Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at u = 0 in a domain with many small holes

In the present paper we perform the homogenization of the semilinear elliptic problem

$\{\begin{array}{cc}{u}^{\epsilon }\ge 0\hfill & \text{in}{\mathrm{\Omega }}^{\epsilon },\hfill \\ ?divA(x)D{u}^{\epsilon }=F(x,u^{\epsilon })\hfill & \text{in}{\mathrm{\Omega }}^{\epsilon },\hfill \\ u^{\epsilon }=0\hfill & \text{on}?{\mathrm{\Omega }}^{\epsilon }.\hfill \end{array}$

In this problem $F(x,s)$ is a Carathéodory function such that $0\le F(x,s)\le h(x)/\mathrm{\Gamma }(s)$ a.e. $x\in \mathrm{\Omega }$ for every $s>0$, with h in some $L^r(\mathrm{\Omega })$ and Γ a $C^1([0,+\infty [)$ function such that $\mathrm{\Gamma }(0)=0$ and ${\mathrm{\Gamma }}^{\prime }(s)>0$ for every $s>0$. On the other hand the open sets ${\mathrm{\Omega }}^{\epsilon }$ are obtained by removing many small holes from a fixed open set Ω in such a way that a “strange term” $\mu u^0$ appears in the limit equation in the case where the function $F(x,s)$ depends only on x.We already treated this problem in the case of a “mild singularity”, namely in the case where the function $F(x,s)$ satisfies $0\le F(x,s)\le h(x)(\frac{1}{s}+1)$. In this case the solution $u^{\epsilon }$ to the problem belongs to $H_0^1({\mathrm{\Omega }}^{\epsilon })$ and its definition is a “natural” and rather usual one.In the general case where $F(x,s)$ exhibits a “strong singularity” at $u=0$, which is the purpose of the present paper, the solution $u^{\epsilon }$ to the problem only belongs to $H_{\text{loc}}^1({\mathrm{\Omega }}^{\epsilon })$ but in general does not belong to $H_0^1({\mathrm{\Omega }}^{\epsilon })$ anymore, even if $u^{\epsilon }$ vanishes on $?{\mathrm{\Omega }}^{\epsilon }$ in some sense. Therefore we introduced a new notion of solution (in the spirit of the solutions defined by transposition) for problems with a strong singularity. This definition allowed us to obtain existence, stability and uniqueness results.In the present paper, using this definition, we perform the homogenization of the above semilinear problem and we prove that in the homogenized problem, the “strange term” $\mu u^0$ still appears in the left-hand side while the source term $F(x,u^0)$ is not modified in the right-hand side.     

Robustness in complex information systems: The role of information “barriers” in Boolean networks

In this supposed “information age,” a high premium is put on the widespread availability of information. Access to as much information as possible is often cited as key to the making of effective decisions. While it would be foolish to deny the central role that information and its flow has in effective decision‐making processes, this chapter explores the equally important role of “barriers” to information flows in the robustness of complex systems. The analysis demonstrates that (for simple Boolean networks at least) a complex system's ability to filter out, i.e., block, certain information flows is essential if it is not to be beholden to every external signal. The reduction of information is as important as the availability of information. © 2009 Wiley Periodicals, Inc. Complexity, 2010     

Interactive evolutionary multi-objective optimization for quasi-concave preference functions

We present a new hybrid approach to interactive evolutionary multi-objective optimization that uses a partial preference order to act as the fitness function in a customized genetic algorithm. We periodically send solutions to the decision maker (DM) for her evaluation and use the resulting preference information to form preference cones consisting of inferior solutions. The cones allow us to implicitly rank solutions that the DM has not considered. This technique avoids assuming an exact form for the preference function, but does assume that the preference function is quasi-concave. This paper describes the genetic algorithm and demonstrates its performance on the multi-objective knapsack problem.     

Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.     

A multi-objective multi-period stochastic programming model for public debt management

While raising debt on behalf of the government, public debt managers need to consider several possibly conflicting objectives and have to find an appropriate combination for government debt taking into account the uncertainty with regard to the future state of the economy. In this paper, we explicitly consider the underlying uncertainties with a complex multi-period stochastic programming model that captures the trade-offs between the objectives. The model is designed to aid the decision makers in formulating the debt issuance strategy. We apply an interactive procedure that guides the issuer to identify good strategies and demonstrate this approach for the public debt management problem of Turkey.     

A Geant4 Monte Carlo method for synthesizing radioxenon beta-gamma coincidence spectra

This paper describes a Monte Carlo (MC) simulation method for calculating radioxenon beta-gamma coincidence spectral information. These spectral components include detector response simulations by Geant4 modeling, detector energy and resolution calibrations using the histograms of detector response, beta-gamma coincidence efficiency values and spectral interference ratios. The work presented in this paper demonstrates the feasibility of using the spectral information to create beta-gamma coincidence spectra at various radioxenon activity concentrations. The analysis of these synthetic spectra by XECON software shows an excellent correlation between the analysed radioxenon activity concentration and number of MC samplings.     

Geant4 Monte Carlo radioxenon beta-gamma coincidence efficiency simulation for a phoswich detector

In this work, a Monte Carlo (MC) simulation model is established to accurately characterize a phoswich beta-gamma coincidence detector system. This model can be easily used to predict the beta-gamma coincidence efficiencies of xenon radioisotopes at various stable xenon concentrations in the counting cell. The results demonstrate that there is a significant inverse correlation between beta-gamma coincidence efficiency and stable xenon concentration. The influence of stable xenon concentration on beta-gamma coincidence counting efficiency has been investigated for each individual xenon radioisotope. The results indicate that the effect of stable xenon concentration on beta-gamma coincidence efficiency depends on the xenon radioisotope and its decay modes. The coincidence efficiency of ¹³³Xe with 31.0-keV X-ray decay mode is the most affected one; and then followed by ^131mXe, ¹³³Xe with 81.0-keV gamma-ray decay mode, ^133mXe and finally ¹³⁵Xe. The study also indicates that the gamma absorption by xenon gas plays more of a role in the decrease of beta-gamma coincidence efficiency for ¹³³Xe and ¹³⁵Xe, and that the conversion electron spectrum shifting and broadening plays more of a role in the reduction of beta-gamma coincidence efficiency for the metastable radioxenon of ^131mXe and ^133mXe.     

Syntheses and properties of two-dimensional, dicationic nonlinear optical chromophores based on pyrazinyl cores

Six new dicationic 2D nonlinear optical (NLO) chromophores with pyrazinyl-pyridinium electron acceptors have been synthesized by nucleophilic substitutions of 2,6-dichloropyrazine with pyridyl derivatives. These compounds have been characterized as their PF(6)(-) salts by using various techniques including electronic absorption spectroscopy and cyclic voltammetry. Large red shifts in the intense, π → π* intramolecular charge-transfer (ICT) transitions on replacing -OMe with -NMe(2) substituents arise from the stronger π-electron donor ability of the latter. Each compound shows a number of redox processes which are largely irreversible. Single crystal X-ray structures have been determined for five salts, including two nitrates, all of which adopt centrosymmetric packing arrangements. Molecular first hyperpolarizabilities β have been determined by using femtosecond hyper-Rayleigh scattering at 880 and 800 nm, and depolarization studies show that the NLO responses of the symmetric species are strongly 2D, with dominant "off-diagonal" β(zyy) components. Stark (electroabsorption) spectroscopic measurements on the ICT bands afford estimated static first hyperpolarizabilities β(0). The directly and indirectly derived β values are large, and the Stark-derived β(0) response for one of the new salts is several times greater than that determined for (E)-4'-(dimethylamino)-N-methyl-4-stilbazolium hexafluorophosphate. These Stark spectroscopic studies also permit quantitative comparisons with related 2D, binuclear Ru(II) ammine complex salts.     

Investigation of reagent gases for the positive chemical ionization of select polybrominated diphenyl ethers

Polybrominated diphenyl ethers (PBDEs) fall into the class of compounds known as brominated flame retardants and their incorporation in a multitude of products is responsible for saving numerous lives. However, toxicology studies have alerted researchers to the potential adverse health effects that may develop as a result of prolonged or extreme exposure to these compounds. Frequent disposal and subsequent leaching has focused concern on environmental concentrations and current reports cite increasing levels. Method development continues in support of this research and the present work examines the feasibility of utilizing gas chromatography ion trap mass spectrometry operating in positive ion chemical ionization mode. In the evaluation of reagents for chemical ionization (methane, methanol and acetonitrile), comparative results of all three reagents demonstrated more difficult protonation as the number of bromine atoms increased. Methane, possessing the lowest proton affinity, provided the highest response for the analytes. Further, when methane chemical ionization was compared to electron impact ionization, the tetra-congener showed approximately 8× greater sensitivity and the penta- and hexa-congeners demonstrated approximately 2× greater. CI parameters, such as ionization and reaction times, were optimized to provide the highest analyte response and this was followed by the investigation of the employment of MSⁿ. In the this mode, optimal excitation amplitude delivered sufficient fragmentation while maintaining maximum signal, yielding final instrument detection limits in the sub µg L^{− 1} range.     

DNA-templated covalent coupling of G4 PAMAM dendrimers

Generation-4 polyamidoamine (PAMAM) dendrimers were surface-functionalized with azides or alkynes and conjugated to one DNA strand. DNA-controlled self-assembly of alternating azide and alkyne dendrimers on a DNA template enabled the coupling of the dendrimers by the azide-alkyne "click" reaction to form covalently coupled dimers, trimers, and tetramers. Polymerization of the DNA-dendrimer conjugates was also demonstrated, as well as assembly in a circular structure on DNA origami and imaging by atomic force microscopy.