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.     

Inner Radius of Univalence for a Strongly Starlike Domain

 The inner radius of univalence of a domain D with Poincaré density ρ _D is the possible largest number σ such that the condition ∥ S _f ∥ _D  = sup _{w∈ D} ρ _D (w) ⁻²∥ S _f (z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S _f is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms of the order α. The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088. A part of this work was carried out during his visit to the University of Helsinki under the exchange programme of scientists between the Academy of Finland and the JSPS. Received November 26, 2001; in revised form September 24, 2002 Published online May 9, 2003     

Photoluminescence properties of trace amounts of Pr and Tb in yttria-stabilized zirconia

We have investigated the photoluminescence (PL) properties of trace amounts of Pr and Tb in single-crystal samples of yttria-stabilized zironia (YSZ), and found that Pr of the order of 10⁻⁶ mass% and Tb of the order of 10⁻⁵ mass% in YSZ can be detected by the PL spectroscopy. The PL spectra of the YSZ samples for the 280 nm excitation were comprised of several peaks and a broad emission. The peaks were attributed to transitions of Pr³⁺ and Tb³⁺ in the YSZ samples, whereas the broad emission seemed to be attributed to the yttria-associated oxygen vacancies. The peak intensities corresponded to the amounts of Pr and Tb in the YSZ samples, the amounts of which were analyzed by glow discharge mass spectrometry. In the PL excitation spectra, but not in the photoabsorption spectra, small peaks at 376 and 381 nm were observed, and were attributed to the transitions of Tb³⁺ in the YSZ samples. The results of the PL excitation spectra corresponding to the Pr³⁺ line emissions suggest that the charge transfer occurs between the YSZ and Pr ion in it. The trace amounts of these lanthanoids in YSZ would disturb the decay process of the photoinduced electrons to the yttria-associated oxygen vacancies.     

Electroweak radiative corrections to the top quark decay

The top quark, once produced, should be an important window to the electroweak symmetry breaking sector. We compute electroweak radiative corrections to the decay processt→b+W ⁺ in order to extract information on the Higgs sector and to fix the background in searches for a possible new physics contribution. The large Yukawa coupling of the top quark induces a new form factor through vertex corrections and causes discrepancy from the tree-level longitudinalW-boson production fraction, but the effect is of order 1% or less form _H<1 TeV.     

Proper action on a homogeneous space of reductive type

Partially supported by Grant-in-Aid for Scientific Research (No. 63740074)     

Synthesis of spherical and hemispherical sugar‐containing poly(ornithine) dendrimers

A novel sugar‐containing poly(ornithine) dendrimer is synthesized for possible antigen delivery and related applications. The dendrimer contains an ornithine dendron as interior scaffolding and oligosaccharides on the periphery, which provide an attachment site for a peptide antigen. Maltose or lactose is bound to both hemispherical and spherical poly(ornithine) dendrimer generation 3 (G3) by reductive amination between its reducing end and the peripheral amino group of the dendrimer using a borane‐pyridine complex in a buffer solution at 50 °C. The degree of substitution of sugar is changed by varying the molar ratio of sugar to dendrimer. When the surface of spherical poly(ornithine) dendrimer G3 is modified by binding β‐alanine to the 16 amino groups, highly substituted maltose‐ or lactose‐β‐alanine‐poly(ornithine) dendrimer G3 is obtained in high yield after 7 days of reaction. The structures of these sugar‐containing dendrimers are characterized by NMR and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry analyses. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1400–1414, 2004     

Lithographic design of photosensitive polyarylates based on reaction development patterning

The factors affecting pattern‐forming properties in reaction development patterning were examined with polyarylates with various bisphenol moieties. The developability of the photosensitive polyarylates was dependent on the properties of the subtituent (R) in the bisphenol moieties. The development time decreased in the following order: R?C(CH₃)₂ > fluorenyl unit ? phenolphthalein unit > C(CF₃)₂ > SO₂. This order agreed with that of the reactivity between the polyarylates and ethanolamine, and these orders can be explained by pK_a of the bisphenol used to prepare the polyarylates. The development with NH₂? R′? OH resulted in successful positive‐tone pattern formation. However, pattern formation with the developers containing NH₂? R′? OCH₃ was unsuccessful. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2694–2706, 2006     

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: