Far infrared optical properties of high Tc superconductors LnBa2Cu3Ox (Ln=Y, Ho, Er, Sm, GD, Dy, Eu, Pr)

Systematic measurements of the far infrared reflection spectra of high T_c superconductors LnBa₂Cu₃O_x for various Ln as shown in the title were performed. Infrared reflection spectra of tetragonal LnBa₂Cu₃O_x exhibit Reststrahlen vibration near 640, 590, 530, 355 and 250 cm^–1, common to these materials, and the spectra of the orthorhombic LnBa₂Cu₃O_x exhibit the characteristics of free carriers except PrBa₂Cu₃O_x with weak phonon structures near 617, 570, 317 and 285 cm^–1. PrBa₂Cu₃O_x is not a superconductor, and it has no characteristic broad band due to free carriers for all x in the range of 6 to 7. Lattice dynamical calculation was performed by the use of the shell model and the calculated results express quite well the characteristic features of infrared experiments.     

A Practical See-Through Head Mounted Display Using a Holographic Optical Element

This paper describes a practical method for design and fabrication of holographic optical elements (HOEs) as off-axis imaging optics. The authors have designed and fabricated a compact glass-like and see-through display using HOE and a total internal reflection prism. Observers can see through the display because wavelength selectivity of the HOE provides high transparency. Wave front of the HOE is designed by commercial software, though the actual fabrication method is not provided. The authors propose a practical method to fabricate HOEs, which can be applied to a wide range of imaging optics.This paper was originally presented at the 2nd International Conference on Optical Design and Fabrication, ODF2000 which was held on November 15–17, 2000 at the International Conference Center, Tokyo, Waseda University, Japan.     

Electrochemically regenerative visible light-induced reactivity of α-Fe2O3 films with Ag(core)–AgCl(shell) microcrystal composites

Ag(core)–AgCl(shell) microcrystal composites (Ag@AgCl) have been formed on an α-Fe₂O₃ film-coated SnO₂ electrode by a 2 step method consisting of the electrochemical reduction of Ag⁺ ions and the subsequent electrochemical oxidation. The synergy of α-Fe₂O₃ and Ag@AgCl gave rise to a high visible light-induced reactivity (λ_ex > 420 nm) for the oxidation of 2-naphthol (2-NAP) used as a model water pollutant in the presence and absence of oxygen. These findings were attributable to the function of Ag@AgCl composites as an excellent charge-separation promoter and built-in acceptor.     

Synthesis of 5,10-dideazaminopterin

The synthesis of 5,10-dideazaaminopterin by two independent routes is described. Condensation of the piperidine enamine of 4-p-carbomethoxyphenylbutyraldehyde ( 4 ) with ethoxymethylenemalononitrile followed by treatment of the resultant arylethylenaminomalononitrile ( 5 ) with methanolic ammonia produced 2-amino-3-cyano-5-p-carbomethoxyphenethylpyridine ( 6 ). Cyclization of the aminocyanopyridine with guanidine afforded 4-amino-4-deoxy-5,10-dideazapteroic acid ( 8 ). Coupling of the pteroate intermediate with glutamate yielded the target 5,10-dideazaaminopterin ( 10 ). Alternatively, reduction of 2,4-diamino-6-formyl-5-deazapteridine ( 11 ) with sodium borohydride gave the 6-hydroxymethyl compound 12 . Conversion to the bromide was followed by alkylation of dimethyl homoterephthalate to afford methyl 4-amino-4-deoxy-10-carbomethoxy-5,10-dideazapteroate ( 14 ). Decarboxylation with ester cleavage (sodium cyanide in dimethyl sulfoxide at 180°) also gave the diaminopteroic acid ( 8 ). 5,10-dideazaaminopterin ( 10 ) was an effective growth inhibitorof folate dependent bacteria, S. faecium and L. casei.     

Lie superalgebraic approach to super Toda lattice and generalized super KdV equations

We propose a super Lax type equation based on a certain class of Lie superalgebra as a supersymmetric extension of generalized (modified) KdV hierarchy. We are able to construct an infinite set of conservation laws and the consistent time evolution generators for generalized modified super KdV equations. Thefirst few of the conserved currents, the (modified) super KdV equation and the super Miura transformation are worked out explicitly in the case of twisted affine Lie superalgebraOSp(2/2)⁽²⁾.Partially supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (#01540246 and #01790203).RIFP will be known as Yukawa Institute for Theoretical Physics from June 8, 1990     

Theoretical study of resonant tunneling in rectangular double-, triple-, quadruple-, and quintuple-barrier structures

The transmission coefficient and the resonance condition in the one-dimensional rectangular double-, triple-, quadruple-, and quintuple-barrier structures are derived theoretically under the assumption of the constant tunneling effective mass. It is found that the resonance energies are different from the eigenvalues in the quantum well due to coupling between wells in the multiple-barrier (much more than triple-barrier) structures. It is confirmed that the transmission spectrum is a Lorentzian near to energies of resonance.     

Optimal consumption models in economic growth

We study the optimal consumption problem in the one-sector model of economic growth under uncertainty. We show the existence of a classical solution of the Hamilton-Jacobi-Bellman equation associated with the stochastic optimization problem, and then give an optimal consumption policy in terms of its solution.     

The Euler multiplicity and addition-deletion theorems for multiarrangements

The addition–deletion theorems for hyperplane arrangements,which were originally shown by Terao [J. Fac. Sci. Univ. TokyoSect. IA Math. 27 (1980) 293–320.], provide useful waysto construct examples of free arrangements. In this article,we prove addition–deletion theorems for multiarrangements.A key to the generalization is the definition of a new multiplicity,called the Euler multiplicity, of a restricted multiarrangement.We compute the Euler multiplicities in many cases. Then we applythe addition–deletion theorems to various arrangements,including supersolvable arrangements and the Coxeter arrangementof type A₃, to construct free and non-free multiarrangements.