A Coupled AKNS-Kaup-Newell Soliton Hierarchy

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of the systems lead to the AKNS hierarchy and the Kaup-Newell hierarchy, and thus those two soliton hierarchies also possess tri-Hamiltonian structures.Comment: 15 pages, late

Domain structure in the monoclinic Pm phase of Pb(Mg1/3Nb2/3)O3 - PbTiO3 single crystals

The domain structure of (1-x)Pb(Mg1/3Nb2/3)O3- xPbTiO3 single crystals with composition x ~ 0.33 in the range of the morphotropic phase boundary (MPB) was studied. Based on the analysis of spontaneous strain compatibility and charge of domain walls, we have established the permissible domain arrangements for the ferroelectric phases of different symmetry, which are expected to occur in the range of the MPB. Examination of (001)-oriented unpoled and electrically poled (along the [001] direction) crystal plates in polarizing microscope reveals a monophase state with the domain structure compatible with the structure theoretically predicted for the Mc monoclinic phase (space group Pm), which was recently discovered in the compositions close to the MPB by x-ray and neutron diffraction studies. In the unpoled crystal the 180 deg. walls between the domains whose spontaneous polarization vectors are parallel to the plane of the crystal plate (i.e. a-domains) are observed. The domain structure of the poled crystal is predominantly composed of crystallographically prominent Wf walls parallel to (001) (i.e. the plane of the crystal plate) and inclined S walls parallel to [110] or [1-10] direction. In poled and unpoled samples the optical rotatory polarization effect is found, which is related to the inhomogeneity of the sample resulting from the mixture of domains.Comment: PDF file, 30 pages, 15 figures (3 in color) collected on pp.18-3

Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy

Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite dimensional integrable systems and the general involutive system engendered by binary nonlinearization is reduced to a specific involutive system generated by mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento

Specific heats of dilute neon inside long single-walled carbon nanotube and related problems

An elegant formula for coordinates of carbon atoms in a unit cell of a single-walled nanotube (SWNT) is presented and the potential of neon (Ne) inside an infinitely long SWNT is analytically derived out under the condition of the Lennard-Jones potential between Ne and carbon atoms. Specific heats of dilute Ne inside long (20, 20) SWNT are calculated at different temperatures. It is found that Ne exhibits 3-dimensional (3D) gas behavior at high temperature but behaves as 2D gas at low temperature. Especially, at ultra low temperature, Ne inside (20, 20) nanotubes behaves as lattice gas. A coarse method to determine the characteristic temperature $\mathcal{T}_c$ for low density gas in a potential is put forward. If $\mathcal{T}\gg \mathcal{T}_c$, we just need to use the classical statistical mechanics without solving the Shr\"{o}dinger equation to consider the thermal behavior of gas in the potential. But if $\mathcal{T}\sim \mathcal{T}_c$, we must solve the Shr\"{o}dinger equation. For Ne in (20,20) nanotube, we obtain $\mathcal{T}_c\approx 60$ K.Comment: 14 pages, 7 figure

Probing Quantum Hall Pseudospin Ferromagnet by Resistively Detected NMR

Resistively Detected Nuclear Magnetic Resonance (RD-NMR) has been used to investigate a two-subband electron system in a regime where quantum Hall pseudo-spin ferromagnetic (QHPF) states are prominently developed. It reveals that the easy-axis QHPF state around the total filling factor $\nu =4$ can be detected by the RD-NMR measurement. Approaching one of the Landau level (LL) crossing points, the RD-NMR signal strength and the nuclear spin relaxation rate $1/T_{1}$ enhance significantly, a signature of low energy spin excitations. However, the RD-NMR signal at another identical LL crossing point is surprisingly missing which presents a puzzle

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe

miRNA-1-3p is an early embryonic male sex-determining factor in the Oriental fruit fly Bactrocera dorsalis

Regulation of male sexual differentiation by a Y chromosome-linked male determining factor (M-factor) is one of a diverse array of sex determination mechanisms found in insects. By deep sequencing of small RNAs from Bactrocera dorsalis early embryos, we identified an autosomal-derived microRNA, miR-1-3p, that has predicted target sites in the transformer gene (Bdtra) required for female sex determination. We further demonstrate by both in vitro and in vivo tests that miR-1-3p suppresses Bdtra expression. Injection of a miR-1-3p mimic in early embryos results in 87–92% phenotypic males, whereas knockdown of miR-1-3p by an inhibitor results in 67–77% phenotypic females. Finally, CRISPR/Cas9-mediated knockout of miR-1-3p results in the expression of female-specific splice variants of Bdtra and doublesex (Bddsx), and induced sex reversal of XY individuals into phenotypic females. These results indicate that miR-1-3p is required for male sex determination in early embryogenesis in B. dorsalis as an intermediate male determiner