Constructing finitely presented monoids which have no finite complete presentation

Squier (1987) showed that if a monoid is defined by a finite complete rewriting system, then it satisfies the homological finiteness condition FP₃, and using this fact he gave monoids (groups) which have solvable word problems but cannot be presented by finite complete systems. In the present paper we show that a monoid cannot have a finite complete presentation if it contains certain special elements. This observation enables us to construct monoids without finite complete presentation in a direct and elementary way. We give a finitely presented monoid which has (1) a word problem solvable in linear time and (2) linear growth but (3) no finite complete presentation. We also give a finitely presented monoid which has (1) a word problem solvable in linear time, (2) finite derivation type in the sense of Squier and (3) the property FP_∞, but (4) no finite complete presentation.     

Acoustic properties of the disordered relaxor ferroelectric PbSc1/2Ta1/2O3

The behavior of acoustic phonons in crystals of a relaxor ferroelectric, namely, the lead scandium tantalate PbSc_1/2Ta_1/2O₃ (PST), is studied in the vicinity of the diffuse phase transition. The behavior of longitudinal and transverse acoustic phonons in a PST single crystal is examined using Brillouin scattering. The phonon subsystem is found to behave anomalously in the vicinity of T = 297 K, which can probably be assigned to the existence of a phase transition. Analysis of the results obtained yields the values of the elastic moduli C₁₁, C₁₂, and C₄₄ for the cubic phase of the crystal over a wide temperature range.     

Laser spectroscopy of trapped 7Be and 10Be at a prototype slow RI-beam facility of RIKEN

A next-generation slow radioactive nuclear ion beam facility (SLOWRI) which provides slow, high-purity and small emittance ion beams of all elements is being build as one of the principal facilities at the RIKEN RI-beam factory (RIBF). High energy radioactive ion beams from the projectile fragment separator BigRIPS are thermalized in a large gas catcher cell. The thermalized ions in the gas cell are guided and extracted to a vacuum environment by a combination of dc electric fields and inhomogeneous rf fields (rf carpet ion guide). From there the slow ion beam is delivered via a mass separator and a switchyard to various devices: such as an ion trap, a collinear fast beam apparatus, and a multi-reflection time of flight mass spectrometer. In the R&D works at the present RIKEN facility, an overall efficiency of 5% for a 100A MeV ⁸Li ion beam from the present projectile fragment separator RIPS was achieved and the dependence of the efficiency on the ion beam intensity was investigated. Recently our first spectroscopy experiment at the prototype SLOWI was performed on Be isotopes. Energetic ions of ¹⁰Be and ⁷Be from the RIPS were trapped and laser cooled in a linear rf trap and the specific mass shifts of these isotopes were measured for the first time.     

Spin gap systems: What can be measured by muon spin relaxation?

Muon spin relaxation (μSR) and nuclear magnetic resonance (NMR) are powerful probes of magnetism, which have been extensively applied to studies of spin gap systems. Comparison of results obtained with the two techniques gives complementary results, as each is sensitive to different aspects of spin gap magnetism. We discuss recent μSR measurements of the spin ladder compounds Sr _n?1Cu _n+1O_2n , pure and doped Haldane materials (Y_2?x Ca _x )Ba(Ni_1?y Mg _y )O₅, and doped spin Peierls compounds (Cu_1?x Zn _x )(Ge_1?y Si _y )O₃.     

Melting behavior of poly(oxytetramethylene)-<Emphasis Type="Italic">alt</Emphasis>-(aromatic oligoamide) block copolymers

Using temperature-modulated differential scanning calorimetry, the melting behaviour of poly(oxytetramethylene)-alt-(aromatic oligoamide) (POTM-alt-AOA) has been studied in comparison with that of polyoxytetramethylene glycohols (POTMGs). The apparent melting temperature of the block copolymers is found to be less than that of the corresponding POTMGs by approximately 30°C. The relaxation time of melting of a POTM segment has been estimated and compared with that of POTMG. The relaxation time of POTM-alt-AOA is slightly shorter than that of POTMG when the molar mass of the POTM segment is 2900; however, it is longer when the molar mass is 1400.     

TG of polytetrahydrofuran/ isophoronediisocyanate reaction products

TG, swelling, and viscometric studies are presented for the residues, PTHF/IPDI polymer networks, and the extracts, the linear polymers and unreacted IPDI, after Soxhlet extraction of PTHF/IPDI reaction products. The products are obtained by reacting PTHF with 650, 1400, (2×650+1×2900), or 2900 of molecular mass with IPDI at various concentrations in bulk. The results on the swelling and the viscosity experiments suggest that the PTHF/IPDI reaction products have a usual expectable structure. All the TG curves are a double stage curve. The initial stage and the last stage seem to reflect decomposition of PTHF chains and vaporization of the remainder, IPDI, respectively. These are analyzed by a trial-and-error construction, supposing double event behavior. The values of ratio of mass loss associated with the initial event, W0₁, to the mass loss associated with the last event, W0₂, are smaller than the expectable those. This suggests that Event 2 involves vaporization of the decomposition products of PTHF moieties bonded to IPDI in addition to vaporization of IPDI. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal analysis of polymer networks consisting of different homopolymers

TG and DSC were carried out on PMAA-net-POTM in order to elucidate the relation between the heterogeneity and the thermal changes; moreover, TG and DSC were carried out on PPOTMDM and PMAA to compare the results. The onset temperature in the last stage in the TG curve of PMAA-net-POTM increases as the concentrations of DMF and POTMDM in the polymerization decrease. This is explained in terms of plasticizers effects. A single peak due to fusion of POTM chains appears in the DSC curves of most copolymers. However, it is not seen in the DSC curves of copolymers with high heterogeneity. This is explained in terms of the freezing of POTM chains by frozen heterogeneous moieties.     

Automata accepting primitive words

LeA be an automaton whose set of inputs equalsX (|X|≧2) and whose cardinality of the set of states equalsn (n≧2), and letQ be the set of all primitive words overX. ByT(A) we denote the language accepted byA. In this paper, we give the following results: