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Register a new userSymmetries of 2nd order ODE: y + G(x)y + H(x)y = 0
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This paper is devoted to study the Lie algebra of linear symmetries of a homogenous 2nd order ODE, by the method of Kushner, Lychagin and Robstov.
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P/As-substitution effects on the transport properties of polycrystalline LaFeP$_{1-x}$As$_{x}$O$_{1-y}$F$_{y}$ with $x$ = 0 -- 1.0 and $y$ = 0 -- 0.1 have been studied. In the F-free samples ($y$ = 0), a new superconducting (SC) dome with a maximum $T_{c}$ of 12 K is observed around $x$ = 0 -- 0.3. This is separated from another SC dome with $T_{c}$ $sim$10 K at $x$ = 0.6 -- 0.8 by an antiferromagnetic region ($x$ = 0.3 -- 0.6), giving a two-dome feature in the $T_{c}-x$ phase diagram. As $y$ increases, the two SC domes merge together, changing to a double peak structure at $y$ = 0.05 and a single dome at $y$ = 0.1. This proves the presence of two different Fermi surface states in this system.
The (Li$_{1-x}$Fe$_{x}$OH)FeSe superconductor has been suspected to exhibit long-range magnetic ordering due to Fe substitution in the LiOH layer. However, no direct observation such as magnetic reflection from neutron diffraction has be reported. Here, we use a chemical design strategy to manipulate the doping level of transition metals in the LiOH layer to tune the magnetic properties of the (Li$_{1-x-y}$Fe$_{x}$Mn$_{y}$OD)FeSe system. We find Mn doping exclusively replaces Li in the hydroxide layer resulting in enhanced magnetization in the (Li$_{0.876}$Fe$_{0.062}$Mn$_{0.062}$OD)FeSe superconductor without significantly altering the superconducting behavior as resolved by magnetic susceptibility and electrical/thermal transport measurements. As a result, long-range magnetic ordering was observed below 12 K with neutron diffraction measurements. This work has implications for the design of magnetic superconductors for the fundamental understanding of superconductivity and magnetism in the iron chalcogenide system as well as exploitation as functional materials for next generation devices.
In this article we describe our experiences with a parallel SINGULAR-implementation of the signature of a surface singularity defined by z^N+g(x,y)=0.
Many new states in the charmonium mass region were recently discovered by BaBar, Belle, CLEO-c, CDF, D0, BESIII, LHCb and CMS Collaborations. We use the QCD Sum Rule approach to study the possible structure of some of these states.
We study the equivalence problem of classifying second order ordinary differential equations $y_{xx}=J(x,y,y_{x})$ modulo fibre-preserving point transformations $xlongmapsto varphi(x)$, $ylongmapsto psi(x,y)$ by using Mosers method of normal forms. We first compute a basis of the Lie algebra ${frak{g}}_{{{y_{xx}=0}}}$ of fibre-preserving symmetries of $y_{xx}=0$. In the formal theory of Mosers method, this Lie algebra is used to give an explicit description of the set of normal forms $mathcal{N}$, and we show that the set is an ideal in the space of formal power series. We then show the existence of the normal forms by studying flows of suitable vector fields with appropriate corrections by the Cauchy-Kovalevskaya theorem. As an application, we show how normal forms can be used to prove that the identical vanishing of Hsu-Kamran primary invariants directly imply that the second order differential equation is fibre-preserving point equivalent to $y_{xx}=0$.
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