Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

We prove some optimal logarithmic estimates in the Hardy space H ^∞(G) with Hölder regularity, where G is the open unit disk or an annular domain of ?. These estimates extend the results established by S.Chaabane and I.Feki in the Hardy-Sobolev space H ^k,∞ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem for the Laplace operator and the Robin inverse problem.     

Weighted completion time minimization on a single-machine with a fixed non-availability interval: Differential approximability

This paper is the first successful attempt on differential approximability study for a scheduling problem. Such a study considers the weighted completion time minimization on a single machine with a fixed non-availability interval. The analysis shows that the Weighted Shortest Processing Time (WSPT) rule cannot yield a differential approximation for the problem under consideration in the general case. Nevertheless, a slight modification of this rule provides an approximation with a differential ratio of $\frac{3?\sqrt{5}}{2}\approx 0.38$.     

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.     

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.     

Prime Orders All of Whose Prime Suborders Are Selfdual

Let P be an order on a set V. A subset A of V is autonomous in P if every element of V not in A is either less than or greater than or incomparable to all elements of A. The empty set, the singletons from V and the set V are autonomous sets and are called trivial. Call an order prime if all its autonomous sets are trivial. We give the complete list of all finite prime orders all of whose prime suborders are selfdual.     

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.     

Estimates in the Hardy-Sobolev space of the annulus and stability result

The main purpose of this work is to establish some logarithmic estimates of optimal type in the Hardy-Sobolev space H ^k,∞; k ∈ ?* of an annular domain. These results are considered as a continuation of a previous study in the setting of the unit disk by L.Baratchart and M. Zerner, On the recovery of functions from pointwise boundary values in a Hardy-Sobolev class of the disk, J. Comput. Appl. Math. 46 (1993), 255–269 and by S.Chaabane and I. Feki, Optimal logarithmic estimates in Hardy-Sobolev spaces H ^k,∞, C. R., Math., Acad. Sci. Paris 347 (2009), 1001–1006. As an application, we prove a logarithmic stability result for the inverse problem of identifying a Robin parameter on a part of the boundary of an annular domain starting from its behavior on the complementary boundary part.     

The Order on the Rationals has an Orthogonal Order with the Same Order Type

Two orders on the same set are orthogonal if the constant maps and the identity map are the only maps preserving both orders. We construct linear orders orthogonal to the order on the rationals.     

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.