Abstract:
The paper presents a way of constructing quasimonotone nonautonomous systems ensuring x-stability of the nonautonomous system. There are described extensions quasimonotone with respect to an arbitrary cone, Perron condition and invariant surface stability under perturbations U-stability on the set of non wandering points is proved to imply u-stability of quasimonotone nonlinear system and exponential u-stability on minimal attraction center provides u-stability of the total systems Examples are available.

Abstract:
We present the waveform digitiser used in the Double Chooz experiment. We describe the hardware and the custom-built firmware specifically developed for the experiment. The performance of the device is tested with regards to digitising low light level signals from photomultiplier tubes and measuring pulse charge. This highlights the role of quantisation effects and leads to some general recommendations on the design and use of waveform digitisers.

Abstract:
This final article about the CHOOZ experiment presents a complete description of the electron antineutrino source and detector, the calibration methods and stability checks, the event reconstruction procedures and the Monte Carlo simulation. The data analysis, systematic effects and the methods used to reach our conclusions are fully discussed. Some new remarks are presented on the deduction of the confidence limits and on the correct treatment of systematic errors.

Abstract:
We present new results based on the entire CHOOZ data sample. We find (at 90% confidence level) no evidence for neutrino oscillations in the anti_nue disappearance mode, for the parameter region given by approximately Delta m**2 > 7 x 10**-4 eV^2 for maximum mixing, and sin**2(2 theta) = 0.10 for large Delta m**2. Lower sensitivity results, based only on the comparison of the positron spectra from the two different-distance nuclear reactors, are also presented; these are independent of the absolute normalization of the anti_nue flux, the cross section, the number of target protons and the detector efficiencies.

Abstract:
The CHOOZ experiment measured the antineutrino flux at a distance of about 1 Km from two nuclear reactors in order to detect possible neutrino oscillations with squared mass differences as low as 10**-3 eV**2 for full mixing. We show that the data analysis of the electron antineutrino events, collected by our liquid scintillation detector, locates the antineutrino source within a cone of half-aperture of about 18 degrees at the 68% C.L.. We discuss the implications of this experimental result for tracking down a supernova explosion.

Abstract:
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the scalar charge density is derived from an energy functional of the polarization vector field. This energy functional represents the true energy of the system even in non-equilibrium states. Arbitrary accuracy is achieved by solving the integral equation for the charge density via a series expansion in terms of the equation's kernel, which depends only on the geometry of the dielectrics. The streamlined formalism operates with volume charge distributions only, not resorting to introducing surface charges by hand. Therefore, it can be applied to any spatial variation of the dielectric susceptibility, which is of particular importance in applications to biomolecular systems. The simplicity of application of the formalism to real problems is shown with analytical and numerical examples.

Abstract:
Results of molecular dynamics simulations of fission reactions $Na_{10}^{2+} \to Na_7^+ + Na_3^+$ and $Na_{18}^{2+} \to 2 Na_9^+$ are presented. Dependence of the fission barriers on isomer structure of the parent cluster is analyzed. It is demonstrated that the energy necessary for removing homothetic groups of atoms from the parent cluster is largely independent of the isomer form of the parent cluster. Importance of rearrangement of the cluster structure during the fission process is elucidated. This rearrangement may include transition to another isomer state of the parent cluster before actual separation of the daughter fragments begins and/or forming a "neck" between the separating fragments.

Abstract:
This publication provides a coherent treatment for the reactor neutrino flux uncertainties suppression, specially focussed on the latest $\theta_{13}$ measurement. The treatment starts with single detector in single reactor site, most relevant for all reactor experiments beyond $\theta_{13}$. We demonstrate there is no trivial error cancellation, thus the flux systematic error can remain dominant even after the adoption of multi-detector configurations. However, three mechanisms for flux error suppression have been identified and calculated in the context of Double Chooz, Daya Bay and RENO sites. Our analysis computes the error {\it suppression fraction} using simplified scenarios to maximise relative comparison among experiments. We have validated the only mechanism exploited so far by experiments to improve the precision of the published $\theta_{13}$. The other two newly identified mechanisms could lead to total error flux cancellation under specific conditions and are expected to have major implications on the global $\theta_{13}$ knowledge today. First, Double Chooz, in its final configuration, is the only experiment benefiting from a negligible reactor flux error due to a $\sim$90\% geometrical suppression. Second, Daya Bay and RENO could benefit from their partial geometrical cancellation, yielding a potential $\sim$50\% error suppression, thus significantly improving the global $\theta_{13}$ precision today. And third, we illustrate the rationale behind further error suppression upon the exploitation of the inter-reactor error correlations, so far neglected. So, our publication is a key step forward in the context of high precision neutrino reactor experiments providing insight on the suppression of their intrinsic flux error uncertainty, thus affecting past and current experimental results, as well as the design of future experiments.

Abstract:
An evidence of importance of the T-shaped configuration of coronene dimer is presented. That is, the dimer's lowest energy configuration is not necessarily a stack, as it might had been expected a priori. This is a surprising result for dimer of such a large polycyclic aromatic hydrocarbon (PAH) as coronene. The energy of the T-shaped configuration at all considered levels of density functional theory (B3LYP,PBE/6-31+G(d),D95,cc-pVDZ,cc-pVTZ) was systematically lower than the energies of three plausible stack configurations. In order to get a better description of the van der Waals interaction,the density functional theory (DFT) results were adjusted by adding a phenomenological Lennard-Jones-type term into the total energy of the system. However, the van der Waals correction is somewhat arbitrary and its magnitude can not be rigorously justified. Depending on the choice of the parameters in the phenomenological term both the T-shaped and the parallel-displaced (PD) stack configurations can be the global energy minimum of the system. A simple model is proposed which is useful for qualitative understanding of possible geometries of the coronene dimer and larger coronene clusters. The model represents coronene dimer as two sets of charged rings interacting via Coulomb and Lennard-Jones potentials. The model provides an intuitively clear explanation why the T-shaped dimers can be of importance even for some of moderately large PAHs such as coronene and, may be, for circumcoronene.

Abstract:
Fission of metastable charged univalent metal clusters has been studied on example of Na_{10}^{2+} and Na_{18}^{2+} clusters by means of density functional theory methods. Energetics of the process, i.e. dissociation energies and fission barriers, as well as its dynamics, i.e. fission pathways, have been analyzed. The dissociation energies and fission barriers have been calculated for the full range of fission channels for the Na_{10}^{2+} cluster. The impact of cluster structure on the fission process has been elucidated. The calculations show that the geometry of the smaller fragment and geometry of its immediate neighborhood in the larger fragment play a leading role in defining the fission barrier height. The present study demonstrates importance of rearrangement of the cluster structure during fission. It may include forming a neck between the two fragments or fissioning via another isomer state of the parent cluster; examples of such processes are given. For several low-lying isomers of Na_{10}^{2+} cluster the potential barriers for transitions between these isomer states are calculated and compared with the corresponding fission barriers. These data suggest that there is a competition between "direct" fission and fission going via intermediate isomer states of the parent cluster. An impact of the cluster geometry on the change of the system's entropy due to fission is also discussed.