Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces

Let H be a real Hilbert space and let T: H→2^H be a maximal monotone operator. In this paper, we first introduce two algorithms of approximating solutions of maximal monotone operators. One of them is to generate a strongly convergent sequence with limit vT⁻¹0. The other is to discuss the weak convergence of the proximal point algorithm. Next, using these results, we consider the problem of finding a minimizer of a convex function. Our methods are motivated by Halpern's iteration and Mann's iteration.     

Multiple ligand transfer reaction between [CpRu(L)(AN)2][PF6] (L=AN, CO, P(OMe)3; AN=acetonitrile) and CpFe(CO)L′X (L′=CO, PMe3, PMe2Ph, PMePh2, PPh3, P(OPh)3; X=Cl, Br, I)

Treatment of ruthenium complexes [CpRu(AN)₃][PF₆] (1a) (AN=acetonitrile) with iron complexes CpFe(CO)₂X (2a–2c) (X=Cl, Br, I) and CpFe(CO)L′X (6a–6g) (L′=PMe₃, PMe₂Ph, PMePh₂, PPh₃, P(OPh)₃; X=Cl, Br, I) in refluxing CH₂Cl₂ for 3 h results in a triple ligand transfer reaction from iron to ruthenium to give stable ruthenium complexes CpRu(CO)₂X (3a–3c) (X=Cl, Br, I) and CpRu(CO)L′X (7a–7g) (L′=PMe₃, PMe₂Ph, PMePh₂, PPh₃, P(OPh)₃; X=Br, I), respectively. Similar reaction of [CpRu(L)(AN)₂][PF₆] (1b: L=CO, 1c: P(OMe)₃) causes double ligand transfer to yield complexes 3a–3c and 7a–7h. Halide on iron, CO on iron or ruthenium, and two acetonitrile ligands on ruthenium are essential for the present ligand transfer reaction. The dinuclear ruthenium complex 11a [CpRu(CO)(μ-I)]₂ was isolated from the reaction of 1a with 6a at 0°C. Complex 11a slowly decomposes in CH₂Cl₂ at room temperature to give 3a, and transforms into 7a by the reaction with PMe₃.     

On a synchronization queue with two finite buffers

In this paper, we consider a synchronization queue (or synchronization node) consisting of two buffers with finite capacities. One stream of tokens arriving at the system forms a Poisson process and the other forms a PH-renewal process. The tokens are held in the buffers until one is available from each flow, and then a group-token is instantaneously released as a synchronized departure. We show that the output stream of a synchronization queue is a Markov renewal process, and that the time between consecutive departures has a phase type distribution. Thus, we obtain the throughput of this synchronization queue and the loss probabilities of each type of tokens. Moreover, we consider an extended synchronization model with two Poisson streams where a departing group-token consists of several tokens in each buffer. This revised version was published online in June 2006 with corrections to the Cover Date.     

Experimental evaluation of side-loads in LE-7A prototype engine nozzle

During development tests of the LE-7A prototype engine, severe side-loads were observed. The side-load peaks appeared only in certain limited conditions during start-up and shut-down transients. To investigate phenomena causing those severe side-loads observed in the LE-7A prototype engine nozzle, series of cold-flow tests and hot-firing tests as well as CFD analyses were conducted. As a result of the hot-firing tests, two different phenomena were found to cause severe side-loads in the LE-7A prototype engine nozzle. One was a restricted shock separation (RSS) flow structure and the other was a phenomenon termed “separation jump,” the rapid movement of the separation location in the vicinity of the step. A step was installed in the LE-7A prototype to supply film-cooling gas. Hot-firing test results showed that RSS can occur for a limited mixture ratio. Detailed flow structure of RSS on the nozzle surface was revealed by the cold-flow tests. Measured pressures and visualized images of cold-flow tests clarified the mechanism causing the separation jump. The key phenomenon ruling the separation jump was found to be the base flow behind the step. Based on the results of the present study, the latest LE-7A engine nozzle design has been changed to eliminate the severe side-load.

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Melt rheology and structure of silicone resins

Rheological investigation and X-ray analysis of silicone resins have been performed to get a fundamental understanding of the relationship between melt rheology and structure. Rheological properties of the melts of silicone resins were characterized by dynamic shear measurements. Samples were a series of silicone resins having different side groups, such as methyl, phenyl, methylphenyl, and propylphenyl. A time-temperature superposition based on the WLF rule was successfully applicable. The free volume fraction at the glass transition temperature and the free volume expansion coefficient were estimated from the C₁ and C₂ values of the WLF-equation. The loss modulus G′′ was found to be proportional to the angular frequency in a double-logarithmic plot over a wide frequency range. However, the storage modulus G′ exhibited a bending in a intermediate frequency region for all silicone resins. The shape of the G′ curve is unexpected from the results of gel permeation chromatography (GPC) and differential scanning calorimeter (DSC), which demonstrate that the silicone resins are amorphous polymers of relatively low molecular weight. To get more insight into the rheological properties of the silicone resins which indicate a heterogeneous structure, X-ray analysis was carried out. The X-ray measurement displayed two peaks, one broad peak around 4.5?Å of d-spacing which corresponds to a random amorphous structure, and the other higher intensity peak from 8.5?Å to 12?Å. This peak strongly depends on the size of organic side groups. From the rheological characterization and the X-ray analysis, it can be concluded that the silicone resins consist of two components; one of them shows a random amorphous and the other a regular structure even in the molten stage.     

Uniaxial elongational viscosity of PS/a small amount of UHMW-PS blends

A series of polystyrene (PS) and a small amount of ultra high molecular weight (UHMW) PS blends have been prepared by using tetrahydrofuran (THF). Matrix PS has an M_w of 423,000 (M_w/M_n= 2.36) and UHMW-PS has either an M_w of 3,220,000 (M_w/M_n= 1.05) or 15,400,000 (M_w/M_n=1.30) in the range of concentration from 0 wt% to 1.5 wt%. The influence of a small amount of UHMW on dynamic viscoelasticity was investigated. At the frequency lower than 0.001 rad/s, the enhancement of G′ was observed by the incorporation of a small amount of UHMW. And the degree of enhancement was in the order of M_w of UHMW and its concentration. The measurement of uniaxial elongational viscosity for the blends was performed and the effects of UHMW on strain-hardening properties were analyzed at equal strain-rate conditions. The concentration of UHMW where the strain-hardening becomes substantially stronger was determined. To get more insight into the cause of enhancement of strain-hardening at a certain concentration, the damping function from step-shear stress relaxation was measured. The influence of a small amount of UHMW on the damping function was found to be small. It was interpreted, from time- and strain-dependency points, that the enhancement of strain-hardening by a small amount of UHMW was governed by the long relaxation time. Received: 6 September 2000 Accepted: 11 January 2001     

DTμ Physics and Its Application

A high-intensity neutron source that is highly correlated spatially and with time and will be used for neutron scattering experiments can be obtained by dt m catalyzed fusion by enhancing the formation rate of dtμ molecules using a high-intensity pulsed laser to dtμ gas. This paper considers the use of dtμ fusion for fast ignition of inertial confinement fusion, and the possibility of ensuring energy balance in energy production. dt fusion can be quickly ignited by depositing dtμ fusion energy into a smaller space than is done in other methods, such as Z-pinch or heavy-ion fusion. Space propulsion can be obtained with a light fuel mass rather than by a fission repulsion system using the muons produced by annihilation of the anti-protons stored in liquid superfluid of condensed He. Using an extremely highly compressed target can create a source of high luminosity muons for muon–muon collider- and neutrino-oscillation experiments. This approach can eliminate the need for a super-conducting solenoidal for capturing the beam of pions and muons generated in a large target, and then these pions and muons can be manipulated by a laser beam instead of by employing RF manipulation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Cinnamomum verum J. Presl Bark Contains High Contents of Nicotinamide Mononucleotide

The global population is aging, and intervention strategies for anti-aging and the prevention of aging-related diseases have become a topic actively explored today. Nicotinamide adenine dinucleotide (NAD⁺) is an important molecule in the metabolic process, and its content in tissues and cells decreases with age. The supplementation of nicotinamide mononucleotide (NMN), an important intermediate and precursor of NAD⁺, has increased NAD⁺ levels, and its safety has been demonstrated in rodents and human studies. However, the high content of NMN in natural plants has not been fully explored as herbal medicines for drug development. Here, we identified that the leaf of Cinnamomum verum J. Presl (C. verum) was the highest NMN content among the Plant Extract Library (PEL) with food experience, using ultra-performance liquid chromatography–tandem mass spectrometry (UPLC-MS/MS). To validate this result, the extraction and quantitative analysis of bark, leaf, root, and stem of fresh C. verum was conducted. The results revealed that the bark had the highest NMN content in C. verum (0.471 mg/100 g). Our study shed light on the prospects of developing natural plants in the context of NMN as drugs for anti-aging and prevention of aging-related diseases. The future should focus on the development and application of C. verum pharmaceutical formulations.     

Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions

This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerical integrations for estimating conditional expectations at each space–time node. Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants.     

Trace determination of uranium preconcentrated using graphene oxide by total reflection X-ray fluorescence spectrometry

A new method based on dispersive microsolid phase extraction using graphene oxide (GO) as a solid adsorbent and total reflection X-ray fluorescence (TXRF) spectrometry is proposed for trace determination of uranium. In the developed methodology, a suspension of GO was injected into uranium-spiked multielement solutions including rubidium; after filtration, the membrane filter with collected GO was placed in a small volume of internal standard acid solution and the eluent containing uranium was deposited onto a fluorine resin-coated slide glass, which is a disposable sample stage. Using GO was effective for removal of rubidium from the measurement solution to avoid interference between Rb Kα peak and U Lα peak. The high enrichment factor of 150 enables obtaining uranium detection limits of 0.042, 0.087, and 0.12 μg L⁻¹ for ionic strength of 0.01, 0.1, and 1 mol L⁻¹, respectively. Such low detection limits were obtained by using a benchtop TXRF spectrometer with 5-min measurement. The proposed method is suitable for trace uranium determination in water, including high salinity samples.