Stabilization of continuum generation from normally dispersive nonlinear optical fibers for a tunable broad bandwidth source for optical coherence tomography

Continuum generation from normally dispersive ultrahigh-numerical-aperture fibers deteriorates in relatively short times, limiting its application as a practical optical source for high-resolution optical coherence tomography. We find that reversible light-induced structural modification of fiber optic materials, rather than permanent optical damage, is responsible for this deterioration. By examining how the optical properties of corresponding light-induced waveguides depend on pumping wavelength, we isolate a waveguide that is beneficial for stable continuum generation. The performance deterioration due to the formation of other waveguides can be reversed by overwriting them with this particular waveguide.     

Solvent and pH Effects on the Fluorescence of 7-(Dimethylamino)-2-Fluorenesulfonate

A novel water-soluble solvatochromic molecule, 7-(dimethylamino)-2-fluorenesulfonate (2,7-DAFS), was prepared by a three-step reaction from 2-nitrofluorene in good overall yield. The pH and solvent effects on the UV-VIS absorption and fluorescence spectra of 2,7-DAFS have been studied. Protonation of the dimethylamino group switches the absorption from intramolecular charge-transfer (ICT) to π → π* transition. The ground state pKa value of 2,7-DAFS was determined as 4.51. The fluorescence spectrum of the excited basic form, *(DAFS), shows a structureless single band with a large Stokes shift, whereas that of the acidic form, *(⁺HDAFS), exhibits a structured band with a small Stokes shift. The emission intensities of the basic and acidic forms versus pH/Ho plots show stretched sigmoidal curves and indicate that (1) the rate of deprotonation of *(⁺HDAFS) is comparable to the fluorescence decay of the species, and (2) the efficient proton-induced quenching of *(DAFS) fluorescence occurs. The pKa* was estimated as −1.7 from the fluorescence titration curve. The fluorescence maximum of *(DAFS) is blue-shifted as the polarity of solvent decreases. However, no clear dependency of the emission intensity and spectral half width, and thus fluorescence quantum yield, on the solvent polarity was revealed. It appears that the fluorescence sensitivity of 2,7-DAFS is 15 ∼ 25 times greater than the sensitivity of a widely utilized fluorescent probe, 5-(dimethylamino)-1-naphthalenesulfonate. This higher sensitivity, together with the ease of derivatization, would provide the fluorene-based fluorescent molecules significant advantages for a variety of applications.     

Two theorems on graceful trees

Let T be a tree on n vertices which are labelled by the integers in N = {1,2,…,n} such that each vertex of T is associated with a distinct number in N. The weight of an edge is defined to be the absolute value of the difference between the two numbers labelled at its end vertices. If the weights of all edges of T are distinct, we call T a graceful tree. In this note, two methods for constructing bigger graceful trees from a given one and a given pair of graceful trees are provided.     

Improved inhomogeneous Strichartz estimates for the Schrödinger equation

We study inhomogeneous Strichartz estimates for the Schrödinger equation for dimension n?3. Using a frequency localization, we obtain some improved range of Strichartz estimates for the solution of inhomogeneous Schrödinger equation except dimension n=3.     

The ac conductivity and complex impedance of CuO-doped (Ba0.5Sr0.5)TiO3 ceramic

The AC conductivity and complex impedance spectroscopy of CuO-doped (Ba_0.5Sr_0.5)TiO₃ ceramic were investigated. X-ray diffraction analysis showed that CuO-doped (Ba_0.5Sr_0.5)TiO₃ has a perovskite structure without any pyrochlore phase. Frequency dependent dielectric permittivity was discussed at a different temperature range. The activation energy was calculated and discussed through the Arrehnius equation from the ac conductivity with different frequency plots. CuO-doped (Ba_0.5Sr_0.5)TiO₃ ceramics have a negative temperature coefficient of resistivity. Dependence of impedance spectroscopy on frequency and temperature showed that the conduction process in the CuO-doped (Ba_0.5Sr_0.5)TiO₃ ceramic follows the thermally activated conduction mechanism.     

Stochastic resonance in an ion channel following the non-Arrhenius gating rate

Stochastic resonance (SR) is a novel cooperative phenomenon occurring in nonlinear systems due to coupling of an ambient noise and an external signal. Biological systems may use SR mechanism to detect the signal efficiently from an external environment. A number of studies have addressed the SR in artificial ion channels considering external voltages as noises. More important than these external noises is the internal, thermal noise which changes the channel conformations essential for biological functions. In this work, we consider that the channel gating rates follow a non-Arrhenius temperature dependence derived from experimental data of a real biological channel. Using the Monte-Carlo simulations, we find that in this channel SR occurs near a physiological temperature in a very distinctive manner compared with that for the Arrhenius gating model.     

1H and 13C NMR spectral assignments of novel chromenylchalcones

Several types of chalcones containing 2H‐chromen group were synthesized. Claisen–Schmidt condensation of 2H‐chromen‐3‐carbaldehydes (I) with methoxy substituted acetophenones afforded (E)‐3‐(2H‐chromen‐3‐yl)‐1‐(methoxyphenyl)prop‐2‐en‐1‐ones (chromenylchalcones, 1–7). Other types of chromenylchalcone, (E)‐1‐(6‐methoxy‐2H‐chromen‐3‐yl)‐3‐(methoxyphenyl)prop‐2‐en‐1‐ones (8–13) were also obtained between reaction of methoxy substituted benzaldehydes and 1‐(6‐methoxy‐2H‐chromen‐3‐yl)ethanone (II). Dichromenylchalcones (14–16) were also synthesized through the same reaction between aldehydes (I) and ketone (II). Their complete ¹H‐NMR and ¹³C‐NMR assignments are reported here and more polysubstituted chromenylchalcones synthesized or isolated from the natural sources in the future can be identified on the basis of the NMR data reported here. Copyright © 2012 John Wiley & Sons, Ltd.     

Indium trichloride mediated intramolecular Prins-type cyclization

[reaction: see text] Intramolecular Prins-type reactions of compounds having both functionalities of homoallyl alcohol and acetal moiety are described. The intramolecular Prins cyclizations were performed using indium trichloride in chloroform or 25% aqueous THF. Both 9-oxabicyclo[3.3.1]nonane and 3,9-dioxabicyclo[3.3.1]nonane compounds were successfully obtained in moderate yields.