Identification of internal cracks in a three-dimensional solid body via Steklov–Poincaré approaches

This Note deals with the identification of internal planar cracks inside a three-dimensional elastic body via two approaches relying on domain decomposition using elastostatic measurements. These approaches consist in recasting the problem in terms of primal or dual Steklov–Poincaré equations. The primal approach is a straightforward continuation to the elastic Cauchy problem of the work presented in J. Ben Abdallah (2007) [1] which is devoted to the Cauchy problem for the scalar Laplace equation. The numerical performances of these formulations are compared.     

C-Totally real pseudo-parallel submanifolds of Sasakian space forms

Let be (2n + 1)-dimensional Sasakian space form of constant ϕ-sectional curvature (c) and M ⁿ be an ⁿ -dimensional C-totally real, minimal submanifold of . We prove that if M ⁿ is pseudo-parallel and , then M ⁿ is totally geodesic.     

Reaction of neptunyl ions with mycobactin S in nonaqueous medium

Addition of solutions of mycobactin S in acetone or methanol/acetone mixtures to solutions of NpO ₂ ²⁺ in the same solvent leads to the immediate reduction of neptunium/VI/ to neptunium/V/. Np/V/ interacts with the ionophore to form a yellow complex with a cation: ligand ratio of 21. The course of these reactions is followed by measurement of changes in characteristic optical absorption and by spectrophotometric titration within the range 700–1350 nm.     

ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES I

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n > 4, satisfying (aC + BR) ?H = LkQ(g, Hk), k = 1,2, 3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

Infinite independent sets in distributive lattices

We show that a poset P contains a subset isomorphic to if and only if the poset J(P) consisting of ideals of P contains a subset isomorphic to the power set of κ. If P is a join-semilattice this amounts to the fact that P contains an independent set of size κ. We show that if κ := ω and P is a distributive lattice, then this amounts to the fact that P contains either or as sublattices, where Γ and Δ are two special meet-semilattices already considered by J. D. Lawson, M. Mislove and H. A. Priestley.Dedicated to the memory of Ivan RivalReceived April 22, 2003; accepted in final form July 11, 2004.This revised version was published online in August 2005 with a corrected cover date.     

Wavelet-type Transform and Bessel Potentials Associated with the Generalized Translation

Wavelet–type transform associated with singular Laplace–Bessel differential operator is introduced and the relevant Calderón–type reproducing formula is established. Representations of the generalized Bessel potentials 0)$ " align="middle" border="0"> and their inverses via the wavelet–type transform are obtained.     

Measurement and thermodynamic modeling of Np(V) solubility in aqueous K2CO3 solutions to high concentrations

The solubility of Np(V) solids was studied in 0.01 to 6.38 mol-Kg^-1 ₂CO₃ solutions. Two series of experiments were conducted from undersaturation using NpO₂OH(s) or KNpO₂CO₃(s) as the starting solid. The Np(V) solid phases observed at steady state are KNpO₂CO₃(s) and K₃NpO₂(CO₃)₂(s). The activity coefficient formalism of Pitzer was used to obtain a thermodynamic interpretation of these data, including the solubility constants: To model these data, we propose values for several binary and ternary ion interaction parameters among the carbonate ion, potassium ion, and the neptunyl triscarbonato ion. With these new parameters, the thermodynamic data base for Np(V) solubility in concentrated aqueous solutions has been extended to the NaK-C1-C1O₄-CO₃-H-OH-H₂O system.     

Kinetics and mechanism of the 1,3-dipolar cycloaddition of phenyl azides to methyl 3-pyrrolidinoacrylate

Kinetics of cycloadditions of phenyl azides to methyl 3-pyrrolidinoacrylate (2) produced Hammett ? = 2.2. An E_a of 13.5 kcal mole ^?1 and Δ S^* of ?37.4 cal.K^?l mole^?1 were calculated for the cycloaddition of p-O₂NC₆H₄N₃ to 2. The cycloadditions are concerted, non-synchronous, and are controlled by LUMO (azide) - HOMO (dipolarophile) interactions.     

Submanifolds and their k-planar number

IfM is a submanifold of ⁿ the normal plane together with a tangent at a pointx M span an affine plane which intersectsM, locally, in a curve called the normal section. This paper introduces, for each integerk, a parameter called(k) which depends on the curvature and torsion of these normal sections. Results are obtained showing how these parameters for a product submanifold depend on the value of this parameter for the factor submanifolds.The first author is supported by Uludag University in TURKEY     

Unprecedented stereoselective synthesis of 3-methylisoxazolidine-5-aryl-1,2,4-oxadiazoles via 1,3-dipolar cycloaddition and study of their in vitro antioxidant activity

The stereoselective 1,3-dipolar cycloaddition between allyl cyanide and a menthone-derived nitrone led to the desired isoxazolidine in good yield. Once the nitrile group transformed to an amidoxime group, the cyclocondensation of various aldehydes with chiral amidoxime led to unprecedented enantiopure 3-methylisoxazolidine-5-aryl-1,2,4-oxadiazoles. The menthone chiral auxiliary was then removed with acid hydrolysis. The new compounds were also screened for their in vitro antioxidant activity using DPPH and FRAP assays. Some of the compounds showed promising antioxidant activity.