Pure Hilbert Algebras with Infimum
In [6], iH-algebras were introduced in order to indicate an equational version of the class of Hilbert algebras where each pair of elements has infimum. These authors also proved that this variety hasthe class of Curry's implicative semilattices ([9]) as a proper subvariety. On the other hand, in [4] a special class of Hilbert algebras associated with ordered sets, which they called order algebras, were investigated. These algebras were also studied in [1] under the name of pure Hilbert algebras.Bearing in mind the above results, in this paper we introduce the notion of pure Hilbert algebras with infimum (or ipH-algebras, for short). Furthermore, we characterize the lattice of ipH-congruences and we determine the subdirectly irreducible ipH-algebras. Besides, we prove that subdirectly irreducible ipH-algebras are alsosubdirectly irreducible iH-algebras.
Prior’s OIC nonconservativity example revisited
In his 1964 note, ‘Two Additions to Positive Implication’, A. N. Prior showed that standard axioms governing conjunction yield a nonconservative extension of the pure implicational intermediate logic OIC (order implicational calculus) of R. A. Bull. Here, after reviewing the situation with the aid of an adapted form of the Kripke semantics for intuitionistic and intermediate logics, we proceed to illuminate this example by transposing it to the setting of modal logic, and then relate it to the propositional logic of what have been called ‘Hilbert algebras with infimum’.
Spectroscopy of high rate events during active interrogation
Abstract Pulsed accelerators are being used for radiographic inspections in homeland security applications. Adding spectroscopic detection capability enables additional information to be extracted but challenges signal processing hardware. This work compares two approaches to cost-effective digital spectroscopy systems designed to handle these high rate scenarios. In the first system, the signal from a PMT is directly digitized and then deconvolved on a PC using standard techniques. Bypassing the preamplifier, this system can handle high count rates (>10 6  cps) from an LaCl 3 detector with no dead time and an energy resolution of 5% at 1.33 MeV. Spectra acquired from fission product gamma rays between interrogation pulses are shown. At higher rates, this approach is limited by the DAQ transfer rate to the PC. Instead, we tested a fast ADC (125 MSPS) and an FPGA that performed onboard, real-time digital signal processing (DSP). The energy spectrum is generated on the FPGA board during the measurement and transferred later. This system was tested in nuclear resonance fluorescence (NRF) experiments. Resonance peaks from NRF reactions are shown.