On some inequalities for Doob decompositions in Banach function spaces

Let ${\Phi : \mathbb{R} \to [0, \infty)}Let F: \mathbbR ? [0, ￥){\Phi : \mathbb{R} \to [0, \infty)} be a Young function and let f = (f_n)_n ? \mathbbZ₊{f = (f_n)_n\in\mathbb{Z}_{+}} be a martingale such that F(f_n) ? L₁{\Phi(f_n) \in L_1} for all n ? \mathbbZ₊{n \in \mathbb{Z}_{+}} . Then the process F(f) = (F(f_n))_n ? \mathbbZ₊{\Phi(f) = (\Phi(f_n))_n\in\mathbb{Z}_{+}} can be uniquely decomposed as F(f_n)=g_n+h_n{\Phi(f_n)=g_n+h_n} , where g=(g_n)_n ? \mathbbZ₊{g=(g_n)_n\in\mathbb{Z}_{+}} is a martingale and h=(h_n)_n ? \mathbbZ₊{h=(h_n)_n\in\mathbb{Z}_{+}} is a predictable nondecreasing process such that h ₀ = 0 almost surely. The main results characterize those Banach function spaces X such that the inequality ||h_￥||_X ￡ C ||F(Mf) ||_X{\|{h_{\infty}}\|_{X} \leq C \|{\Phi(Mf)} \|_X} is valid, and those X such that the inequality ||h_￥||_X ￡ C ||F(Sf) ||_X{\|{h_{\infty}}\|_{X} \leq C \|{\Phi(Sf)} \|_X} is valid, where Mf and Sf denote the maximal function and the square function of f, respectively.     

Over-doping of Tl2Ba2CuO6 due to charge transfer Tl-(Cu-O)

Superconductivity was observed in La substituted Tl₂Ba₂CuO₆. Both T_c and unit cell dimension, a, increase with increasing La concentration, indicating that an over-doping state in Tl₂Ba₂CuO₆, which was due to charge transfer Tl^3−t-(Cu-O)^p as supported from XPS measurements, was relieved by La substitution for Ba.     

Magneto-volume effect in invar-type amorphous Fe—B alloys

Amorphous Fe_100-xB_x(11.5 ≦ x ≦ 22) alloys having the invar characteristics were prepared by a single roller quenching method to investigate the magneto-volume effect. Forced volume magnetostriction, ?ω/?H, increased remarkably with decreasing boron content and the maximum value obtained was about 90 × 10^?10 Oe^?1 at 11.5 at.% boron. The estimated value of the pressure dependence of the Curie temperature, ?T_c/?P, was considerably large, being comparable to those of crystalline FeNi invar alloys. The ?T_c/?P curve plotted as a function of T_c approximately fitted Wohlfarth's expression.     

Grayscale-Memory Spatial Light Modulator with Polymer-Dispersed Phase-Transition Liquid Crystal

A new storage-type spatial light modulator has been developed which uses a polymer-dispersed phase-transition liquid crystal film and a photoconductor for high-brightness projection displays. The liquid crystal film containing micrometer-sized chiral nematic liquid crystal domains subdivided by a unique honeycomb polymer network functions as a memory layer for an input image. The liquid crystal domains independently maintain the binary alignment states in the opaque (light-scattering) cholesteric phase or transparent nematic phase. Grayscale images can be displayed according to the spatial distribution of the bistable liquid crystal domains. The device exhibits rapid response of a few ms and a limiting resolution of 32 lp/mm. It has the advantages of high transmittance without polarizers and ease of fabrication due to the free-standing liquid crystal film.     

Morphology control of liquid crystalline composite gels based on molecular self-assembling kinetics

Liquid crystalline composite gels consisting of a low molecular mass gelator and a low molecular mass liquid crystal were prepared by two types of gelation method (continuous cooling and isothermal gelating), which provide different molecular self-assembling kinetics of the low molecular mass gelator as gelation proceeds. Optical microscopy and atomic force microscopy revealed that numerous fine strands of the one-dimensionally assembled low molecular mass gelators were formed in the composite gels for both the continuous cooling method and the isothermal gelating method. However, the thinner strands were more homogeneously dispersed in the isothermal gelation product at an appropriate temperature, than in the continuous cooling process. This difference in dispersion state of the strands was shown (by polarizing optical microscopy) to have a significant influence on the molecular alignment of the low molecular mass liquid crystal in the liquid crystalline composite gel. The electro-optical response and light scattering-transmitting switching, of the liquid crystalline composite gel in an applied electric field was extremely dependent on the morphology of the gelators. High contrast light switching was achieved for the composite prepared by isothermal gelation. The response time of electro-optical switching was less than 100 µs under 30 V_rms.     

THE ROLE OF A PHOTOCHEMICAL REACTION ON THE DEACTIVATION OF EXCITED 4,5',8-TRIMETHYLPSORALEN IN ETHANOL

The transient absorption of an intermediate R which is formed from an excited state higher than the lowest triplet state was observed in an ethanol solution of 4,5′,8-trimethylpsoralen (TMP). The temperature effects on the fluorescence yield φ_F for TMP and on the initial absorbance D_R of R were studied and it was found that D_R increases with increasing temperature whereas φ_F decreases. These results indicate that a photochemical reaction plays an important role on the deactivation of TMP in the excited singlet state     

Heavy-atom effects on hydrogen-atom transfer reaction from monohalogenated phenols to triplet 7,8-benzoquinoline

The rate constants and the radical yields for the hydrogen-atom transfer reaction from four monohalogenated phenols to triplet 7,8-benzoquinoline were determined by an emission—absorption flash technique. The rate constants are of the order of 10⁹ M⁻¹ s⁻¹ except for 2-bromophenol, and the radical yield Φ_rt decreases on halogen substitution. In the case of monobromophenols, Φ_rt is sensitive to the position of the bromine atom. The rate constant of free radical recombination increases with decreasing Φ_rt. Such heavy-atom effects are explained in terms of the heavy-atom-induced spin relaxation of the triplet radical pair.