A refined invariant subspace method and applications to evolution equations

The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations was analyzed to shed light on the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differential equations and their corresponding exact solutions with generalized separated variables.Comment: 16 page

Correlation length of hydrophobic polyelectrolyte solutions

The combination of two techniques (Small Angle X-ray Scattering and Atomic Force Microscopy) has allowed us to measure in reciprocal and real space the correlation length $\xi$ of salt-free aqueous solutions of highly charged hydrophobic polyelectrolyte as a function of the polymer concentration $C_p$, charge fraction $f$ and chain length $N$. Contrary to the classical behaviour of hydrophilic polyelectrolytes in the strong coupling limit, $\xi$ is strongly dependent on $f$. In particular a continuous transition has been observed from $\xi \sim C_p^{-1/2}$ to $\xi\sim C_p^{-1/3}$ when $f$ decreased from 100% to 35%. We interpret this unusual behaviour as the consequence of the two features characterising the hydrophobic polyelectrolytes: the pearl necklace conformation of the chains and the anomalously strong reduction of the effective charge fraction.Comment: 7 pages, 5 figures, submitted to Europhysics Letter

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

Timing Features of the Accretion--driven Millisecond X-Ray Pulsar XTE J1807--294 in 2003 March Outburst

In order to probe the activity of the inner disk flow and its effect on the neutron star surface emissions, we carried out the timing analysis of the Rossi X-Ray Timing Explorer (RXTE) observations of the millisecond X-ray pulsar XTE J1807--294, focusing on its correlated behaviors in X-ray intensities, hardness ratios, pulse profiles and power density spectra. The source was observed to have a serial of broad "puny" flares on a timescale of hours to days on the top of a decaying outburst in March 2003. In the flares, the spectra are softened and the pulse profiles become more sinusoidal. The frequency of kilohertz quasi-periodic oscillation (kHz QPO) is found to be positively related to the X-ray count rate in the flares. These features observed in the flares could be due to the accreting flow inhomogeneities. It is noticed that the fractional pulse amplitude increases with the flare intensities in a range of $\sim 2$, comparable to those observed in the thermonuclear bursts of the millisecond X-ray pulsar XTE J1814--338, whereas it remains at about 6.5% in the normal state. Such a significant variation of the pulse profile in the "puny" flares may reflect the changes of physical parameters in the inner disk accretion region. Furthermore, we noticed an overall positive correlation between the kHz QPO frequency and the fractional pulse amplitude, which could be the first evidence representing that the neutron-star surface emission properties are very sensitive to the disk flow inhomogeneities. This effect should be cautiously considered in the burst oscillation studies.Comment: Accepted by ApJ, 23 pages, 7 figures, 3 table

Enhanced anticancer activity of a combination of docetaxel and Aneustat (OMN54) in a patient-derived, advanced prostate cancer tissue xenograft model.

The current first-line treatment for advanced metastatic prostate cancer, i.e. docetaxel-based therapy, is only marginally effective. The aim of the present study was to determine whether such therapy can be improved by combining docetaxel with Aneustat (OMN54), a multivalent botanical drug candidate shown to have anti-prostate cancer activity in preliminary in vitro experiments, which is currently undergoing a Phase-I Clinical Trial. Human metastatic, androgen-independent C4-2 prostate cancer cells and NOD-SCID mice bearing PTEN-deficient, metastatic and PSA-secreting, patient-derived subrenal capsule LTL-313H prostate cancer tissue xenografts were treated with docetaxel and Aneustat, alone and in combination. In vitro, Aneustat markedly inhibited C4-2 cell replication in a dose-dependent manner. When Aneustat was combined with docetaxel, the growth inhibitions of the drugs were essentially additive. In vivo, however, the combination of docetaxel and Aneustat enhanced anti-tumor activity synergistically and very markedly, without inducing major host toxicity. Complete growth inhibition and shrinkage of the xenografts could be obtained with the combined drugs as distinct from the drugs on their own. Analysis of the gene expression of the xenografts using microarray indicated that docetaxel + Aneustat led to expanded anticancer activity, in particular to targeting of cancer hallmarks that were not affected by the single drugs. Our findings, obtained with a highly clinically relevant prostate cancer model, suggest, for the first time, that docetaxel-based therapy of advanced human prostate cancer may be improved by combining docetaxel with Aneustat

Mass movement susceptibility mapping using satellite optical imagery compared with InSAR monitoring: Zigui County, Three Gorges region, China

Mass movements on steep slopes are a major hazard to communities and infrastructure in the Three Gorges region, China. Developing susceptibility maps of mass movements is therefore very important in both current and future land use planning. This study employed satellite optical imagery and an ASTER GDEM (15 m) to derive various parameters (namely geology; slope gradient; proximity to drainage networks and proximity to lineaments) in order to create a GIS-based map of mass movement susceptibility. This map was then evaluated using highly accurate deformation signals processed using the Persistent Scatterer (PS) InSAR technique. Areas of high susceptibility correspond well to points of high subsidence, which provides a strong support of our susceptibility map

Self Assembled II-VI Magnetic Quantum Dot as a Voltage-Controlled Spin-Filter

A key element in the emergence of a full spintronics technology is the development of voltage controlled spin filters to selectively inject carriers of desired spin into semiconductors. We previously demonstrated a prototype of such a device using a II-VI dilute-magnetic semiconductor quantum well which, however, still required an external magnetic field to generate the level splitting. Recent theory suggests that spin selection may be achievable in II-VI paramagnetic semiconductors without external magnetic field through local carrier mediated ferromagnetic interactions. We present the first experimental observation of such an effect using non-magnetic CdSe self-assembled quantum dots in a paramagnetic (Zn,Be,Mn)Se barrier.Comment: 4 pages, 4 figure

Exploring Renner-Teller Induced Quenching in the Reaction H(\u3csup\u3e2\u3c/sup\u3e\u3ci\u3eS\u3c/i\u3e)+NH(\u3ci\u3ea\u3c/i\u3e\u3csup\u3e1\u3c/sup\u3eΔ): A Combined Experimental and Theoretical Study

Experimental rate coefficients for the removal of NH(a1Δ) and ND(a1Δ) in collisions with H and D atoms are presented; all four isotope combinations are considered: NH+H, NH+D, ND+H, and ND+D. The experiments were performed in a quasistatic laser-flash photolysis/laser-induced fluorescence system at low pressures. NH(a1Δ) and ND(a1Δ) were generated by photolysis of HN3 and DN3, respectively. The total removal rate coefficients at room temperature are in the range of (3-5) x 1013 cm3 mol-1 s-1. For two isotope combinations, NH+H and NH+D, quenching rate coefficients for the production of NH(X 3Σ-) or ND(X 3Σ-) were also determined; they are in the range of 1x1013 cm3 mol-1 s-1. The quenching rate coefficients directly reflect the strength of the Renner-Teller coupling between the 2A and 2A\u27 electronic states near linearity and so can be used to test theoretical models for describing this nonadiabatic process. The title reaction was modeled with a simple surface-hopping approach including a single parameter, which was adjusted to reproduce the quenching rate for NH+H; the same parameter value was used for all isotope combinations. The agreement with the measured total removal rate is good for all but one isotope combination. However, the quenching rates for the NH+D combination are only in fair (factor of 2) agreement with the corresponding data

Plasticity of motor network and function in the absence of corticospinal projection

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