6,608 research outputs found
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 , the solution flow is
weakly differentiable and for each there is a positive number such
that for all , the solution flow 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
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
RESEARCH ON THE GAlT OF HEALTHY CHILDREN FROM 2 TO 6 YEARS OLDS
In order to show the basic characteristics of gait development of healthy children, this paper involved 320 children aging from 2 to 6 years old to test the gait during walking. The result showed that after two years old, knee joint participated inflexion and extend. 49 to 72-month-old children's knee joint angle can be fully extended when it is stretching. And that is close to the normal adults. From 3 years old and later, ankle joints also started to participate. With the increase of month, impulse from 1 to 5 metatarsal tended to be stable. And the impulse of inner side of foot was all larger than that of the lateral side
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