Negations and contrapositions of complete lattices

AbstractWe introduce the negation CL of a complete lattice L as the concept lattice of the complementary context (TL, ML, ≰), formed by the join-irreducible elements as objects and the meet-irreducible elements as attributes. We show that the double negation CCL is always order-embeddable in L, and that for finite lattices, the sequence (CnL)nϵω runs into a ‘flip-flop’ (i.e., CnL ⋍ Cn + 2 L for some n). Using vertical sums, we provide constructions of lattices which are isomorphic or dually isomorphic to their own negation. The only finite distributive examples among such ‘self-negative’ or ‘self-contrapositive’ lattices are vertical sums of four-element Boolean lattices. Explicitly, we determine all self-negative and all self-contrapositive lattices with less than 11 points

On the isomorphism problem of concept algebras

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in \cite{Kw04}, is whether complete {\wdl}s are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem \ref{T:main}). We also provide a new proof of a well known result due to M.H. Stone \cite{St36}, saying that {\em each Boolean algebra is a field of sets} (Corollary \ref{C:Stone}). Before these, we prove that the boundedness condition on the initial definition of {\wdl}s (Definition \ref{D:wdl}) is superfluous (Theorem \ref{T:wcl}, see also \cite{Kw09}).Comment: 15 page

A New High-intensity, Low-momentum Muon Beam for the Generation of Low-energy Muons at PSI

At the Paul Scherrer Institute (PSI, Villigen, Switzerland) a new high-intensity muon beam line with momentum p < 40MeV/c is currently being commissioned. The beam line is especially designed to serve the needs of the low-energy, polarized positive muon source (LE-μ+) and LE-μ SR spectrometer at PSI. The beam line replaces the existing μ E4 muon decay channel. A large acceptance is accomplished by installing two solenoidal magnetic lenses close to the muon production target E that is hit by the 590-MeV PSI proton beam. The muons are then transported by standard large aperture quadrupoles and bending magnets to the experiment. Several slit systems and an electrostatic separator allow the control of beam shape, momentum spread, and to reduce the background due to beam positrons or electrons. Particle intensities of up to 3.5 × 108 μ+/s and 107 μ−/s are expected at 28MeV/c beam momentum and 1.8mA proton beam current. This will translate into a LE-μ+ rate of 7,000/s being available at the LE-μ SR spectrometer, thus achieving μ+ fluxes, that are comparable to standard μ SR facilitie

Measurement of the Fermi Constant by FAST

An initial measurement of the lifetime of the positive muon to a precision of 16 parts per million (ppm) has been performed with the FAST detector at the Paul Scherrer Institute. The result is tau_mu = 2.197083 (32) (15) microsec, where the first error is statistical and the second is systematic. The muon lifetime determines the Fermi constant, G_F = 1.166353 (9) x 10^-5 GeV^-2 (8 ppm).Comment: 15 pages, 6 figure

Estimation of the Thermodynamic Limit of Overheating for Bulk Water from Interfacial Properties

The limit of overheating or expanding is an important property of liquids, which is relevant for the design and safety assessment of processes involving pressurized liquids. In this work, the thermodynamic stability limit – the so-called spinodal – of water is calculated by molecular dynamics computer simulation, using the molecular potential model of Baranyai and Kiss. The spinodal pressure is obtained from the maximal tangential pressure within a liquid‒vapor interface layer. The results are compared to predictions of various equations of states. Based on these comparisons, a set of equations of state is identified which gives reliable results in the metastable (overheated or expanded) liquid region of water down to −55 MPa

Avalanche photodiodes for the CMS electromagnetic calorimeter

Avalanche photodiodes(APD's) will be used as photodetectors in the CMS barrel electromagnetic crystal calorimeter for high precision energy measurements in a hostile radiation environment. Significant progress has been made in the characteristics of these devices being expressly developed for CMS. Parameters of the final structure APD's together with demonstrations of radiation hardness and plans for quality assurance/control during the production phase are presented