${\rm S}_{3}{\rm MTL}$ in [NOG06]. In this note we justify the study of this logic, which we rechristen DP (for drastic product), by means of some interesting properties relating DP and its algebraic semantics to a weakened law of excluded middle, to the $\Delta$ projection operator and to discriminator varieties. We shall show that the category of finite DP-algebras is dually equivalent to a category whose objects are multisets of finite chains. This duality allows us to classify all axiomatic extensions of DP, and to compute the free finitely generated DP-algebras.Comment: 11 pages, 3 figure

Effective temperatures of a heated Brownian particle

We investigate various possible definitions of an effective temperature for a particularly simple nonequilibrium stationary system, namely a heated Brownian particle suspended in a fluid. The effective temperature based on the fluctuation dissipation ratio depends on the time scale under consideration, so that a simple Langevin description of the heated particle is impossible. The short and long time limits of this effective temperature are shown to be consistent with the temperatures estimated from the kinetic energy and Einstein relation, respectively. The fluctuation theorem provides still another definition of the temperature, which is shown to coincide with the short time value of the fluctuation dissipation ratio

Study of the performance and capability of the new ultra-fast 2 GSample/s FADC data acquisition system of the MAGIC telescope

In February 2007 the MAGIC Air Cherenkov Telescope for gamma-ray astronomy was fully upgraded with an ultra fast 2 GSamples/s digitization system. Since the Cherenkov light flashes are very short, a fast readout can minimize the influence of the background from the light of the night sky. Also, the time structure of the event is an additional parameter to reduce the background from unwanted hadronic showers. An overview of the performance of the new system and its impact on the sensitivity of the MAGIC instrument will be presented.Comment: Contribution to the 30th ICRC, Merida Mexico, July 2007 on behalf of the MAGIC Collaboratio

Detection of Cherenkov light from air showers with Geiger-APDs

We have detected Cherenkov light from air showers with Geiger-mode APDs (G-APDs). G-APDs are novel semiconductor photon-detectors, which offer several advantages compared to conventional photomultiplier tubes in the field of ground-based gamma-ray astronomy. In a field test with the MAGIC telescope we have tested the efficiency of a G-APD / light catcher setup to detect Cherenkov light from air showers. We estimate a detection efficiency, which is 60% higher than the efficiency of a MAGIC camera pixel. Ambient temperature dark count rates of the tested G-APDs are below the rates of the night sky light background. According to these recent tests G-APDs promise a major progress in ground-based gamma-ray astronomy.Comment: 4 pages, 5 figures, to appear in the proceedings of the 30th International Cosmic Ray Conference, Merida, July 200

Inter-molecular structure factors of macromolecules in solution: integral equation results

The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the dilute-to-semidilute crossover of random phase (RPA) like structure are derived for the inter-molecular structure factor on large distances when inter-molecular excluded volume is incorporated at the microscopic level. This leads to a non-linear equation for the excluded volume interaction parameter. For macromolecular size-mass scaling exponents, $\nu$, above a spatial-dimension dependent value, $\nu_c=2/d$, mean field like density scaling is recovered, but for $\nu<\nu_c$ the density scaling becomes non-trivial in agreement with field theoretic results and justifying phenomenological extensions of RPA. The structure of the polymer mesh in semidilute solutions is discussed in detail and comparisons with large scale Monte Carlo simulations are added. Finally a new possibility to determine the correction to scaling exponent $\omega_{12}$ is suggested.Comment: 11 pages, 5 figures; to be published in Phys. Rev. E (1999

Green Up-Conversion Continuous-Wave Er3+Liyf4 Laser At Room-Temperature

We report room-temperature upconversion pumped continuous wave laser emission of 1% Er3+:LiYF4 at 551 nm excited by a Ti:sapphire laser at 810 nm. Output powers of up to 40 mW with output coupling of 6.6% have been obtained by using nearly concentric resonator design

Cognitive Computation sans Representation

The Computational Theory of Mind (CTM) holds that cognitive processes are essentially computational, and hence computation provides the scientific key to explaining mentality. The Representational Theory of Mind (RTM) holds that representational content is the key feature in distinguishing mental from non-mental systems. I argue that there is a deep incompatibility between these two theoretical frameworks, and that the acceptance of CTM provides strong grounds for rejecting RTM. The focal point of the incompatibility is the fact that representational content is extrinsic to formal procedures as such, and the intended interpretation of syntax makes no difference to the execution of an algorithm. So the unique 'content' postulated by RTM is superfluous to the formal procedures of CTM. And once these procedures are implemented in a physical mechanism, it is exclusively the causal properties of the physical mechanism that are responsible for all aspects of the system's behaviour. So once again, postulated content is rendered superfluous. To the extent that semantic content may appear to play a role in behaviour, it must be syntactically encoded within the system, and just as in a standard computational artefact, so too with the human mind/brain - it's pure syntax all the way down to the level of physical implementation. Hence 'content' is at most a convenient meta-level gloss, projected from the outside by human theorists, which itself can play no role in cognitive processing

Chemical enrichment of the complex hot ISM of the Antennae Galaxies: II. Physical properties of the hot gas and supernova feedback

We investigate the physical properties of the interstellar medium (ISM) in the merging pair of galaxies known as The Antennae (NGC 4038/39), using the deep coadded ~411 ks Chandra ACIS-S data set. The method of analysis and some of the main results from the spectral analysis, such as metal abundances and their variations from ~0.2 to ~20-30 times solar, are described in Paper I (Baldi et al. submitted). In the present paper we investigate in detail the physics of the hot emitting gas, deriving measures for the hot-gas mass (~10^ M_sun), cooling times (10^7-10^8 yr), and pressure (3.5x10^-11-2.8x10^-10 dyne cm^-2). At least in one of the two nuclei (NGC 4038) the hot-gas pressure is significantly higher than the CO pressure, implying that shock waves may be driven into the CO clouds. Comparison of the metal abundances with the average stellar yields predicted by theoretical models of SN explosions points to SNe of Type II as the main contributors of metals to the hot ISM. There is no evidence of any correlation between radio-optical star-formation indicators and the measured metal abundances. Although due to uncertainties in the average gas density we cannot exclude that mixing may have played an important role, the short time required to produce the observed metal masses (<=2 Myr) suggests that the correlations are unlikely to have been destroyed by efficient mixing. More likely, a significant fraction of SN II ejecta may be in a cool phase, in grains, or escaping in hot winds. In each case, any such fraction of the ejecta would remain undetectable with soft X-ray observations.Comment: 29 pages, 6 figures, accepted by the Astrophysical Journa