Phytochemical profile and biological activities of Deverra tortuosa (Desf.)DC.: a desert aromatic shrub widespread in Northern Region of Saudi Arabia

The present study describes the chemical composition of the essential oil of different plant parts of Devrra tortuosa; in vivo and in vitro biological activities of plant extract and essential oils. Apiol was found to be the major component of the oil (between 65.73% and 74.41%). The best antioxidant activities were observed for the oil of flowers (IC50 = 175 μg/ml). The samples of stems and roots exhibit lower antioxidant activity (IC50 = 201 μg/ml and 182 μg/ml, respectively). The values of IC50 showed that the extracts of methanol exhibit the highest antioxidants activities (IC50 = 64.8 102 μg/ml). EOs showed excellent antifungal activity against yeasts with low azole susceptibilities (i.e. Malassezia spp. and Candida krusei). The MIC values of oils varied between 2.85 mg/mL and 27 mg/mL. The obtained results also showed that the plant extracts inhibited the germination and the shoot and root growth of Triticum æstivum seedlings.     

Quasiconvexification of sets in optimal design

By a suitable reformulation of a typical optimal design problem in conductivity, we treat the issue of determining the quasiconvexification (to fixed volume fraction) of certain sets of matrices that are union of two manifolds. By means of a helpful lemma, we are able to explicitly compute such hulls in a rather straightforward fashion without the need of seeking laminates by hand, and hence avoiding some tedious computations. We examine the linear case, both elliptic and hyperbolic, in 2 and higher dimension (by looking at a div–curl situation), as well as an interesting non-linear example that provides some clue as to what kind of characterization one may hope for in non-linear situations. This work was supported by the research projects MTM2007-62945 of the MCyT (Spain) and PCI08-0084-0424 of the JCCM (Castilla-La Mancha).     

Limiting Absorption Principle for Some Long Range Perturbations of Dirac Systems at Threshold Energies

We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to studying a family of non-self-adjoint operators. The technique is based on a positive commutator theory for non-self-adjoint operators, which we develop in the Appendix. We also discuss some applications to the dispersive Helmholtz model in the quantum regime.     

Integration and dimensional modeling approaches for complex data warehousing

With the broad development of the World Wide Web, various kinds of heterogeneous data (including multimedia data) are now available to decision support tasks. A data warehousing approach is often adopted to prepare data for relevant analysis. Data integration and dimensional modeling indeed allow the creation of appropriate analysis contexts. However, the existing data warehousing tools are well-suited to classical, numerical data. They cannot handle complex data. In our approach, we adapt the three main phases of the data warehousing process to complex data. In this paper, we particularly focus on two main steps in complex data warehousing. The first step is data integration. We define a generic UML model that helps representing a wide range of complex data, including their possible semantic properties. Complex data are then stored in XML documents generated by a piece of software we designed. The second important phase we address is the preparation of data for dimensional modeling. We propose an approach that exploits data mining techniques to assist users in building relevant dimensional models.     

Relaxation results for functions depending on polynomials changing sign on rank-one matrices

In this paper, we are interested in computing the different convex envelopes of functions depending on polynomials, especially those having it is main part change sign on rank-one matrices. Our main result applies to functions of the type W(F)=φ(P(F)), W(F)=φ(P(F))+f(detF) or W(F)=φ(P(F))+g(adjnF) defined on the space of matrices, where φ, f:R→R and g:R³→R are three continuous functions, and P=P₀+P₁+?+Pd is a polynomial such that Pd has the property of changing sign on rank-one matrices. Then the polyconvex, quasi-convex and rank-one convex envelopes of W are equal.     

Optimization of steam explosion to enhance hemicellulose recovery and enzymatic hydrolysis of cellulose in softwoods

A combination of Douglas fir heartwood and sapwood chips were steam pretreated under three conditions as measured by the Severity Factor (log R_o), which incorporated the time, temperature/pressure of pretreatment. By adjusting the steam pretreatment conditions, it was hoped to recover the majority of the hemicellulose component as monomers in the water-soluble stream, while providing a cellulosic-rich, water-insoluble fraction that could be readily hydrolyzed by cellulases. These three conditions were chosen to represent either high hemicellulose sugar recovery (low severity [L], log R_o=3.08), high-enzyme hydrolyzability of the cellulosic component (high severity [H], log R_o=4.21), and a compromise between the two conditions (medium severity [M], log R_o=3.45). The medium-severity pretreatment conditions (195°C, 4.5 min, 4.5% SO₂ logR_o=3.45) gave the best compromise in terms of relatively high hemicellulose recovery after stream pretreatment and the subsequent efficiency of enzymatic hydrolysis of the water-insoluble cellulosic fraction. The percent recovery of the original hemicellulose in the water-soluble fraction dropped significantly when the severity was increased (L-76.8%, M-64.7%, and H-37.5%). However, the ease of enzymatic hydrolysis of the cellulose-rich, water-insoluble fraction increased with increasing severity (L-24%, M-86.6%, and H-97.9%). Although more severe pretreatment conditions provided optimum hydrolysis of the cellulosic component, less severe conditions resulted in better recovery of the combined hemicellulose and cellulosic components.     

On the phase behavior and structural properties of polyelectrolyte solutions

Correlations between structural properties and phase behavior of polyelectrolyte solutions were discussed along the line of the work reported by Châtellier and Joanny [Joanny JF, Châtellier X. J Phys France II 1996;6:1669]. A multicomponent system made of polyions, salt ions and counterions was considered under poor solvent conditions. Unlike this reference, partial structure factors were derived from the celebrated Zimm’s formula written in the matrix form including the effects of finite chain length. These effects were found to generate significant shifts in phase diagrams and qualitative changes in structural properties. The presence of a charged solid surface was briefly discussed. Here also, the phase diagram was found to shift with an increasing amount as the polyion chain length decreased.     

Virial identity and weak dispersion for the magnetic Dirac equation

We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of view. We also prove a Hardy-type inequality for the perturbed Dirac operator.     

Chemical composition and antioxidant activities of essential oils and methanol extracts of three wild Lavandula L. species

A comparative study of essential oil composition, polyphenol content and antioxidant activities of Lavandula coronopifolia, Lavandula multifida and Lavandula stoechas subsp. stoechas were reported. Qualitative and quantitative variations in the composition of oils according to species were shown. Lavandula coronopifolia's oil was characterised by high proportions of trans-β-ocimene (26.9%), carvacrol (18.5%), β-bisabolene (13.1%) and myrcene (7.5%). The main components of L. multifida oil are carvacrol (65.1%) and β-bisabolene (24.7%). Lavandula stoechas oil is rich in fenchone (34.3%) and comphor (27.4%). The total phenolic and flavonoid contents also significantly varied among species. Lavandula coronopifolia exhibits the highest phenolic and flavonoid contents (31.3?mg GAE?g(-1) and 16.3?mg RE?g(-1), respectively), followed by L. multifida (30.8?mg GAE?g(-1) and 12.3?mg RE?g(-1)). Methanolic extracts and essential oils displayed significant antioxidant activities. The level of antioxidant capacity varied according to extracts and species.     

Stable Directions for Small Nonlinear Dirac Standing Waves

We prove that for a Dirac operator, with no resonance at thresholds nor eigenvalue at thresholds, the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues sufficiently close to each other, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schrödinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation