Phase Transitions for the Growth Rate of Linear Stochastic Evolutions

We consider a discrete-time stochastic growth model on d-dimensional lattice. The growth model describes various interesting examples such as oriented site/bond percolation, directed polymers in random environment, time discretizations of binary contact path process and the voter model. We study the phase transition for the growth rate of the “total number of particles” in this framework. The main results are roughly as follows: If d≥3 and the system is “not too random”, then, with positive probability, the growth rate of the total number of particles is of the same order as its expectation. If on the other hand, d=1,2, or the system is “random enough”, then the growth rate is slower than its expectation. We also discuss the above phase transition for the dual processes and its connection to the structure of invariant measures for the model with proper normalization. Supported in part by JSPS Grant-in-Aid for Scientific Research, Kiban (C) 17540112.     

Heterocyclic effect for optical properties of naphthoquinone-based pigment: 2-methyl-3-heteroarylthio-1,4-naphthalenedione

Three novel naphthoquinone-based heterocyclic pigments, 2-methyl-3-[(1-methyl-1H-imidazol-2-yl)thio-1,4-naphthalenedione, (4-methyl-4H-1,2,4-triazol-3-yl)thio-1,4-naphthalenedione, and (1-methyl-1H-tetrazol-5-yl)thio]-1,4-naphthalenedione, are synthesized, and their optical properties in both solution and solid states are investigated. Depending on the heteroarylthio ring in the pigment, variation in optical properties is observed, e.g. characteristic colours for each pigment in the solution and solid states. The achiral pigment containing the 1-methyl-1H-tetrazol-5-yl ring exhibits a chiral space group and a CD signal in the solid state.     

Test compounds for detecting the silanol effect on the elution of ionized amines in reversed‐phase LC

The effectiveness of several basic compounds for testing silica‐based stationary phases was reviewed by applying them to recent columns for reversed‐phase HPLC. Most octadecylsilylated (C18) stationary phases, prepared as a base‐deactivated material from high‐purity silica gel with endcapping, provided excellent peak shape and column efficiency for the bases including benzylamine and amitriptyline that once caused problems and were subsequently employed for testing silanol activities. However, a cyclic tertiary amine, dextrometorphan, was eluted as an acceptable peak from only a few columns at neutral pH. Such a more sensitive probe is expected to contribute to further improvement of the stationary phase for reversed‐phase HPLC.     

Lightcone dualities for hypersurfaces in the sphere

In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space.     

Effects of loading conditions and temperature on environmental stress cracking of low-density polyethylene

Fracture mechanics was used to investigate the environmental stress cracking (ESC) of low density polyethylene (LDPE). Annealed and quenched samples were prepared; a single edge notch was made and the samples were fractured under constant load in a liquid methanol environment. The relation between the stress intensity factor K and the crack speed ? has been investigated. There is a large difference between annealed and quenched samples in the variation of this relation with temperature and applied load. The cause of this difference is discussed in detail. We propose that thermally activated molecular motion is essential to ESC of the annealed LDPE while stress concentration contributes markedly to ESC of the quenched LDPE.     

Lightlike surfaces of spacelike curves in de Sitter 3-space

The Lorentzian space form with the positive curvature is called de Sitter space which is an important subject in the theory of relativity. In this paper we consider spacelike curves in de Sitter 3-space. We define the notion of lightlike surfaces of spacelike curves in de Sitter 3-space. We investigate the geometric meanings of the singularities of such surfaces. Work partially supported by Grant-in-Aid for formation of COE. ‘Mathematics of Nonlinear Structure via Singularities’     

Highly efficient formation of metal and metal alloy particles from methyl metal compounds by a single pulse laser irradiation

Highly efficient processes for fine particle formation of metal alloys and metal oxides were developed using a high-power laser. In these processes, laser light was used only for the ignition of a thermal chain reaction. This reaction was suppressed by adding inert gases, and the suppression effect was in the order C₃H₈ > C₂H₆ > CH₄ > He > Ar > Xe. Oxygen accelerated the reaction because of the large exothermicity of the reaction of oxygen with methyl metal compounds.     

Asymptotic distribution of maximal autoregressive process with weight tending to 1

The maximal operator plays the similar role as the summation operator in the sense of stability of operation. So, we could discussARMA processes in the maximal operation by the same way as in the summation operation. However, many papers already treated with moving order statistics. In this paper, we discuss asymptotic behaviors of maximal autoregressive (MAR) processes with the weight tending to 1.