On NP-hardness of the clique partition—Independence number gap recognition and related problems

We show that for a graph G it is NP-hard to decide whether its independence number α(G) equals its clique partition number even when some minimum clique partition of G is given. This implies that any α(G)-upper bound provably better than is NP-hard to compute.To establish this result we use a reduction of the quasigroup completion problem (QCP, known to be NP-complete) to the maximum independent set problem. A QCP instance is satisfiable if and only if the independence number α(G) of the graph obtained within the reduction is equal to the number of holes h in the QCP instance. At the same time, the inequality always holds. Thus, QCP is satisfiable if and only if . Computing the Lovász number ?(G) we can detect QCP unsatisfiability at least when . In the other cases QCP reduces to gap recognition, with one minimum clique partition of G known.     

Magnetic and luminescent properties of manganese-doped ZnSe crystals

Magnetic and photoluminescent properties of manganese-doped ZnSe crystals with different impurity concentrations were investigated. The concentration of Mn²⁺ ions in ZnSe crystals has been varied from 0.01 to 0.3 at%. Magnetic and photoluminescent studies have confirmed the introduction of Mn in ZnSe crystals. It was established that Mn²⁺ ions are responsible for the emission bands with maximum at 616 nm and 633 nm, which correspond to ⁴T₂→⁶A₁ and ⁴T₁→⁶A₁ intracentre transitions of Mn²⁺ ions respectively. It was found that the concentration quenching of the photoluminescent bands is associated with Mn²⁺ ions, which are due to the formation of Mn–Mn clusters. Magnetic properties studies have shown that at high doping levels the manganese atoms form Mn–Mn clusters in ZnSe. From the temperature dependence of magnetic susceptibility of ZnSe:Mn crystals that follows the Curie–Weiss law, it was possible to estimate the Curie–Weiss temperature Θ(x) and the effective Mn–Mn antiferromagnetic exchange constant (J₁).     

A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures

Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures. High frequency techniques, such as statistical energy analysis (SEA), often miss important information such as dominant resonance behavior due to stiff or small scale parts of the structure. Hybrid methods circumvent this problem by coupling FEM/BEM and SEA models in a given built-up structure. In the approach adopted here, the whole system is split into a number of subsystems that are treated by either FEM or SEA depending on the local wavelength. Subsystems with relative long wavelengths are modeled using FEM. Making a diffuse field assumption for the wave fields in the short wave length components, the coupling between subsystems can be reduced to a weighted random field correlation function. The approach presented results in an SEA-like set of linear equations that can be solved for the mean energies in the short wavelength subsystems.     

Algorithms for solving multiobjective discrete control problems and dynamic c-games on networks

In this paper we study a special class of multiobjective discrete control problems on dynamic networks. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize his own integral-time cost by a certain trajectory. Applying Nash and Pareto optimality principles we study multiobjective control problems on dynamic networks where the dynamics is described by a directed graph.Polynomial-time algorithms for determining the optimal strategies of the players in the considered multiobjective control problems are proposed exploiting the special structure of the underlying graph. Properties of time-expanded networks are characterized. A constructive scheme which consists of several algorithms is presented.     

π‐Extended Indenofluorenes

A series of π‐extended aromatic indenofluorene (IF) analogues with naphthalene and anthracene cores have been synthesized through acid‐catalyzed intramolecular cyclization. The regioselectivity of the reaction is controlled by a combination of steric and electronic factors and in some cases several possible regioisomers have resulted from the same precursor. The effects of ring connectivity on the optoelectronic properties were investigated by DFT calculations, absorption/emission spectroscopy, cyclic voltammetry, and spectroelectrochemical studies. All regioisomers exhibited a redshift of their absorption/emission bands relative to the parent IF analogues, but the magnitude of this shift and other optoelectronic properties (luminescence quantum yield, etc.) depends on the ring connectivity in a less obvious manner.     

Probing the Exciton Density of States in Semiconductor Nanocrystals Using Integrated Photoluminescence Spectroscopy

 We present the results of a comparative analysis of the absorption and photoluminescence excitation (PLE) spectra vs. integrated photoluminescence (IPL) measured as a function of the excitation wavelength for a number of samples containing II–VI semiconductor nanocrystals (NCs) produced by different techniques. The structure of the absorption and PL spectra due to excitons confined in NCs and difficulties with the correct interpretation of the transmittance and PLE results are discussed. It is shown that, compared to the conventional PLE, the IPL intensity plotted against the excitation wavelength (IPLE spectra) reproduce better the structure of the absorption spectra. Therefore, IPLE spectroscopy can be successfully used for probing the quantized electron-hole (e-h) transitions in semiconductor nanocrystals.     

Translocation of a beta-hairpin-forming peptide through a cylindrical tunnel

We use Langevin dynamics simulations of a minimalist off-lattice model to study the translocation of a beta hairpin forming peptide through a tunnel that mimics the exit tunnel in a ribosome. We have computed the free energy of the peptide as a function of its position relative to the tunnel exit and also studied the properties of the conformational ensemble, when the peptide's position is restricted at different points along the tunnel. Confining the peptide within a sufficiently wide tunnel stabilizes the folded state. The protein then remains folded as it moves towards the tunnel exit. However, when the diameter D of the tunnel is below a certain critical value D(c), confinement destabilizes the folded state and forces the peptide to assume an extended configuration. In this case, as the peptide progresses towards the tunnel exit and eventually leaves the tunnel, it goes through a series of compact, misfolded conformations and eventually folds when it gets close to the exit. The critical tunnel diameter D(c) is comparable to the width of ribosomal tunnels. Our results suggest that co-translational folding is probably not universal, but rather a protein-specific phenomenon.