Brownian motion characterization of some Besov-Lipschitz spaces on domains

We characterize the Besov-Lipschitz spaces with zero boundary conditions on bounded smooth domains. We prove that the appropriate first and second difference norms are equivalent to the norm given in terms of the transition kernel of the Brownian motion killed upon exit from the domain.     

Epidemic centrality — is there an underestimated epidemic impact of network peripheral nodes?

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as “superspreaders”, are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed.     

Energy Properties and Biomass Yield of Miscanthus x Giganteus Fertilized by Municipal Sewage Sludge

The application of municipal sewage sludge as fertilizer in the production of non-food energy crops is an environmentally and economically sustainable approach to sewage sludge management. In addition, the application of municipal sewage sludge to energy crops such as Miscanthus x giganteus is an alternative form of recycling nutrients and organic material from waste. Municipal sewage sludge is a potential source of heavy metals in the soil, some of which can be removed by growing energy crops that are also remediation agents. Therefore, the objective of the research was to investigate the effect of municipal sewage sludge applied at three different rates of 1.66, 3.22 and 6.44 t/ha on the production of Miscanthus. Based on the analyses conducted on the biomass of Miscanthus fertilized with sludge from the wastewater treatment plant in three fertilization treatments, it can be concluded that the biomass of Miscanthus is a good feedstock for the process of direct combustion. Moreover, the application of the largest amount of municipal sewage sludge during cultivation had no negative effect on the properties of Miscanthus biomass. Moreover, the cellulose and hemicellulose content of Miscanthus is ideal for the production of second-generation liquid biofuels. Fertilizer treatments had no effect on the content of cellulose and lignin, while a significant statistical difference was found for hemicellulose.     

Substrate specificity of the acyl transferase domains of EpoC from the epothilone polyketide synthase

The production of epothilone mixtures is a direct consequence of the substrate tolerance of the module 3 acyltransferase (AT) domain of the epothilone polyketide synthase (PKS) which utilises both malonyl- and methylmalonyl-CoA extender units. Particular amino acid motifs in the active site of AT domains influence substrate selection for methylmalonyl-CoA (YASH) or malonyl-CoA (HAFH). This motif appears in hybrid form (HASH) in epoAT3 and may represent the molecular basis for the relaxed specificity of the domain. To investigate this possibility the AT domains from modules 2 and 3 of the epothilone PKS were examined in the heterologous DEBS1-TE model PKS. Substitution of AT1 of DEBS1-TE by epoAT2 and epoAT3 both resulted in functional PKSs, although lower yields of total products were observed when compared to DEBS1-TE (2% and 11.5% respectively). As expected, epoAT3 was significantly more promiscuous in keeping with its nature during epothilone biosynthesis. When the mixed motif (HASH) of epoAT3 within the hybrid PKS was mutated to HAFH (indicative of malonyl-CoA selection) it resulted in a non-productive PKS. When this mixed motif was converted to YASH (indicative of methylmalonyl-CoA selection) the selectivity of the hybrid PKS for methylmalonyl-CoA showed no statistically significant increase, and was associated with a loss of productivity.     

Presmectic wetting and supercritical-like phase behavior of octylcyanobiphenyl liquid crystal confined to controlled-pore glass matrices

The influence of controlled-pore glass (CPG) confinement on the phase behavior of octylcyanobiphenyl liquid crystal (LC) is studied by means of x-ray scattering and high precision calorimetry. For CPG samples with pore diameter 2R>24 nm, the smectic order parameter temperature dependence eta(T) reveals apparent presmectic ordering far above the bulk smectic A-nematic (SmA-N) phase transition for both nontreated and silane-treated CPG matrices. The behavior of eta(T) is qualitatively similar in all samples, well obeying the mean field approach (MFA) in which the surface wetting tendency plays the dominant role. In contrast, the critical fluctuations remain important in the specific heat data, which cannot be described within the MFA. We show experimentally that randomness and surface wetting become dominant over finite-size effects for 2R approximately<10 nm, in agreement with theoretical analysis. In nontreated samples, the noncritical character of the static disorder and the interfacial LC-CPG coupling almost completely suppress the quasi-SmA-N and nematic-isotropic phase transitions at 2R approximately 15.1 and approximately 7.5 nm, respectively.     

High-resolution calorimetric study of pb(mg_{1/3}nb_{2/3})o_{3} single crystal

Motivated by the long-standing unresolved enigma of the relaxor ferroelectric ground state, we performed a high-resolution heat capacity and polarization study of the field-induced phase transition in the relaxor ferroelectric single crystal Pb(Mg_{1/3}Nb_{2/3})O_{3} (PMN) oriented along the [110] direction. We show that the discontinuous evolution of polarization as a function of the electric field or temperature is a consequence of a true first order transition from a glassy to ferroelectric state, which is accompanied by an excess heat capacity anomaly and released latent heat. We also find that in a zero field there is no ferroelectric phase transition in bulk PMN at any temperature, indicating that the nonergodic dipolar glass phase persists down to the lowest temperatures.     

Volatile organic compounds from Centaurium erythraea Rafn (Croatia) and the antimicrobial potential of its essential oil

GC and MS were used for the analysis of Croatian Centaurium erythraea Rafn essential oil (obtained by hydrodistillation) and headspace (applying headspace solid-phase microextraction). The headspace contained numerous monoterpene hydrocarbons (the major ones were terpinene-4-ol, methone, p-cymene, γ-terpinene and limonene). Oxygenated monoterpenes were present in the headspace and oil, while 1,8-cineole, bornyl acetate and verbenone were present only in the headspace. High headspace percentages of toluene and naphthalene were found, followed by hemimellitene. Lot of similarities were observed with Serbian C. erythraea oil [neophytadiene (1.4%), thymol (2.6%), carvacrol (6.1%) and hexadecanoic acid (5.7%)], but different features were also noted such as the presence of menthol, menthone and phytone. The oil fractionation enabled identification of other minor compounds not found in total oil such as norisoprenoides, alk-1-enes or chromolaenin. The essential oil showed antimicrobial potential on Escherichia coli, Salmonella enteritidis, Staphylococcus aureus and Bacillus cereus. On the other hand, no antibacterial activity of the oil was observed on Pseudomonas fluorescens and Lysteria monocytogenes.     

Genetic Algorithm for Network Cost Minimization Using Threshold Based Discounting

We present a genetic algorithm for heuristically solving a cost minimization problem applied to communication networks with threshold based discounting. The network model assumes that every two nodes can communicate and offers incentives to combine of from different sources. Namely, there is a prescribed threshold on every link, and if the total of on a link is greater than the threshold, the cost of this of is discounted by a factor. A heuristic algorithm based on genetic strategy is developed and applied to a benchmark set of problems. The results are compared with former branch and bound results using the CPLEX(r)solver. For larger data instances we were able to obtain improved solutions using less CPU time, confirming the effectiveness of our heuristic approach.     

Potential Theory of Geometric Stable Processes

In this paper we study the potential theory of symmetric geometric stable processes by realizing them as subordinate Brownian motions with geometric stable subordinators. More precisely, we establish the asymptotic behaviors of the Green function and the Lévy density of symmetric geometric stable processes. The asymptotics of these functions near zero exhibit features that are very different from the ones for stable processes. The Green function behaves near zero as 1/(|x|^d log ²|x|), while the Lévy density behaves like 1/|x|^d. We also study the asymptotic behaviors of the Green function and Lévy density of subordinate Brownian motions with iterated geometric stable subordinators. As an application, we establish estimates on the capacity of small balls for these processes, as well as mean exit time estimates from small balls and a Harnack inequality for these processes. The research of this author is supported in part by MZT grant 0037118 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167. The research of this author is supported in part by a joint US-Croatia grant INT 0302167. The research of this author is supported in part by MZT grant 0037107 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167.