Large time behavior of small solutions to subcritical derivative nonlinear Schrödinger equations

We consider the derivative nonlinear Schrödinger equations

where the coefficient satisfies the time growth condition

is a sufficiently small constant and the nonlinear interaction term consists of cubic nonlinearities of derivative type

where and . We suppose that the initial data satifsfy the exponential decay conditions. Then we prove the sharp decay estimate , for all , where . Furthermore we show that for there exist the usual scattering states, when and the modified scattering states, when

     

UV dose measurements of photosensitive dermatosis patients by polycrystalline GaN-based portable self-data-acquisition UV monitors

We have developed a UV monitor with polycrystalline (poly-) gallium nitride (GaN) UV sensors and evaluated its performance from the viewpoint of its effectiveness for use with photosensitive dermatosis patients. The poly-GaN UV sensor is sensitive to UV light from 280 to 410 nm even without optical filters. The UV monitor is a portable self-data-acquisition instrument with a minimum detection level (defined as average UV intensity over 290 to 400 nm) of 2 microW/cm2 and can store UV dose data for 128 days. It allows easy measurement of four orders of magnitude of ambient UV intensity and dose from indoor light to direct solar radiation in summer. Trial use of the UV monitor by five xeroderma pigmentosum patients started in June 2000 and was carried out for 1 year. It was demonstrated that the UV monitor was useful in improving their quality of life.     

A cyclic oligophenylene containing two 1,8-naphthalene units bridged by two face-to-face biphenyl linkages exhibiting unusual strain and pi-pi interaction

1,8-[1,8-Naphthalenediylbis(4',4-biphenyldiyl)]naphthalene, a very stable strained cyclophane, has been synthesized in moderate yield using the copper-catalyzed coupling of 1, 8-bis(4-(tributylstannyl)phenyl)naphthalene. The X-ray analysis of the titled compound discloses bent p,p'-biphenylylene chains with splayed naphthalene rings, and the p,p'-biphenylylene chains located face-to-face indicate a fairly strong pi-pi interaction.     

Anomalous spatio-temporal chaos in a two-dimensional system of nonlocally coupled oscillators

A two-dimensional system of nonlocally coupled complex Ginzburg-Landau oscillators is investigated numerically for the first time. As previously shown for the one-dimensional case, this two-dimensional system exhibits anomalous spatio-temporal chaos characterized by power-law spatial correlations. In this chaotic regime, the amplitude difference between neighboring elements displays temporal noisy on-off intermittency. The system is also spatially intermittent in this regime, as revealed by multiscaling analysis: The amplitude field is multiaffine and the difference field is multifractal. Correspondingly, the probability distribution function of the measure defined for each field is strongly non-Gaussian, exhibiting scale-dependent deviations in the tail due to intermittency. (c) 1999 American Institute of Physics.     

Hydrodynamic resistance of concentration polarization boundary layers in ultrafiltration

The influence of concentration polarization on the permeate flux in the ultrafiltration of aqueous Dextran T70 solutions can be described by (i) the osmotic pressure model and (ii) the boundary layer resistance model. In the latter model the hydrodynamic resistance of the non-gelled boundary layer is computed using permeability data of the Dextran molecules obtained by sedimentation experiments. It is shown both in theory and experiment that the two models are equivalent.     

Application of pattern recognition to structure-activity problems: Use of minimal spanning tree

A graph-theoretical algorithm based on the minimal spanning tree (MST) is applied to structure—activity problems. The method is helpful in interpreting the results of cluster analysis, and becomes useful by combining with the mapping method that illustrates approximations of a multidimensional data structure. The antibacterial spectra of cephalosporins are analyzed by the MST approach and a linear mapping method. The main diameter obtained by MST gives the representative data set and clarifies the substituent effect on the antibacterial spectra. Relations between the central nervous system activity of benzodiazepine derivatives and their physicochemical parameters are also analyzed by MST and nonlinear mapping methods. These results for cephalosporins and benzodiazepines prove that MST is very useful in understanding the position of compounds in feature space and their activities.     

Photolysis of tris(trimethylsilyl)-phenylsilane in alcohols: A consecutive generation of sililene species

Photolysis of tris(trimethylsilyl)phenylsilane, in alcohols yielded 1-aikoxy-1-phenyl-2, 2,2-trimethyldisilane, dialkoxyphenylsilane, hexamethyldistlane, and trimethylstlane as major products. The formation of the products was explained by a mechanssm which included the consecutive generatinn of phenyltrimethylsilylsilyleses and alkoxyphenylsilylenes.     

Charge-order pattern of the low-temperature phase from a monoclinic single domain of NaV2O5 uniquely determined by resonant x-ray scattering

The present resonant x-ray scattering has been performed on a monoclinically split single domain of NaV(2)O(5). The observation of a critically enhanced contrast between V(4+) and V(5+) ions has led us to the unequivocal conclusion of the charge-order pattern of the low-temperature phase of NaV(2)O(5) below T(c) = 35 K. In spite of the possible four types of configuration of the zigzag-type charge-order patterns in the ab plane (A,A',B and B'), the stacking sequence along the c axis is determined as the AAA'A' type by comparison with model calculations.