Generalized r-matrix structure and algebro-geometric solution for integrable systems

The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a generalized Lax matrix instead of usual Lax pair. The generalized r-matrix structure and Hamiltonian functions are presented on the basis of fundamental Poisson bracket. It can be clearly seen that various nonlinear constrained (c-) and restricted (r-) systems, such as the c-AKNS, c-MKdV, c-Toda, r-Toda, c-Levi, etc, are derived from the reduction of this structure. All these nonlinear systems have {\it r}-matrices, and are completely integrable in Liouville's sense. Furthermore, our generalized structure is developed to become an approach to obtain the algebro-geometric solutions of integrable NLEEs. Finally, the two typical examples are considered to illustrate this approach: the infinite or periodic Toda lattice equation and the AKNS equation with the condition of decay at infinity or periodic boundary.Comment: 41 pages, 0 figure

Single-polarization, dual-wavelength mode-locked Yb-doped fiber laser by a 45°-tilted fiber grating

We experimentally demonstrate an all-fiber single-polarization dual-wavelength Yb-doped fiber laser passively mode-locked with a 45°-tilted fiber grating for the first time. Stable dual-wavelength operation exhibits double-rectangular spectral profile centered at 1033 and 1053 nm, respectively. The 3 dB bandwidth of each rectangular optical spectrum is estimated as 10 nm. The separation of two fundamental repetition rates is 6 kHz. By employing the 45° TFG with the polarization-dependent loss of 33 dB, output pulses with 27 dB polarization extinction ratio are implemented in the experiment. The single pulse centered at 1053 nm is researched by using a filter at the output port of the laser, and the experimental results denote that the output ps pulses are highly chirped. The formation mechanism of dual-wavelength operation is investigated

Fully gapped topological surface states in Bi2_2Se3_3 films induced by a d-wave high-temperature superconductor

Topological insulators are a new class of materials, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay between such symmetry-protected topological surface states and symmetry-broken states (e.g. superconductivity) provides a platform for exploring novel quantum phenomena and new functionalities, such as 1D chiral or helical gapless Majorana fermions, and Majorana zero modes which may find application in fault-tolerant quantum computation. Inducing superconductivity on topological surface states is a prerequisite for their experimental realization. Here by growing high quality topological insulator Bi$_2$Se$_3$ films on a d-wave superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ using molecular beam epitaxy, we are able to induce high temperature superconductivity on the surface states of Bi$_2$Se$_3$ films with a large pairing gap up to 15 meV. Interestingly, distinct from the d-wave pairing of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, the proximity-induced gap on the surface states is nearly isotropic and consistent with predominant s-wave pairing as revealed by angle-resolved photoemission spectroscopy. Our work could provide a critical step toward the realization of the long sought-after Majorana zero modes.Comment: Nature Physics, DOI:10.1038/nphys274

The calcimimetic R-568 induces apoptotic cell death in prostate cancer cells

<p>Abstract</p> <p>Background</p> <p>Increased serum level of parathyroid hormone (PTH) was found in metastatic prostate cancers. Calcimimetic R-568 was reported to reduce PTH expression, to suppress cell proliferation and to induce apoptosis in parathyroid cells. In this study, we investigated the effect of R-568 on cellular survival of prostate cancer cells.</p> <p>Methods</p> <p>Prostate cancer cell lines LNCaP and PC-3 were used in this study. Cellular survival was determined with MTT, trypan blue exclusion and fluorescent Live/Death assays. Western blot assay was utilized to assess apoptotic events induced by R-568 treatment. JC-1 staining was used to evaluate mitochondrial membrane potential.</p> <p>Results</p> <p>In cultured prostate cancer LNCaP and PC-3 cells, R-568 treatment significantly reduced cellular survival in a dose- and time-dependent manner. R-568-induced cell death was an apoptotic event, as evidenced by caspase-3 processing and PARP cleavage, as well as JC-1 color change in mitochondria. Knocking down calcium sensing receptor (CaSR) significantly reduced R-568-induced cytotoxicity. Enforced expression of Bcl-xL gene abolished R-568-induced cell death, while loss of Bcl-xL expression led to increased cell death in R-568-treated LNCaP cells,.</p> <p>Conclusion</p> <p>Taken together, our data demonstrated that calcimimetic R-568 triggers an intrinsic mitochondria-related apoptotic pathway, which is dependent on the CaSR and is modulated by Bcl-xL anti-apoptotic pathway.</p

STM imaging of symmetry-breaking structural distortion in the Bi-based cuprate superconductors

A complicating factor in unraveling the theory of high-temperature (high-Tc) superconductivity is the presence of a "pseudogap" in the density of states, whose origin has been debated since its discovery [1]. Some believe the pseudogap is a broken symmetry state distinct from superconductivity [2-4], while others believe it arises from short-range correlations without symmetry breaking [5,6]. A number of broken symmetries have been imaged and identified with the pseudogap state [7,8], but it remains crucial to disentangle any electronic symmetry breaking from pre-existing structural symmetry of the crystal. We use scanning tunneling microscopy (STM) to observe an orthorhombic structural distortion across the cuprate superconducting Bi2Sr2Can-1CunO2n+4+x (BSCCO) family tree, which breaks two-dimensional inversion symmetry in the surface BiO layer. Although this inversion symmetry breaking structure can impact electronic measurements, we show from its insensitivity to temperature, magnetic field, and doping, that it cannot be the long-sought pseudogap state. To detect this picometer-scale variation in lattice structure, we have implemented a new algorithm which will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials.Comment: 4 figure