Stability of a Cubically Convergent Method for Generalized Equations

In Geoffroy et al, Acceleration of convergence in Dontchev's iterative method for solving variational inclusions Serdica Math. J. 29 (2003), pp. 45–54] we showed the convergence of a cubic method for solving generalized equations of the form 0 ∈ f(x) +- G(x) where f is a function and G stands for a set-valued map. We investigate here the stability of such a method with respect to some perturbations. More precisely, we consider the perturbed equation y ∈ f(x) +- G(x) and we show that the pseudo-Lipschitzness of the map (f +- G)⁻¹ is closely tied to the uniformity of our method in the sense that the attraction region does not depend on small perturbations of the parameter y. Finally, we provide an enhanced version of the convergence theorem established by Geoffroy, et al.     

UV photolysis of C4N2 in water ices: new possible route of synthesis of ammonium bicarbonate and ammonium formate

Laboratory experiments involving ultraviolet (UV) irradiation of dicyanoacetylene (C(4)N(2)) trapped in water ice at 10 K have been conducted and monitored by infrared spectroscopy (FTIR). By the support of isotopic experiments and theoretical calculations, the irradiation of a DCA/H(2)O ice mixture at lambda > 230 nm has been found to be a possible source of NH(4)(+)HCO(3)(-) (ammonium bicarbonate) and NH(4)(+)HCOO(-) (ammonium formate). These latter compounds can arise from a proton-transfer reaction between H(2)O and the CN radical, which is issued from photolyzed C(4)N(2).     

Strong correlation effects and new phase transition at high pressure-low temperature in La0.5Ba0.5FeO3

The physical properties of La_0.5Ba_0.5FeO₃ perovskite have been investigated. The resistivity and magnetism change at around the charge disproportionation temperature. The ferromagnetic cluster-glass state appears when . Under 5 kbar pressure a new phase transition at 5.5 K is found in the magnetization measurement. The transition temperature increases with the increase of the applied pressure. It is suggested that this transition is induced by the spin state transition from to with the pressure increase.     

On the Characterization of Maximal Planar Graphs with a Given Signed Cycle Domination Number

Let G =(V, E) be a simple graph. A function f : E → {+1,-1} is called a signed cycle domination function(SCDF) of G if ∑_(e∈E(C))f(e) ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ'_(sc)(G) = min{∑_(e∈E)f(e)| f is an SCDF of G}. This paper will characterize all maximal planar graphs G with order n ≥ 6 and γ'_(sc)(G) = n.     

Energy levels and their correlations in quasicrystals

Quasicrystals can be considered, from the point of view of their electronic properties, as being intermediate between metals and insulators. For example, experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have conductivities far smaller than those of the metals that these alloys are composed from. Wavefunctions in a quasicrystal are typically intermediate in character between the extended states of a crystal and the exponentially localized states in the insulating phase, and this is also reflected in the energy spectrum and the density of states. In the theoretical studies we consider in this review, the quasicrystals are described by a pure hopping tight binding model on simple tilings. We focus on spectral properties, which we compare with those of other complex systems, in particular, the Anderson model of a disordered metal. We discuss ‘strong‘ and ‘weak’ quasicrystals, which are described by different universal laws. We find similarities and universal behaviour, but also significant differences between quasiperiodic models and models with disorder. Like weakly disordered metals, the quasicrystal can be described by the universal level statistics that can be derived from random matrix theory. These level statistics are only one aspect of the energy spectrum, whose very large fluctuations can also be described by a level spacing distribution that is log-normal. An analysis of spectral rigidity shows that electrons diffuse with a bigger exponent (super-diffusion) than in a disordered metal. Adding disorder attenuates the singular properties of the perfect quasicrystal, and leads to improved transport. Spectral properties are also used in computing conductances of such systems, and to attempt to resolve the experimental enigmas such as whether quasicrystals are intrinsically conductors, and if so, how conductances depend on the structure.     

Indeno[1,2‐b]fluorene‐Based [2,2]Cyclophanes with 4n/4n and 4n/[4n+2] π Electrons: Syntheses,Structural Analyses,and Excitonic Coupling Properties

Indeno[1,2‐b]fluorene‐based [2,2]cyclophanes with 4n/4n and 4n/[4n+2] π‐electron systems were prepared, and their structures were identified by X‐ray crystallography. With short π–π distances around 3.0 Å, [2.2](5,11)indeno[1,2‐b]fluorenophane and its precursor [2.2](5,11)indeno[1,2‐b]fluorene‐6,12‐dionophane exhibit remarkable transannular interactions, leading to their unusual electrochemical and photophysical properties. With the aid of femtosecond transient absorption spectroscopy, the transition from the monomeric excited state to the redshifted H‐type dimeric state was first observed, correlating to the calculated excitonic energy splitting and the steady‐state absorption spectra induced by charge‐transfer‐mediated superexchange interaction.     

Novel optical orthogonally modulation scheme for superimposing DPSK signals on dark RZ signals

A configuration of transmitter for superimposing DPSK signals on dark RZ signals was proposed. The transmitter comprises two optical phase modulators and a delayed line Mach-Zehnder interferometer. A new orthogonally modulation format with tunable duty cycle and extinction ratio in the optical domain was generated and discussed. The results show that the proposed modulation format offers significant advantages in offering high spectral efficiency values, high extinction ratio, and requiring electronics with reduced bandwidth.