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     

A convenient method for the preparation of α-vinylfurans by phosphine-initiated reactions of various substituted enynes bearing a carbonyl group with aldehydes

α-Vinylfurans were obtained by phosphine-initiated cyclization of various enynes bearing a carbonyl group at the ene end in the presence of various aldehydes, in moderate to high yields. The reaction may consist of 1,6-addition of phosphine to the enynes, ring closure, and Wittig reaction between the ylid resulting from cyclization and an aldehyde. Thus, various aldehydes were able to be used in the reaction. The reaction was influenced greatly by the substituents at the acetylene position (R¹) and the α-position of the carbonyl group (R³).     

Surfaces which contain helical geodesics

LetM be a complete smooth surface of constant mean curvature in the Euclidean 3-space. If there exists two helical geodesics onM through each point ofM, thenM is either a plane, a sphere, or a circular cylinder.     

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).     

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.