Cohomology of $${\mathfrak{osp}}(1|2)$$ Acting on Linear Differential Operators on the Supercircle S1|1

We compute the first cohomology spaces of the Lie superalgebra with coefficients in the superspace of linear differential operators acting on weighted densities on the supercircle S ^1|1. The structure of these spaces was conjectured in (Gargoubi et al. in Lett Math Phys 79:5165, 2007). In fact, we prove here that the situation is a little bit more complicated.      

On 𝔬𝔰𝔭(1 | 2)-Relative Cohomology on S 1|1

We compute the second 𝔬𝔰𝔭(1 | 2) ?relative cohomology space of 𝒦(1) with coefficients in the module of λ-densities 𝔉_λ on S ^1|1. This result allows us to compute the second 𝔬𝔰𝔭(1 | 2) ?relative cohomology space of 𝒦(1) with coefficients in the Poisson superalgebra 𝒮𝒫. We explicitly give 2-cocycles spanning these cohomology spaces.     

Deformation of \mathfrak{sl}\, (2) and \mathfrak{osp}\, (1|2)-modules of symbols

We consider the $\mathfrak{sl}\, (2)$ -module structure on the spaces of symbols of differential operators acting on the spaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this structure and prove that any formal deformation is equivalent to its infinitesimal part. We study also the super analogue of this problem getting the same results.     

New mechanistic insight into electronically excited CO-NiO(100): a quantum dynamical analysis

In a recent study Redlich et al. [Redlich et al., Chem. Phys. Lett. 2006, 420, 110] measured the velocity distribution of CO molecules desorbing from a NiO(100) surface after irradiation with an ultraviolet (UV) laser pulse. Due to the complexity of the involved processes no experimental evidence on the excitation and desorption mechanism could be obtained. In recent ab initio studies Mehdaoui et al. [Mehdaoui et al., Phys. Rev. Lett. 2007, 98, 037601] have shown that a 5sigma --> 2pi* (a (3)Pi) like transition within the CO adsorbate is most likely the crucial excitation step in the CO-NiO(100) system. At first sight this seems unlikely, since the interaction of CO molecules with the NiO(100) surface is very weak (-0.30 eV) and the corresponding CO gas phase transition energy is about 1.5 eV higher than the laser pulse energy of 4.66 eV used in the experiment. In this work we give further insight into relevant electronically excited states and identify the desorption mechanism by analysing the dynamical processes after laser excitation by quantum dynamical wave packet simulations on the basis of three-dimensional (3D) ab initio potential energy surfaces. The results corroborate the so far discussed excitation mechanism, which proposes the formation of a genuine C-Ni bond as the driving force for photodesorption, as the crucial excitation step.     

Understanding surface photochemistry from first principles: the case of CO-NiO(100)

The excitation mechanism in the CO-NiO(100) system induced by a uv-laser pulse has been investigated from first principles. For the laser-driven process, the relevant electronically excited states are identified, and it is shown that a transition within the CO molecule is the crucial excitation step rather than substrate mediated processes. A new mechanism is proposed, in which the formation of a genuine C-Ni bond in the excited state is the driving force for photodesorption rather than electrostatic interactions, as has been found in similar systems. This results in very high velocities of CO molecules desorbing from the NiO(100) surface after electronic relaxation.     

Inhibition of Pro-inflammatory Secreted Phospholipase A2 by Extracts from <Emphasis Type="Italic">Cynara cardunculus L</Emphasis>.

The aim of the present work was to evaluate the anti-inflammatory properties of Cynara cardunculus L. (Asteraceae) during its growth using various solvents such as n-hexane, dichloromethane, acetone, and methanol for air-dried leaves and stems. The anti-inflammatory activities of crude extracts were evaluated by measuring the inhibition potency of mammalian non-pancreatic phospholipases A2 (hG-IIA). The methanol and acetone extracts of leaves harvested in February exhibit potent inhibition of hG-IIA (IC₅₀ = 50 and 70 μg/ml, respectively). However, the acetone extract of stems harvested in December inhibits the hG-IIA with a lower IC₅₀ around 130 μg/ml. Fractionation on silica gel and hydrophobic gel of the methanol extract of leaves harvested in February increases the inhibitory effect, and the IC₅₀ reached 10 μg/ml.     

Study of <Superscript>239</Superscript>Pu, <Superscript>144</Superscript>Ce,and <Superscript>90</Superscript>Sr Behavior During Radioactive Wastes Treatment by Thermal Plasma Technology

A computer model is used to study the volatility of some radioelements (Cerium, Plutonium and Strontium) during radioactive wastes treatment by thermal plasma technology. This model is based on the calculation of system composition using the free enthalpy minimization method, coupled with the equation of mass transfer at the reactional interface. The model enables the determination of the effects of various parameters (e.g., temperature, plasma current, and presence of oxygen in the carrier gas) on the radioelement volatility. The obtained results indicate that any increase in molten bath temperature causes an increase in the radioelement volatility. It is also found that the oxygen flux in the carrier gas strengthens the radioelement incorporation in the containment matrix. For electrolyses effects, an increase in the plasma current increases both the vaporization speed and the vaporized quantities of ²³⁹Pu, ¹⁴⁴Ce, and ⁹⁰Sr.     

Existence and Global Asymptotic Behavior of Positive Solutions for Sublinear and Superlinear Fractional Boundary Value Problems

In this paper, the authors aim at proving two existence results of fractional differential boundary value problems of the form(P_(a,b)){D~αu(x) + f(x, u(x)) = 0, x ∈(0, 1),u(0) = u(1) = 0, D~(α-3)u(0) = a, u(1) =-b,where 3 α≤ 4, Dαis the standard Riemann-Liouville fractional derivative and a, b are nonnegative constants. First the authors suppose that f(x, t) =-p(x)t~σ, with σ∈(-1, 1)and p being a nonnegative continuous function that may be singular at x = 0 or x = 1and satisfies some conditions related to the Karamata regular variation theory. Combining sharp estimates on some potential functions and the Sch¨auder fixed point theorem, the authors prove the existence of a unique positive continuous solution to problem(P_(0,0)).Global estimates on such a solution are also obtained. To state the second existence result, the authors assume that a, b are nonnegative constants such that a + b 0 and f(x, t) = tφ(x, t), with φ(x, t) being a nonnegative continuous function in(0, 1)×[0, ∞) that is required to satisfy some suitable integrability condition. Using estimates on the Green's function and a perturbation argument, the authors prove the existence and uniqueness of a positive continuous solution u to problem(P_(a,b)), which behaves like the unique solution of the homogeneous problem corresponding to(P_(a,b)). Some examples are given to illustrate the existence results.