Crossover Critical Behavior in the Three-Dimensional Ising Model

The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by fluctuations of the order parameter. If the interaction range is finite, the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class. A variety of systems, including fluids and anisotropic ferromagnets, belongs to the three-dimensional Ising universality class. Recent numerical studies of Ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation-induced critical behavior and mean-field-type critical behavior. In this work, we compare these numerical results with a crossover Landau model based on renormalization-group matching. For this purpose we consider an application of the crossover Landau model to the three-dimensional Ising model without fitting to any adjustable parameters. The crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range (ten orders) of the scaled distance to the critical temperature. The dependence of the coupling constant on the interaction range, governing the crossover critical behavior, is discussed.     

Some functional equations originating from number theory

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.     

Ideals and Subalgebras in BCI-Algebras

We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal.AMS Subject Classification (1991): 06F35, 03G25.The second author was supported by the LG Yonam Foundation (1995).     

Evaluation of compatibility in polymer blend systems by simultaneous DSC-FTIR measurement

The concept of crystallization dynamics method evaluating the miscibility of binary blend system including crystalline component was proposed. Three characteristic rates, nucleation, crystal growth rates (N*, G*) and growth rate of conformation (G _c*) were used to evaluate the miscibility of PVDF/at-PMMA and PVDF/iso-PMMA by the simultaneous DSC-FTIR. N*, G* and G _c* depended remarkably on both temperature and blend fraction (ϕ_PMMA) for PVDF/at-PMMA system, which indicated the miscible system. PVDF/iso-PMMA showed small ϕ_PMMA dependency of N*, G* and G _c*, was estimated the immiscible system. The ΔT/T _m⁰ values, corresponding to Gibbs energy required to attend the constant G* and G _c*, evaluated from G* and G _c* showed the good linear relationships with different slope. The experimental results suggested that the concentration fluctuation existed in PVDF/iso-PMMA system.     

Characteristics of Ti0.97Co0.03O2:Sb0.01 dilute magnetic semiconducting thin films deposited at 500 °C by pulsed laser deposition

Epitaxial Ti_0.97Co_0.03O₂:Sb_0.01(TCO:Sb) films were deposited on R-Al₂O₃ (1 1 0 2) substrates at 500 °C in various deposition pressures by pulsed laser deposition. The solubility of cobalt within the films increases with decreasing deposition pressure at a deposition temperature of 500 °C. The TCO:Sb films deposited at 5×10⁻⁶ Torr exhibit a p-type anomalous Hall effect having a hole concentration of 6.1×10²²/cm³ at 300 K. On the other hand, films deposited at 4×10⁻⁴ Torr exhibits an n-type anomalous Hall effect having an electron concentration of about 1.1×10²¹/cm³. p- or n-type DMS characteristics depends on the change of the structure of TCO:Sb films and the solubility of Co is possible by controlling the deposition pressure.     

Codes Over the p-adic Integers

We study codes over the p-adic integers and correct errors in the existing literature. We show that MDS codes exist over the p-adics for all lengths, ranks and p. We show that self-dual codes exist over the 2-adics if and only if the length is a multiple of 8 and that self-dual codes exist over the p-adics with p odd if and only if the length is 0 (mod 4) for p ≡ 3 (mod 4) and 0 (mod 2) for p ≡ 1 (mod 4).     

In‐line monitoring of UV photopolymerization with a quartz crystal resonator

An in‐line monitoring device using a quartz crystal resonator for thin film polymerization was proposed, and its performance has been evaluated by implementing in the UV polymerization of 2‐hydroxyethyl methacrylate with a photoinitiator of 1‐chloroanthraquinone. Because the variation of resonant resistance of the resonator is proportional to the square root of viscosity change that is closely related to the polymerization degree, the resistance can be used as a measure of the polymerization degree. The resistance measurements were compared with the outcome of instrumental analyses of polymerization degree using an FTIR spectrometer and a gel permeation chromatograph. The experimental results showed that the resistance measurements were consistent with the experimental outcome of the instrumental analyses, and this indicates the effectiveness of the proposed device. Owing to the simplicity and availability of the resonator system, its wide utilization in the monitoring of a variety of film polymerization processes, including photoresistor application, is expected. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2428–2439, 2006     

Synthesis and luminescence characteristics of conjugated dendrimers with 2,4,6‐triaryl‐1,3,5‐triazine periphery

We have synthesized conjugated dendrimer with triazine peripheries, and their luminescence properties were investigated. The dendrimers consist of dendritic triazine wedges for electron transport, distyrylbenzene core as an emitting moiety, and t‐butyl peripheral groups for good processing properties. The dendrimers have LUMO values of about ?2.7 eV possibly because of the triazine moiety with high electron affinity. Photoluminescence study indicates that energy transfer occurs from the triazine wedges to the stilbene bridge, and finally to the core chromophore units due to a cascade decrease of bandgap from the peripheral wedge to core moiety. Therefore, the emission wavelength was determined by the structure of the core unit. The energy transfer efficiency of distyrylbenzene‐cored dendrimers was about 75 and 55% for Trz‐1GD‐DSB and Trz‐2GD‐DSB, respectively. A preliminary electroluminescence property also was investigated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 254–263, 2006