A simple characterization of tightness for convex solid sets of positive random variables

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient to be is radially bounded, i.e. that every ray passing through one of its elements eventually leaves the set. The result is motivated by problems arising in mathematical finance.     

On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces

An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying \(x=\theta _X\) whenever \(p(x)=p(-x)=0\). Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a linear space, the theory is different in the asymmetric case. The main purpose of this study is to define bounded and continuous linear operators acting between asymmetric cone normed spaces. After examining the differences with symmetric case, we give some results related to Baire’s characterization of completeness in asymmetric cone normed spaces.     

Transport in a disordered tight-binding chain with dephasing

We studied transport properties of a disordered tight-binding model (XX spin chain) in the presence of dephasing. Focusing on diffusive behaviour in the thermodynamic limit at high energies, we analytically derived the dependence of conductivity on dephasing and disorder strengths. As a function of dephasing, conductivity exhibits a single maximum at the optimal dephasing strength. The scaling of the position of this maximum with disorder strength is different for small and large disorders. In addition, we studied periodic disorder for which we found a resonance phenomenon, with conductivity having two maxima as a function of dephasing strength. If the disorder is non-zero only at a random fraction of all sites, conductivity is approximately the same as in the case of a disorder on all sites but with a rescaled disorder strength.     

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.     

Dispersive micro-solid phase extraction of 16 priority polycyclic aromatic hydrocarbons from water by using thermally treated clinoptilolite,and their quantification by GC-MS

The authors report on a novel sorbent (thermally treated natural zeolite; clinoptilolite) for use in dispersive micro-solid phase extraction (D-μ-SPE) of polycyclic aromatic hydrocarbons (PAHs) from water samples. The method was applied to the D-μ-SPE of 16 priority PAHs which then were quantified by gas chromatography with mass spectrometric detection (GC-MS). The method was validated in terms of specificity and selectivity, linearity and linear range, accuracy, precision, uncertainty, limits of detection and quantification. Figures of merit include (a) linear analytical ranges between 2.08 and 208 ppb, and (b) detection limits in the range from 0.01 to 0.92 ppb. The method was successfully applied to the determination of PAHs in river waters.

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Graphical abstract Schematic representation of dispersive micro-solid phase extraction (D-μ-SPE) of trace levels of PAHs in water samples by using thermally treated clinoptilolite as sorbent prior to gas chromatography-mass spectrometry analysis (GC-MS).

     

C–H⋅<Emphasis Type="Italic">s</Emphasis>O hydrogen bond networks in <Emphasis Type="Italic">E</Emphasis>- and Z-unsaturated esters of C-glycosides

Methyl E(Z)-4,7 anhydro-5-benzamido-6,8-di-O-benzoyl-2,3,5-trideoxy-d-allo-oct-2-enoate have been synthesized like intermediates and isolated as single crystals during the synthesis of pyrazole-related C nucleosides as synthetic product with cytotoxic activity.¹ Crystal structures of E(Z) isomers were determined by X-ray analysis. E isomer crystallizes in the triclinic crystal system, space group P1, a = 5.319(1) Å, b = 10.758(2) Å, c = 12.229(2) Å, α = 72.38(2)^∘, β = 89.97(2)^∘, γ = 87.07(2)^∘, D_x = 1.320 Mgm⁻³ and Z isomer in the orthorhombic crystal system, space group P2₁2₁2₁, a = 5.1297(13) Å, b = 19.667(5) Å, c = 25.871(6) Å, D_x = 1.348 Mgm⁻³. The molecular structure was solved by direct method on the basis of 2609 and 2727 unique reflections recorded at the temperature 293 K (E-isomer) and 173 K (Z-isomer) up to the final R-factor 0.0378 and 0.0435, respectively. C–H⋅sO contact networks were analyzed and the correlation established between the existence of the weak C–H⋅sO hydrogen bonds and the melting point of the single crystals.