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For a connected graph $G$ and $\alpha\in [0,1)$, the distance $\alpha$-spectral radius of $G$ is the spectral radius of the matrix $D_{\alpha}(G)$ defined as $D_{\alpha}(G)=\alpha T(G)+(1-\alpha)D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. We give bounds for the distance $\alpha$-spectral radius, especially for graphs that are not transmission regular, propose some graft transformations that decrease or increase the distance $\alpha$-spectral radius, and determine the unique graphs with minimum and maximum distance $\alpha$-spectral radius among some classes of graphs.

We perform a comprehensive first-principles study of the electronic properties of van der Waals (vdW) trilayers via intercalating a two-dimensional (2D) monolayer (ML = BN, MoSe2, WS2, or WSe2) between MoS2 bilayer to form various MoS2/ML/MoS2 sandwich trilayers. We find that the BN monolayer is the most effective sheet to decouple the interlayer vdW coupling of the MoS2 bilayer, and the resulting sandwich trilayer can recover the electronic structures of the MoS2 monolayer, particularly the direct-gap character. Further study of the MoS2/BN superlattices confirms the effectiveness of the BN monolayer for the decoupling of the MoS2-MoS2 interaction. In addition, the intercalation of transition-metal dichalcogenide (TMDC) MoSe2 or WSe2 sheet renders the sandwich trilayer undergoing an indirect-gap to direct-gap transition due to the newly formed heterogeneous S/Se interfaces. In contrast, the MoS2/WS2/MoS2 sandwich trilayer still retains the indirect-gap character of the MoS2 bilayer due to the lack of the heterogeneous S/Se interfaces. Moreover, the 3D superlattice of the MoS2/TMDC heterostructures also exhibits similar electronic band characters as the MoS2/TMDC/MoS2 trilayer heterostructures, albeit slight decrease of the bandgap than the trilayers. Compared to the bulk MoS2, the 3D MoS2/TMDC superlattice can give rise to new and distinctive properties. Our study offers not only new insights into electronic properties of the vdW multilayer heterostructures but also guidance in designing new heterostructures to modify electronic structures of 2D TMDC crystals., Comment: Nanoscale, 2014

3C 66A was monitored by the BATC(Beijing-Arizona-Taipei-Connecticut) telescope from 2005 to 2008,1994 observations were obtained on 89 nights. Detailed research and analysis was performed on these observations in this paper. A long term burst occurred in the whole light curve. No intra-day variability was claimed in our campaign by intra-night light curve analysis. Time lag of shorter wavelenth preceding longer wavelength was shown by correlation analysis. The results showed that the optical spectral shape turned flatter when the source brightened, and the spectral variability indicator was bigger on shorter time-scale as determined by the color indices variation analysis., Comment: 11 pages, 6 figures. arXiv admin note: text overlap with arXiv:1001.5206 by other authors

Many quasi-simultaneous optical observations of 17 blazars are obtained from previous papers published over the last 19 years in order to investigate the spectral slope variability and understand the radiation mechanism of blazars. The long-period dereddened optical spectral slopes are calculated. We analyse the average spectral slope distribution, which suggests that the spectra of flat spectrum radio quasars (FSRQs) and high energy peaked BL Lac objects (HBLs) are probably deformed by other emission components. The average spectral slopes of low energy peaked BL Lac objects(LBLs), which scatter around 1.5, show a good accordance with the synchrotron self-Compton (SSC) loss-dominated model. We present and discuss the variability between the spectral slope and optical luminosity. The spectra of all HBLs and LBLs get flatter when they turn brighter, while for FSRQs this trend does not exist or may even be reversed. This phenomenon may imply that there is a thermal contribution to the optical spectrum for FSRQs. For the FSRQ 1156+295, there is a hint that the slope gets flatter at both the brightest and faintest states. Our result shows that three subclasses locate in different regions in the pattern of slope variability indicator versus average spectral slope. The relativistic jet mechanism is supported by the significant correlation between the optical Doppler factor and the average spectral slope., Comment: 17 pages, 7 figures, Accepted by MNRAS

We study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncomutative differential geometry. By virtue of this variational principle, we get the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory. We also explore the difference discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both Lagrangian and Hamiltonian formalism. In terms of the difference discrete Euler-Lagrange cohomological concepts, we show that the symplectic or multisymplectic geometry and their difference discrete structure preserving properties can always be established not only in the solution spaces of the discrete Euler-Lagrange/canonical equations derived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrange cohomological conditions are satisfied. We also apply the difference discrete variational principle and cohomological approach directly to the symplectic and multisymplectic algorithms., Comment: 45 pages, 0 figures

AdS dynamics for massive scalar field is studied both by solving exactly the equation of motion and by constructing bulk-boundary propagator. A Robertson-Walker-like metric is deduced from the familiar SO(2,n) invariant metric. The metric allows us to present a time-like Killing vector, which is not only invariant under space-like transformations but also invariant under the isometric transformations of SO(2,n) in certain sense. A horizon appears in this coordinate system. Singularities of field variables at boundary are demonstrated explicitly. It is shown that there is a one-to-one correspondence among the exact solutions and the bulk fields obtained by using the bulk-boundary propagator., Comment: LaTeX, 18 pages, 3 eps figures

We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case respectively. By virtue of the Euler-Lagrange cohomology that is nontrivial in the configuration space, we show that the symplectic or multisymplectic geometry and related preserving property can be established not only in the solution space but also in the function space if and only if the relevant closed Euler-Lagrange cohomological condition is satisfied in each case. We also apply the cohomological approach directly to Hamiltonian-like ODEs and Hamiltonian-like PDEs no matter whether there exist known Lagrangian and/or Hamiltonian associated with them., Comment: 24 pages, 0 figure

We present the symplectic algorithm in the Lagrangian formalism for the Hamiltonian systems by virtue of the noncommutative differential calculus with respect to the discrete time and the Euler--Lagrange cohomological concepts. We also show that the trapezoidal integrator is symplectic in certain sense., Comment: 8 pages, 0 figure

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variational principle with the difference being regarded as an entire geometric object and the noncommutative differential calculus on regular lattice. In order to show that in all these cases the symplectic and multisymplectic preserving properties do not necessarily depend on the relevant Euler-Lagrange equations, the Euler-Lagrange cohomological concepts and content in the configuration space are employed., Comment: 8 pages, 0 figure

On the basis of graded RTT formalism,the defining relation of the super-Yangian Y(gl(1|1)) is derived and its oscillator realization is constructed., Comment: 7 pages, latex, no figures, to appaer in the International Workshop on Frontiers in Quantum Field Theory,Urumqi,11-18,Augast,1996