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     

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     

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).     

Metal components analysis of metallothionein-III in the brain sections of metallothionein-I and metallothionein-II null mice exposed to mercury vapor with HPLC/ICP-MS

Mercury vapor is effectively absorbed via inhalation and easily passes through the blood–brain barrier; therefore, mercury poisoning with primarily central nervous system symptoms occurs. Metallothionein (MT) is a cysteine-rich metal-binding protein and plays a protective role in heavy-metal poisoning and it is associated with the metabolism of trace elements. Two MT isoforms, MT-I and MT-II, are expressed coordinately in all mammalian tissues, whereas MT-III is a brain-specific member of the MT family. MT-III binds zinc and copper physiologically and is seemed to have important neurophysiological and neuromodulatory functions. The MT functions and metal components of MTs in the brain after mercury vapor exposure are of much interest; however, until now they have not been fully examined. In this study, the influences of the lack of MT-I and MT-II on mercury accumulation in the brain and the changes of zinc and copper concentrations and metal components of MTs were examined after mercury vapor exposure by using MT-I, II null mice and 129/Sv (wild-type) mice as experimental animals. MT-I, II null mice and wild-type mice were exposed to mercury vapor or an air stream for 2 h and were killed 24 h later. The brain was dissected into the cerebral cortex, the cerebellum, and the hippocampus. The concentrations of mercury in each brain section were determined by cold vapor atomic absorption spectrometry. The concentrations of mercury, copper, and zinc in each brain section were determined by inductively coupled plasma mass spectrometry (ICP-MS). The mercury accumulated in brains after mercury vapor exposure for MT-I, II null mice and wild-type mice. The mercury levels of MT-I, II null mice in each brain section were significantly higher than those of wild-type mice after mercury vapor exposure. A significant change of zinc concentrations with the following mercury vapor exposure for MT-I, II null mice was observed only in the cerebellum analyzed by two-way analysis of variance. As for zinc, the copper concentrations only changed significantly in the cerebellum. Metal components of metal-binding proteins of soluble fractions in the brain sections were analyzed by size-exclusion high-performance liquid chromatography (HPLC) connected with ICP-MS. From the results of HPLC/ICP-MS analyses, it was concluded that the mercury components of MT-III and high molecular weight metal-binding proteins in the cerebellum of MT-I, II null mice were much higher than those of wild-type mice. It was suggested that MT-III is associated with the storage of mercury in conditions lacking MT-I, and MT-II. It was also suggested that the physiological role of MT-III and some kind of high molecular weight proteins might be impaired by exposure to mercury vapor and lack of MT-I and MT-II.     

Structures of americanol A and isoamericanol A having a neurotrophic property from the seeds of Phytolacca americana.

The structures of new neo-lignans, isoamericanol A (1) and americanol A (2) isolated from the seeds of Phytolacca americana have been elucidated on the basis of spectroscopic data and then confirmed by chemical correlation with the previously known isoamericanin A (3) and americanin A (4). Isoamericanol A, americanol A, and americanin A have been found to enhance choline acetyltransferase activity at 10(-5) M in a cultured neuronal cell system derived from fetal rat hemisphere.     

Regional cerebral blood flow measurement in brain tumors

The regional cerebral blood flow (CBF) was determined on seventeen patients with brain tumors. Ring type single photon emission CT (SPECT) was used following intravenous injection of 133Xe. Case materials included eleven meningiomas and six malignant gliomas. Evaluation was performed with emphasis on the following points; Correlation of the flow data within tumors to the angiographic tumor stains, Influence of tumors on the cerebral blood flow of the normal brain tissue, Correlation between degree of peripheral edema and the flow data of the affected hemispheres. There was significant correlation between flow data within tumors and angiographic tumor stains in meningiomas. Influence of tumors on cerebral blood flow of the normal tissue was greater in meningiomas than in gliomas. There was negative correlation between the degree of peripheral edema and the flow data of the affected hemisphere. It has been concluded that the measurement of CBF in brain tumors is a valuable method in evaluation of brain tumors.