[en] This paper studies the vibrational behavior of nonuniform single-walled carbon nanotube (SWCNT) carrying a nanoparticle. A nonuniform cantilever beam with a concentrated mass at the free end is analyzed according to the nonlocal Timoshenko beam theory. A governing equation of a nonuniform SWCNT with attached mass is established. The transfer function method incorporating with the perturbation method is utilized to obtain the resonant frequencies of a vibrating nonlocal cantilever-mass system. The effects of the nonlocal parameter, taper ratio and attached mass on the natural frequencies and frequency shifts are discussed. Obtained results indicate that the sensitivity of the frequency shifts on the attached mass increases when the length-to-diameter ratio decreases. Tapered SWCNT possesses higher fundamental frequencies if the taper ratio becomes larger.

[en] An explicit N-fold Darboux transformation with multi-parameters for coupled mKdV equation is constructed with the help of a gauge transformation of the Ablowitz-Kaup-Newell-Segur (AKNS) system spectral problem. By using the Darboux transformation and the reduction technique, some multi-soliton solutions for the complex mKdV equation are obtained

[en] A Darboux transformation of the generalized derivative nonlinear Schrödinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schrodinger equation are explicitly given. (general)

[en] A new coupled integrable dispersionless equation is presented by considering a spectral problem. A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems. As an application, the N-soliton solution of the coupled integrable dispersionless equation is explicitly given

[en] Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)–(G/G') expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method

[en] Highlights: • Red-emissive carbon dots (R-CDs) are synthesized via simple solvothermal treatment. • R-CDs show stable long-wavelength dual emission centered at 597 and 645 nm. • The as-prepared R-CDs have high photoluminescence quantum yield of 33%. • R-CDs exhibit fast sensitive selective fluorescence response to veterinary drugs. • R-CDs are potentially useful for ratiometric fluorescence sensors. Carbon dots have been rapidly developed as a kind of luminescent nanomaterials. However, methods for the synthesis of long-wavelength-emissive carbon dots are still not mature enough. Meanwhile, developing a fast and highly sensitive method to detect residual veterinary drugs in food is particularly significant for food safety. Herein, we report the facile fabrication of red-emissive carbon dots (R-CDs) for ratiometric sensing of veterinary drugs. With use of sorbitol and o-phenylenediamine as precursors, R-CDs was prepared via a one-pot solvothermal approach. The resulting R-CDs show mainly excitation-independent and dual-emissive photoluminescence (PL) located at 597 and 645 nm. Meanwhile, the PL quantum yield (QY) of R-CDs without further surface treatment is 33% under 540 nm excitation. Interestingly, the R-CDs exhibit fast fluorescence response to malachite green oxalate (MG oxalate), 1-aminohydantoin hydrochloride (AHD) and pefloxacin, which are abused widely and retained easily in animals. Ratiometric sensing of these veterinary drugs were successfully performed taking the advantage of dual-emissive PL property; the detection limits of MG oxalate, AHD and pefloxacin were 0.79, 0.25 and 0.85 μM, respectively.

[en] Using the generic hydrodynamic model of gamma-ray burst (GRB) afterglows, we calculate the radio afterglow light curves of low luminosity, high luminosity, failed and standard GRBs in different observational bands of FAST's energy window. The GRBs are assumed to be located at different distances from us. Our results rank the detectability of GRBs in descending order as high luminosity, standard, failed and low luminosity GRBs. We predict that almost all types of radio afterglows except those of low luminosity GRBs could be observed by a large radio telescope as long as the domains of time and frequency are appropriate. It is important to note that FAST can detect relatively weak radio afterglows at a higher frequency of 2.5 GHz for very high redshift up to z = 15 or even more. Radio afterglows of low luminosity GRBs can only be detected after the completion of the second phase of FAST. FAST is expected to significantly expand the sample of GRB radio afterglows in the near future. (research papers)