A reduction theorem for the Alperin weight conjecture

The Alperin Weight Conjecture was stated by J. Alperin in 1986 and constitutes one of the main problems in the representation theory of finite groups. In this paper, we provide a reduction to simple groups and as an application we prove the conjecture in several cases.     

Globally solving a nonlinear UAV task assignment problem by stochastic and deterministic optimization approaches

In this paper, we consider a task allocation model that consists of assigning a set of m unmanned aerial vehicles (UAVs) to a set of n tasks in an optimal way. The optimality is quantified by target scores. The mission is to maximize the target score while satisfying capacity constraints of both the UAVs and the tasks. This problem is known to be NP-hard. Existing algorithms are not suitable for the large scale setting. Scalability and robustness are recognized as two main issues. We deal with these issues by two optimization approaches. The first approach is the Cross-Entropy (CE) method, a generic and practical tool of stochastic optimization for solving NP-hard problem. The second one is Branch and Bound algorithm, an efficient classical tool of global deterministic optimization. The numerical results show the efficiency of our approaches, in particular the CE method for very large scale setting.     

Inclusion of SWCNTs in Nb/Pt co-doped TiO2 thin-film sensor for ethanol vapor detection

Nb-Pt co-doped TiO₂ and the hybrid SWCNTs/Nb-Pt co-doped TiO₂ thin films have been prepared by the sol–gel spin-coating process for gas-sensor fabrication. Field emission scanning electron microscope (FE-SEM, TEM and X-ray diffraction (XRD) characterizations indicated that the SWCNTs inclusion did not affect the morphology of the TiO₂ thin film and the particle size. Additionally, the SWCNTs were well embedded in the TiO₂ matrix. The gas-sensing properties of Nb–Pt co-doped TiO₂ thin films with and without SWCNTs inclusion were investigated. The hybrid sensors with the inclusion of different SWCNTs contents are examined to elucidate the effect of SWCNTs content on the gas-sensing properties. Experimental results revealed that the responses to ethanol of Nb–Pt co-doped TiO₂ sensors with SWNCTs inclusion increase by factors of 2–5 depending on the operating temperature and the ethanol concentration, compared to that of the sensor without SWCNTs inclusion. Moreover, all hybrid sensors can operate with high sensitivity and stability at a relatively low operating temperature (<335 °C). The responses of the hybrid sensors are greatly affected by SWCNTs content inclusion. The optimized SWCNTs content of 0.01% by weight was obtained for our experiment. The improved gas-sensing performance should be attributed to the additional formation of the p/n junction between SWCNTs (p-type) and TiO₂ (n-type).     

Nilpotency degree of cohomology rings in characteristic 3

The purpose of this note is to provide a -group whose mod-3 cohomology ring has a nilpotent element satisfying .

     

Tuning of nanotube mechanical resonances by electric field pulling

We show here that field emission (FE) can be used to directly observe the vibration resonances nu(R) of carbon nanotubes (CNTs) and that the tension created by the applied field allows the tuning of these resonances by up to a factor of 10. The resonances are observable by the changes they create in the FE pattern or the emitted FE current. The tuning is shown to be linear in voltage and to follow from the basic physics of stretched strings. The method allows one to study the mechanical properties of individual multiwall carbon nanotubes within an ensemble and follow their evolution as the CNTs are modified. The tuning and detection should be useful for nanometric resonant devices.     

Almost unique determination of neutral-current couplings in neutrino-hadron interactions

Simultaneous analyses of inclusive and semi-inclusive reactionns in neutrino-nucleon collisions and elastic neutrino-proton scattering uniquely determine the neutral-current couplings between neutrinos and hadrons up to a two-fold “vector-axial-vector ambiguity”. One of the preferred solutions coincides with the Salam-Weinberg model within errors while the other solution, also compatible with SU(2) ? U(1) models with the simplest Higgs mechanism, may be helpful in understanding the bismuth puzzle.     

Modification of the chemical properties of silicon by ion implantation with high doses of Ar and P

The behaviour of Si implanted with high doses of P and Ar (5·10¹⁴ to 10¹⁷ cm⁻²) in HF solutions was investigated using radioactive isotopes. The reaction products were analyzed by ion exchange and electrochemical polarization. An increased dissolution was found and a possible reaction mechanism given.     

Experimental charge density of a potential DHO synthetase inhibitor: dimethyl-trans-2-oxohexahydro-pyrimidine-4,6-dicarboxylate

The experimental charge density distribution of dimethyl-trans-2-oxohexahydro-pyrimidine-4,6-dicarboxylate 1 has been determined using single-crystal X-ray diffraction data measured at 100 K, in terms of the rigid-pseudoatom formalism. Multipole refinement converged at R(F) = 0.034 for 7283 reflections with I > 3 sigma (I) and sin theta/lambda < or = 1.13 A(-1). Covalent and hydrogen bonding interactions are analyzed using a topological analysis of the Laplacian of the charge density. The experimentally derived electrostatic potential mapped onto the reactive surface of the molecule reveals the potential binding sites of 1.