Intertrimer and intratrimer metallophilic and excimeric bonding in the ground and phosphorescent States of trinuclear coinage metal pyrazolates: a computational study

The interactions present in cyclic trinuclear coinage metal pyrazolates were studied computationally. Cuprophilic interaction was found to bind the singlet ground state of the dimer of trimers [[Cu(Pz)](3)](2), overcoming electrostatic repulsion. The large variation in intertrimer separations found in the literature for coinage metal pyrazolates is consistent with the relatively weak metallophilic interaction. The emissive triplet excited-state geometry of [[M(Pz)](3)](2) is predicted by density functional calculations to show major geometric distortion caused by Jahn-Teller instability and excimeric M-M bonding. Large calculated Stokes' shifts, which are also observed for experimental models, are consistent with significant excited-state distortions for these materials. The major finding derived from the present study is that the intertrimer M...M contraction in the emissive T(1) state is much more than the intratrimer contraction in all [[M(Pz)](3)](2) models, giving rise to a lower T(1) --> S(0) phosphorescence energy in these models than in analogous monomer-of-trimer models. The observations made here point to a great potential for rationally tuning the emission properties of trinuclear coinage metal complexes through choice of the metal and ligands.     

A perturbed hard-sphere equation of state extended to imidazolium-based ionic liquids

A perturbed hard-sphere equation of state (EOS) has been previously employed to predict pressure–volume–temperature properties of some ionic liquids (ILs) with phosphonium-, pyridinium-, and pyrrolidinium cations. In this work, we have extended the considered EOS to another class of ILs in compressed states. This class consists of 14 imidazolium-based ILs. The predicted densities were compared with those obtained from the experiment, over a broad pressure range from 0.1 to 200 MPa. From 1,122 data points examined for the aforementioned ILs, the total average absolute deviation was found to be 1.05%.     

Tracking noisy limit cycle oscillation with nonlinear filters

For engineering systems, the dynamic state estimates provide valuable information for the detection and prediction of failure due to noise and vibration. From this perspective, nonlinear filtering techniques are applied to the problem of state estimation of dynamical systems undergoing noisy limit cycle oscillation. Specifically, the extended Kalman filter, ensemble Kalman filter and particle filter are used to track the limit cycle oscillations of a Duffing oscillator using noisy observational data. The noisy limit cycle oscillations feature highly non-Gaussian trends. The efficiency and limitations of the extended Kalman filter, ensemble Kalman filter and particle filter in tracking limit cycle oscillations are examined with respect to the model and measurement noise and sparsity of measurement data. For the limit cycle oscillations considered here, it is demonstrated that the ensemble Kalman filter and particle filter outperform the extended Kalman filter in the presence of sparse observational data or strong measurement noise. For moderate measurement noise and frequent measurement data, the ensemble Kalman filter and particle filter perform equally well in comparison to the extended Kalman filter.     

Numerical analysis and optimization of a dual-concentric-core photonic crystal fiber for broadband dispersion compensation

In this article, a novel dual-concentric-core photonic crystal fiber (DC-PCF) for dispersion compensation is presented. The proposed DC-PCF has relatively high negative dispersion over a wide wavelength range, which covers E, S, C, L and U telecommunication wavelength bands. The validity of the proposed design is carried out by employing a 2-D finite difference frequency domain method (FDFD) with perfectly matched layers (PML). By using the numerical method, the dispersion profile of the DC-PCF is optimized in terms of three air-hole diameters to achieve desirable negative dispersion. The influence of the location of ring-core, the number of air-hole rings on dispersion and loss characteristics are also studied.     

Mitigation of phase noise in dispersion compensated quasi-linear optical transmission systems: Analysis

We theoretically investigate the phase noise in quasi-linear optical transmission systems and study the mitigation of phase noise by properly choosing periodic dispersion compensation and amplification. Variational method is used to deduce the analytical formula for calculating the phase fluctuations of a Gaussian pulse. The analytical predictions are then checked against direct simulations by numerically solving the nonlinear Schrödinger equation. We find that stronger dispersion compensation maps can be used to reduce phase noise and it can be further mitigated by modifying the dispersion map appropriately. It is also found that shorter amplifier spacing yields lower phase noise. We also explore the effect of pre-, post- and bi-end dispersion compensation configurations on phase noise with full compensation and check the reduction of phase noise along the fiber link.     

Cross-phase modulation induced phase fluctuations in optical RZ pulse propagating in dispersion compensated WDM transmission systems

The basic mechanism of cross-phase modulation induced phase fluctuations in optical RZ pulse propagating in a periodically dispersion compensated transmission line has been investigated. Ordinary differential equations have been derived using variational analysis to estimate the phase fluctuation and the analytical result is verified by numerical simulations based on split-step Fourier method. We therefore explore the impact of different dispersion compensation maps on phase fluctuation for 10 Gb/s and 40 Gb/s WDM transmission systems. The effects of initial pulse spacing between channels, channel spacing and residual dispersion on phase shift have been studied. We find that cross-phase modulation induced phase fluctuation can be mitigated by proper adjustment of channel spacing and/or residual dispersion.     

160 GHz harmonic mode-locked AlGaInAs 1.55 μm strained quantum-well compound-cavity laser

We characterized the reflectivity and the modal discrimination of intracavity reflectors (ICRs) with different numbers of slots and presented harmonic mode-locking operation of a monolithic semiconductor laser comprising a compound cavity formed by a single deeply etched slot ICR fabricated from 1.55 μm AlGaInAs strained quantum well material. Gaussian pulses were generated at a 161.8 GHz repetition rate with a pulse duration of 1.67 ps and a time-bandwidth product of 0.81.     

Erdős–Gyárfás conjecture for some families of Cayley graphs

The Paul Erd?s and András Gyárfás conjecture states that every graph of minimum degree at least 3 contains a simple cycle whose length is a power of two. In this paper, we prove that the conjecture holds for Cayley graphs on generalized quaternion groups, dihedral groups, semidihedral groups and groups of order \(p^3\).     

The Σ1-provability logic of HA

In this paper we introduce a modal theory ${\mathsf{iH}}_{\sigma }$ which is sound and complete for arithmetical ${\mathrm{\Sigma }}_1$-interpretations in $\mathsf{HA}$, in other words, we will show that ${\mathsf{iH}}_{\sigma }$ is the ${\mathrm{\Sigma }}_1$-provability logic of $\mathsf{HA}$. Moreover we will show that ${\mathsf{iH}}_{\sigma }$ is decidable. As a by-product of these results, we show that $\mathsf{HA}+\square \perp$ has de Jongh property.     

2-Domination number of generalized Petersen graphs

Let \(G=(V,E)\) be a graph. A subset \(S\subseteq V\) is a k-dominating set of G if each vertex in \(V-S\) is adjacent to at least k vertices in S. The k-domination number of G is the cardinality of the smallest k-dominating set of G. In this paper, we shall prove that the 2-domination number of generalized Petersen graphs \(P(5k+1, 2)\) and \(P(5k+2, 2)\), for \(k>0\), is \(4k+2\) and \(4k+3\), respectively. This proves two conjectures due to Cheng (Ph.D. thesis, National Chiao Tung University, 2013). Moreover, we determine the exact 2-domination number of generalized Petersen graphs P(2k, k) and \(P(5k+4,3)\). Furthermore, we give a good lower and upper bounds on the 2-domination number of generalized Petersen graphs \(P(5k+1, 3), P(5k+2,3)\) and \(P(5k+3, 3).\)