Strong completeness for a class of stochastic differential equations with irregular coefficients

We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\cdot)$ belongs to the Sobolev space W_{\loc}^{1,p}. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained

Facile Synthesis and Versatilities of Polyanthraquinoylamine Nanofibril Bundles with Self Stability and High Carbon Yield

A facile synthesis for nanosized conducting polymers with inherent self-stability and multi-functionalities is a main challenge. Here we simply synthesize intrinsically self-stabilized nanofibril bundles of poly(1-anthraquinoylamine) (PAQ) by a template-free method. The critical polymerization parameters were studied to significantly optimize the synthesis, size, properties, and functionalities of the resulted fine nanofibrils with a diameter of ca. 30 nm and length of ~6 &#x3bc;m. The PAQ obtained with ammonium persulfate possesses higher polymerization yield, purer composition, higher conductivity, better melting behaviour, higher thermostability, lower burning enthalpy, and slower degradation than that with other oxidants. Furthermore, the polymer nanofibrils exhibit high self-stability, powerful redispersibility, high purity, and clean surface because of a complete avoidance of the contamination from external stabilizer. The PAQ exhibits widely controllable conductivity moving across ten orders of magnitudes from 10^-9^ to 50 S/cm, photoluminescence, lead-ion adsorbability, very high thermostability in air and extremely high char yield in nitrogen at 1000&#x2da;C. These materials would be useful as advanced materials including photoluminescent materials, highly cost-effective carbon precursors, sorbents of toxic metal ions, and cost-efficient conductive nanocomposite with low percolation threshold

Interfacial chemical oxidative synthesis of multifunctional polyfluoranthene.

A novel polyfluoranthene (PFA) exhibiting strong visual fluorescence emission, a highly amplified quenching effect, and widely controllable electrical conductivity is synthesized by the direct cationic oxidative polymerization of fluoranthene in a dynamic interface between n-hexane and nitromethane containing fluoranthene and FeCl3, respectively. A full characterization of the molecular structure signifies that the PFAs have a degree of polymerization from 22-50 depending on the polymerization conditions. A polymerization mechanism at the interface of the hexane/nitromethane biphasic system is proposed. The conductivity of the PFA is tunable from 6.4 × 10-6 to 0.074 S cm-1 by doping with HCl or iodine. The conductivity can be significantly enhanced to 150 S cm-1 by heat treatment at 1100 °C in argon. A PFA-based chemosensor shows a highly selective sensitivity for Fe3+ detection which is unaffected by other common metal ions. The detection of Fe3+ likely involves the synergistic effect of well-distributed π-conjugated electrons throughout the PFA helical chains that function as both the fluorophore and the receptor units

Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus as far as is known at present, they are the most important family of quantum MDS codes.Comment: 9 pages, no figure

3-Methoxy-4-(4-nitro­benz­yloxy)­benzaldehyde

In the title compound, C15H13NO5, the vanillin group makes a dihedral angle of 4.95 (8)° with the benzene ring of the nitro­benzene group. The packing is stabilized by weak, non-classical inter­molecular C—H⋯O inter­actions which link mol­ecules into chains running along the c axis