Symplectic duality between complex domains

In this paper after extending the definition of symplectic duality [given in Di Scala and Loi (Adv Math 217:2336–2352, 2008) for bounded symmetric domains] to arbitrary complex domains of \({{\mathbb{C}}^n}\) centered at the origin we generalize some of the results proved in Di Scala and Loi (Adv Math 217:2336–2352, 2008) and Di Scala et al. (Trans Groups 13(2):283–304, 2008) to those domains.     

Solving a minimum-power covering problem with overlap constraint for cellular network design

We consider a type of covering problem in cellular networks. Given the locations of base stations, the problem amounts to determining cell coverage at minimum cost in terms of the power usage. Overlap between adjacent cells is required in order to support handover. The problem we consider is NP-hard. We present integer linear models and study the strengths of their continuous relaxations. Preprocessing is used to reduce problem size and tighten the models. Moreover, we design a tabu search algorithm for finding near-optimal solutions effectively and time-efficiently. We report computational results for both synthesized instances and networks originating from real planning scenarios. The results show that one of the integer models leads to tight bounds, and the tabu search algorithm generates high-quality solutions for large instances in short computing time.     

The Shapley value for arbitrary families of coalitions

We address the problem of finding a suitable definition of a value similar to that of Shapley’s, when the games are defined on a subfamily of coalitions with no structure. We present two frameworks: one based on the familiar efficiency, linearity and null player axioms, and the other on linearity and the behavior on unanimity games. We give several properties and examples in each case, and give necessary and sufficient conditions on the family of coalitions for the approaches to coincide.     

Accurate finite difference schemes for solving a 3D micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates

In this study, we propose a 3D generalized micro heat transfer model in an N-carrier system with the Neumann boundary condition in spherical coordinates, which can be applied to describe the non-equilibrium heating in biological cells. Two improved unconditionally stable Crank-Nicholson schemes are then presented for solving the generalized model. In particular, we delicately adjust the location of the interior grid point that is next to the boundary so that the Neumann boundary condition can be applied directly without discretization. As such, a second-order accurate finite difference scheme without using any fictitious grid points is obtained. The convergence rates of the numerical solution are tested by an example. Results show that the convergence rates of the present schemes are about 2.0 with respect to the spatial variable r, which improves the accuracy of the Crank-Nicholson scheme coupled with the conventional first-order approximation for the Neumann boundary condition.     

格点系统存在指数吸引子的充分条件及应用

本文给出了一般格点动力系统存在指数吸引子的充分条件,然后将得到的结果应用到下面的格点非线性Schr(o|¨)dinger方程:iu_m-γ(2u_m-u_(m+1)-u_(m-1))+iκu_m+δ|u_m|~(2σ)u_m=g_m,m∈Z.设γ,κ,δ,σ和g_m满足适当的条件,证明了该格点方程存在指数吸引子.     

Representation of MV-algebras by regular ultrapowers of [0, 1]

We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable way, thus providing a sort of “canonical” set of values for the functional representation.     

Thermal stability and thermodynamic properties of hybrid proton-conducting polyaryl etherketones

The thermal and structural stability of sulfonated cross-linked PEEK (polyether ether ketone) and its silicon-containing class II hybrid derivatives were characterized by combination of mass spectrometry, infrared spectroscopy, X-ray diffraction, thermogravimetric analysis, and differential scanning calorimetry. Thermodynamic properties of the hybrids were determined, including glass-transition temperature, degree of crystallinity, and thermal stability. The decomposition processes of the hybrid polymers could be consistently interpreted and their energetics quantitatively determined. The introduction of inorganic silanol moieties improves the thermal stability compared to sulfonated products.     

Stability and migration of metal ions in G4-wires by molecular dynamics simulations

We present a molecular dynamics investigation of guanine quadruple helices based on classical force fields. We analyze the dependence of the helical conformation on various compositional factors, such as the length of the G4-wire, as well as the incorporation into the helix channel of alkali ions of different species and in different amounts. In compliance with previous indications, our results suggest that monovalent alkali cations assist the stability of the quadruplex arrangement against disruption on the few nanoseconds time scale in the order of increasing van der Waals radius. Whereas very short G4-wire fragments immediately unfold in the absence of coordinating metal ions or in the presence of tiny ions (e.g., Li+) in agreement with the experimental evidence that empty short guanine quadruplexes are not formed in any synthetic conditions, our simulations show that longer empty helices do not discompose. This finding supports the possibility of producing long G4-wires with different guanine-cation stoichiometries than those routinely known. The classical trajectories allow us to identify different stationary axial sites for the different metal species, which are confirmed by complementary quantum calculations.     

Ultrathin wagon-wheel-like TiOx phases on Pt(111): a combined low-energy electron diffraction and scanning tunneling microscopy investigation

Ultrathin ordered titanium oxide films on a Pt(111) surface have been prepared by reactive deposition and characterized by low-energy electron diffraction and scanning tunneling microscopy (STM). According to the postdeposition annealing condition, three different phases have been prepared which show a wagon-wheel-like (hereafter ww) morphological pattern. Two of them can be prepared as single phases (w- and w'-TiO(x)) and one (w(int)-TiO(x)) as a mixed phase which always coexists with at least one of the other two phases. All of them are formed by a Ti-O bilayer, where the Ti atoms are located at the interface with the substrate, but they show a rather distinct STM ww pattern. The experimental STM contrast has been discussed on the basis of a Moiré-like model, i.e., as deriving from a modulation of the Ti occupancy of the different substrate sites (i.e., hollow, bridge and on-top sites). The major part of the STM data can be easily interpreted on the basis of this simplified model.