Coupling proximal methods and variational convergence

An approximation method which combines a data perturbation by variational convergence with the proximal point algorithm, is presented. Conditions which guarantee convergence, are provided and an application to the partial inverse method is given.     

Absolute Valued Algebras with Involution

We study absolute valued algebras with involution, as defined in Urbanik (1961 Urbanik , K. ( 1961 ). Absolute valued algebras with an involution . Fundamenta Math. 49 : 247 – 258 . [Google Scholar]). We prove that these algebras are finite-dimensional whenever they satisfy the identity (x, x ², x) = 0, where (·, ·, ·) means associator. We show that, in dimension different from two, isomorphisms between absolute valued algebras with involution are in fact *-isomorphisms. Finally, we give a classification up to isomorphisms of all finite-dimensional absolute valued algebras with involution. As in the case of a parallel situation considered in Rochdi (2003 Rochdi , A. ( 2003 ). Eight-dimensional real absolute valued algebras with left unit whose automorphism group is trivial . Int. J. Math. Math. Sci. 70 : 4447 – 4454 .[Crossref] , [Google Scholar]), the triviality of the group of automorphisms of such an algebra can happen in dimension 8, and is equivalent to the nonexistence of 4-dimensional subalgebras.     

Investigation of the threshold intensity versus gas pressure in the breakdown of helium by 248 nm laser radiation

An investigation of the unexpectedly strong dependence of the threshold intensity on the gas pressure in the experimental study on the breakdown of He by short laser wavelength (Turcu et al., in Opt Commun, 134:66–68, 1997) is presented. A modified electron cascade model is applied (Evans and Gamal, in J Phys D Appl Phys, 13:1447–1458, 1980). Computations revealed reasonable agreement between the calculated thresholds and the measured ones. Moreover, the calculated electron energy distribution function and its parameters proved that multiphoton ionization of ground and excited atoms is the main source for the seed electrons, which contributes to the breakdown of helium. The effect of diffusion losses over pressures <1,000 Torr elucidated the origin of the strong dependence of the threshold intensity on the gas pressure. Collisional ionization dominates only at high pressures. No evidence for recombination losses is observed for pressures up to 3,000 Torr.     

Surjective linear maps preserving local spectra

Let B(X) be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We characterize linear surjective and continuous maps on B(X) preserving different local spectral quantities at a nonzero fixed vector.     

Symmetric multi-box splines for higher degree

We consider the space S _n =S _n (v ₀,…,v _n+r ) of compactly supported C ^n?1 piecewise polynomials on a mesh M of lines through ?² in directions v ₀,…,v _n+r . A sequence ψ=(ψ ₁,…,ψ _r ) of elements of S _n is called a multi-box spline if every element of S _n is a finite linear combination of shifts of (the components of) ψ. For the case n=2, 3 we give some examples for multi-box splines and show that they are not always stable. It is further shown that any C ^n?1 piecewise polynomial of degree n≥2 on M, is possibly a symmetric multi-box spline.     

Recent Advances in Electrochemical Sensors Based on Molecularly Imprinted Polymers and Nanomaterials

This review focuses on the recent achievement during period of 2013–2018 related to the electrochemical sensors based on molecularly imprinted polymers (MIPs) combined with nanomaterials for various kinds of applications. MIPs based electrochemical sensors have found a great interest due to their high stability, short time required for electropolymerization, and high specificity towards the target analyte. The sensitivity is considered as one of the important parameter in electrochemical sensing strategies that should be improved by the combination of highly conductive nanomaterials with selective MIPs. In general, the most employed nanomaterials are magnetic nanoparticles, gold nanoparticles (AuNPs), carbon nanotubes and graphene. This review discusses the main current achievement as well as the current challenges regarding the development of biomimetic sensors in electroanalysis.     

Synthesis of fluoromethylated materials derived from 2-trifluoromethyl acrylic acid phenethyl ester in an ionic liquid

Synthesis of fluoromethylated materials via Michael addition reaction catalyzed by l-proline in an ionic liquid, is described. Further, the synthesis and synthetic application of zinc reagents generated in an ionic liquid, giving trifluoromethylated materials, are described.