Background: MicroRNAs (miRNAs) are small RNA molecules that regulate gene expression by targeting messenger RNAs (mRNAs) and causing mRNA cleavage or translation blockage. Of the 355 Arthropod miRNAs that have been identified, only 21 are B. mori miRNAs that were predicted computationally; of these, only let-7 has been confirmed by Northern blotting.

Chaundy and Jolliffe [4] proved that if {a n } is a non-increasing (monotonic) real sequence with lim n→∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∞ n=1 a n sin nx is lim n→∞ na n = 0. We generalize (or weaken) the monotonic condition on the coefficient sequence {a n } in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy and Jolliffe theorem in the complex space.2000 Mathematics Subject Classification. 42A20 42A32.

Photoresponsive nanochannel systems whose ionic transportation properties can be controlled by the photoelectric effect, such as for green chlorophyll pigments in plants, are attracting widespread attention. Herein, we prepared photoresponsive heterogeneous nanochannels by decorating self-assembled tetra­(4-sulfonatophenyl)­porphyrin (TPPS) nanofiber membranes on a membrane of hourglass-shaped alumina (Al2O3) nanochannels using the diffusion-limited patterning (DLP) method. The close arrangement of large-area nanofibers promoted the photoresponse sensitivity of the heterogeneous nanochannels, which showed the highest ionic transportation current. With illumination comparable to sunlight in intensity, the photoresponsive ionic current was approximately 9.7 μA, demonstrating photoswitching, which could be used to regulate the reversible transformation of ionic currents. Meanwhile, the cooperative effect of the TPPS nanofibers assembled at the entrance to the nanochannels and the TPPS molecules inside the nanochannels allowed the heterogeneous nanochannels to exhibit a good rectifying performance.

ABSTRACT. The present paper proposes a new condition to replace both the (O-regularly varying) quasimonotone condition and a certain type of bounded variation condition, and shows the same conclusion for the uniform convergence of certain trigonometric series still holds. Theorem CJ. Suppose that {b n } is a non-increasing real sequence with lim n→∞ b n = 0. Then a necessary and sufficient condition for the uniform convergence of the seriesis lim n→∞ nb n = 0. Recently, Leindler [2] considered to generalize the monotonicity condition to a certain type of bounded variation condition and proved the following Theorem L. Let b= {b n } ∞ n=1 be a nonnegative sequence satisfying lim n→∞ b n = 0 andfor some constant M(b) depending only upon b and m = 1, 2, · · ·. Then a necessary and sufficient condition either for the uniform convergence of series (1), or for the continuity of its sum function f (x), is that lim n→∞ nb n = 0.