Quantum set theory: Transfer Principle and De Morgan's Laws

In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws.     

Determination of average ion energy in turbulently heated plasmas by secondary emission detector

An average energy of a high temperature part of ions in turbulently heated plasmas was measured by use of a secondary emission detector, and availability of this simple method for a determination of an average ion energy was discussed.     

Scattering time in GaAs/AlGaAs narrow wires in the presence of magnetic field

Magnetoresistance measurements have been performed in narrow GaAs/AlGaAs wires in order to study the scattering process in mesoscopic wires. Amplitude analysis of the Shubnikov -de Haas oscillations shows that electrons have two scattering times, depending upon the magnetic field range. The critical field which separates these scattering times seems to be determined by the relation between the wire width and the electron cyclotron radius. This effect is discussed in terms of the electron trajectories in a wire under the magnetic field.     

Color confining parton model for heavy quarkonium decay

We present a gluon jet model for the heavy quarkonium decay incorporating the color neutralization mechanism. Postulating that final hadrons are produced from the color singlet quark-antiquark pair originated each from different gluons, we formulate the production mechanism of hadrons from gluons explicitly. The fragmentation function thus obtained can describe the hadron production not only in the fragmentation region but also in the central one owing to the usage of the Sudakov variables. The result of the average charged multiplicity from Υ(9.46) is in reasonable agreement with the data, in contrast to the naive estimates. Furthermore, the inclusive momentum and multiplicity distributions are discussed.     

Diquarks in nucleons

Under the assumption that a scalar diquark coexists in part of the time with a single quark within a nucleon, which is favored to describe the higher twist effects of both γ and ν induced nucleon structure functions consistently, we consider how its presence affects nucleon properties. It is shown that the sum rule and the magnetic moment constrain its contribution strongly and the asymmetry is quite sensitive to it. In particular, theR=σ _L /σ _T ratio can be explained in terms of the large transverse momentum of the diquark which arises from the consideration on the neutron charge radius value.     

Synthetic studies on cell surface glycans 3: Branching pentasaccharides of glycoprotein

Synthetic routes for the branching pentasaccharides 4 and 5 of glycoproteins are described in a regio- and stereo- controlled way.     

On the chiral connection between the ferromagnet,the axisymmetric gravitational problem and the SU(2) vacuum gauge field

A single chiral structure is shown to underly several three-dimensional field equations of physics, e.g., the ferromagnet, the stationary axi-symmetric gravitational problem, and the vacuum SU(2) gauge field in the Coulomb gauge. This connection invites cross-fertilization of exact solutions. As illustrations, exact finite energy solutions are obtained for the ferromagnet via the corresponding Weyl, Kerr, and Tominatsu-Sato solutions of Einstein's gravitational equations. Comments are made on the “local gauge invariance” of the ferromagnet and the gravitational field.     

Solid-state polymerization of N-carboxy-L-leucine anhydride crystals in n-hexane

4-Isobutyloxazolidinedione, L -leucine N-carboxy anhydride, was polymerized to produce high molecular weight polymer with triethylamine in n-hexane which is not a solvent for the N-carboxy anhydride and poly-L -leucine. It was found that as the crystal size became smaller, the total surface area was increased, the initial rate of polymerization was increased, and inherent viscosity of the formed polymer was decreased.     

Asymmetric information and macroeconomic dynamics

We show how macroeconomic dynamics can be derived from asymmetric information. As an illustration of the utility of this approach we derive the equilibrium density, non-equilibrium densities and the equation of motion for the response to a demand shock for productivity in a simple economy. Novel consequences of this approach include a natural incorporation of time dependence into macroeconomics and a common information-theoretic basis for economics and other fields seeking to link micro-dynamics and macro-observables.