On the Whitham Equations for the Defocusing Nonlinear Schrodinger Equation with Step Initial Data

The behavior of solutions of the finite-genus Whitham equations for the weak dispersion limit of the defocusing nonlinear Schrodinger equation is investigated analytically and numerically for piecewise-constant initial data. In particular, the dynamics of constant-amplitude initial conditions with one or more frequency jumps (i.e., piecewise linear phase) are considered. It is shown analytically and numerically that, for finite times, regions of arbitrarily high genus can be produced; asymptotically with time, however, the solution can be divided into expanding regions which are either of genus-zero, genus-one, or genus-two type, their precise arrangement depending on the specifics of the initial datum given. This behavior should be compared to that of the Korteweg-de Vries equation, where the solution is divided into regions which are either genus-zero or genus-one asymptotically. Finally, the potential application of these results to the generation of short optical pulses is discussed: The method proposed takes advantage of nonlinear compression via appropriate frequency modulation, and allows control of both the pulse amplitude and its width, as well as the distance along the fiber at which the pulse is produced     

Short-step synthesis of tamoxifen and its derivatives via the three-component coupling reaction and migration of the double bond

The anti-tumor agent, tamoxifen, is easily synthesized by the successive allylation of benzaldehyde and the Friedel-Crafts alkylation reaction of anisole with the intermediary homoallyl silyl ethers, followed by the migration of the double bond to form the desired tetra-substituted ethylenes. Several derivatives of tamoxifen are also produced according to a similar synthetic strategy.     

Discrimination of poly(vinyl chloride) samples with different plasticizers and prediction of plasticizer contents in poly(vinyl chloride) using near-infrared spectroscopy and neural-network analysis.

In the recycling of poly(vinyl chloride) (PVC), it is required to discriminate every plasticizer for quality control. For this purpose, the near-infrared spectra were measured for 41 kinds of PVC samples with different plasticizers (DINP, DOP, DOA, TOTM and Polyester) and different plasticizer contents (0-49%). A neural-network analysis was applied to the near-infrared spectra pretreated by second-derivative processing. They were discriminated from one another. The neural-network analysis also allowed us to propose a calibration model which predicts the contents of plasticizers in PVC. The correlation coefficient (R) and the root-mean-square error of prediction (RMSEP) for the DINP calibration model were found to be 0.999 and 0.41 wt%, respectively. In comparison, a partial least-squares regression analysis was carried out. The R and RMSEP of the DINP calibration model were calculated to be 0.993 and 1.27 wt%, respectively. It is found that a near-infrared spectra measurement combined with a neural-network analysis is useful for plastic recycling.     

Precise synthesis of porphyrin array scaffolding polyisocyanides

Aryl isocyanides bearing free‐base and metallo‐porphyrins were prepared and polymerized with a Pd–Pt μ‐ethynediyl complex as the initiator to give polymers with narrow polydispersity indices. The molecular weights of the resulting polymers were precisely controlled by the initial feed ratio of the porphyrin monomer to the initiator. The UV–VIS spectra suggested that the porphyrin pendants are regularly arranged to form stacked columns. Metallo‐porphyrin polymers were also prepared by reacting free‐base porphyrin polymers with metal salts. The successive reactions of free‐base and zinc‐porphyrin monomers resulted in the formation of diblock polymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 585–595, 2006     

Preparation and certification of the new reference materials; plastics (disk form, JSAC 0621-0625) for determination of mercury using x-ray fluorescent analysis.

The Japan Society for Analytical Chemistry has developed some new plastic certified reference materials (CRMs) for the analysis of mercury in polyester disks using XRF analysis. These CRMs (named as JSAC 0621-0625) were prepared by casting polyesters including a toluene solution of organometallic compounds as a standard. Concentrations of the five levels of mercury ranged from 0 to 250 mg/kg. Homogeneity tests of prepared disks had shown excellent results. Interlaboratory comparison study for the certification was performed by 15 laboratory participants. The z-scores in robust statistical method was applied for the evaluation of outliers. The certified values were assigned after discarding outliers. The uncertainties of certified values were determined as the confidence levels of 95%.     

Hasse-Witt matrices of Fermat curves

Let m be an integer with m3. Let K and K be perfect fields of characteristic p and p such that (p,m)=1 and (p,m)=1, respectively. Moreover let A and A be algebraic function fields over K and K defined by x^m+y^m=a(0, ak) and x^m+y^m=a(a0 ak), respectively. Put g=(m–1)(m–2)/2. Denote by M(K,p,a) and M(K,p,a) the Hasse-Witt matrices of A and A with respect to the canonical bases of holomorphic differentials. Then we show that if p+p0(mod.m) then rank M(K,p,a)+rank M(K,p,a)=g and if pp1 (mod.m) then rank M(K,p,a)=rank M(K,p,a).