Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for ``infinite-dimensional second-order cone programs.' We consider as an example a long-step primal-dual algorithm based on the Nesterov-Todd direction. It is shown that this algorithm can be generalized along with complexity estimates to the infinite-dimensional situation under consideration. An application is given to an important problem of control theory: multi-criteria analytic design of the linear regulator. The calculation of the Nesterov-Todd direction requires in this case solving one matrix differential Riccati equation plus solving a finite-dimensional system of linear algebraic equations on each iteration. The number of equations and unknown variables of this algebraic system is m+1, where m is a number of quadratic performance criteria. Key words.polynomial-time primal-dual interior-point methods – JB-algebras – infinite-dimensional problems – optimal control problemsThis author was supported in part by DMS98-03191 and DMS01-02698.This author was supported in part by the Grant-in-Aid for Scientific Research (C) 11680463 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.Mathematics Subject Classification (1991):90C51, 90C48, 34H05, 49N05     

Sonochemical preparation of composite nanoparticles of Au/gamma-Fe2O3 and magnetic separation of glutathione

We prepared Au/gamma-Fe2O3 composite nanoparticles by sonochemically reducing Au(III) ions employing no stabilizer in the aqueous solution to form stable Au nanoparticles and allowing them to attach onto the surface of gamma-Fe2O3 particles with an average size of 21 nm. Size of the formed Au nanoparticle depended on the initial concentration of Au(III) ions. The number of the Au nanoparticles, supported on each gamma-Fe2O3 particle was controlled by changing the relative amounts of Au(III) ions and gamma-Fe2O3 particles. The composite nanoparticles exhibited a high affinity with glutathione, a tripeptide with mercapto group so that separation and manipulation of glutathione in aqueous solutions could be performed by application of external magnetic field. Because the surfaces of the Au nanoparticles were not shielded by any stabilizers, or naked, sonochemically prepared Au/gamma-Fe2O3 composite nanoparticles seemed to show stronger affinity to the glutathione than those by the radiochemical method.     

Evolution of host-parasitoid network through homeochaotic dynamics

Host-parasitoid systems with evolving mutation rates are studied. By increasing the growth rate of hosts, the diversity of both species is maintained dynamically. For the lower growth rate, diversity is brought about by mere parasitism. The average mutation rate for parasites is elevated to a high value, while that for hosts is suppressed at a low level. For the higher growth rate, the mutation rates for both hosts and parasites are elevated to form a symbiotic cluster connected by on-going mutation. This symbiotic state is sustained through a chaotic oscillation keeping some coherency among species. For a flat landscape for hosts, dynamical clustering of oscillation is observed. Lyapunov spectra of such oscillations show that high dimensional chaos with small positive exponents underlies in the symbiotic state. This weak high dimensional chaos, termed "homeochaos," is essential to the maintenance of symbiosis in ecosystems.     

Achievement of a 920-MHz high resolution NMR

We have developed a 920-MHz NMR system and performed the proton NMR measurement of H(2)O and ethylbenzene using the superconducting magnet operating at 21.6 T (920 MHz for proton), which is the highest field produced by a superconducting NMR magnet in the persistent mode. From the NMR measurements, it is verified that both homogeneity and stability of the magnet have a specification sufficient for a high resolution NMR.     

Optical-Optical Double Resonance Spectroscopy of the 1g(P1)-AΠ (1u)-XΣg Transition of I2

Optical-optical double resonance spectroscopy was used to study the 1_g(³P₁) ion-pair state of I₂ correlating to I⁻(¹S)+I⁺³P₁) at the dissociation limit. We gained access to the 1_g(³P₁) state though the A³Π (1_u) state in the (1+1) photon-excitation scheme. The pump laser excited the A³Π (1_u)-X¹Σ_g⁺ transition at a fixed frequency for state selection. The probe laser was scanned to detect the 1_g(³P₁)-A³Π (1_u) resonance by monitoring the ultraviolet emission from the 1_g(³P₁) state at 278 nm. The 1_g(³P₁) state was observed in a vibrational progression consisting of P and R doublets. An energy level analysis was carried out for the 1_g(³P₁) state in the 0≤ v ≤ 14 and 12≤J≤135 range, which led to a set of molecular parameters including the Ω-doubling constant. The Ω-doubling of the 1_g(³P₁) state was discussed by the pure precession model and interpreted to occur through the heterogeneous coupling with the 0_g⁻(³P₁) state correlating to the same ionic asymptote.     

Spacetime correlation functions of dynamic speckles produced by a series of moving phase screens

Spacetime correlation functions of the time-varying speckle intensity have been evaluated for the case where speckle patterns are produced in the Fresnel diffraction region by light propagating through a series of moving random-phase screens. The correlation functions are given by a set of recursion formulae which are useful for numerical computations. Three statistical quantities relating to the motion of speckle patterns are derived to examine the relationship between the velocity distribution of the phase screens and the temporal behaviour of resultant speckle patterns. It is found that the velocity differences between the phase screens have a strong effect on both the decorrelation of speckle patterns and the fluctuating speed of the speckle intensity.     

SDiff(2) Toda equation — Hierarchy,Tau function,and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS ¹×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.     

An anomalous emission excited near the absorption edge of pyrene crystals

Emission spectra and decay times of the fluorescence excited at the absorption edge region in pyrene crystals were measured. At liquid nitrogen temperature, the fluorescence under the excitation at 390 nm is considered as the excimer emission and its band peak shifts a little to the short wavelength in comparison with that of the excimer emission under the excitation at 360 nm. The emission decay times under the excitation at the 390 nm and 360 nm are about 155 ns and 180 ns, respectively, at liquid nitrogen temperature. The former decay time changes its value abruptly near 127 K. This abrupt change of the decay time may be due to the phase transition in pyrene crystals.     

Impaired pulmonary blood flow distribution in congestive heart failure assessed using synchrotron radiation microangiography

Synchrotron radiation microangiography is a powerful tool for assessing adverse changes in pulmonary vessel density associated with primary pulmonary hypertension (PH). Congestive heart failure (CHF) leads to a `secondary' onset of PH, yet it is unknown whether secondary PH is also associated with reduced vessel density. This study utilized synchrotron radiation to assess both pulmonary vessel density and endothelial function in a Dahl rat model of CHF with secondary PH. High salt‐fed Dahl salt‐sensitive (Dahl‐S) and salt‐resistant (Dahl‐R) rats were anesthetized and microangiography was performed to assess the pulmonary vessel density and vascular responses to (i) sodium nitroprusside (5.0 µg kg^?1 min^?1), (ii) acetylcholine (3.0 µg kg^?1 min^?1) and (iii) ET‐1_A receptor blockade, BQ‐123 (1 mg kg^?1). Dahl‐S rats developed CHF and secondary PH as evident by endothelial dysfunction, impaired vasodilatory responses to acetylcholine, enhanced vasodilatory responses to BQ‐123 and extensive pulmonary vascular remodeling. Consequently, the pulmonary vessel density was adversely reduced. Interestingly, the etiology of secondary PH manifests with structural and functional changes that are comparable with that previously reported for primary PH. One important discrepancy, however, is that ET‐1 modulation of pulmonary vessels is most striking in vessels with a diameter range of 100–200 µm in secondary PH, in contrast to a range of 200–300 µm in primary PH. Such discrepancies should be considered in future studies investigating primary and secondary forms of PH.     

Buffer-less Cu(In,Ga)Se2 solar cells by band offset control using novel transparent electrode

Cu(In,Ga)Se₂ (CIGS) solar cells without buffer layers have been demonstrated. Currently, CdS, Zn(O,S,OH), ZnS, or InS buffer layers are used in high efficiency CIGS solar cells to suppress interface recombination. One of the important parameters to reduce the recombination is the conduction band offset (CBO) between the buffer and CIGS layers. In this study, we have proposed the use of a novel transparent conductive oxide (TCO) which can control the CBO to reduce interface recombination and eliminate the buffer layers. The device simulation was used to verify the effect of CBO control theoretically. Then, the novel TCO material of ZnO_1?xS_x:Al prepared by co-sputtering of ZnO:Al₂O₃ and ZnS targets was fabricated to verify the CBO effect experimentally. The efficiency of a CIGS solar cell with a ZnO:Al/CIGS/Mo/soda-lime glass structure, i.e. buffer-less structure using a conventional TCO, was significantly low because of severe shunting. In contrast, the use of ZnO_1-xS_x:Al instead of ZnO:Al increased the shunt resistance of the CIGS solar cell, resulting in higher open-circuit voltage and efficiency. The result is the first proof of the concept of the buffer-less CIGS solar cells.