A Compact Solar Laser Side-Pumping Scheme Using Four Off-Axis Parabolic Mirrors

Journal of Russian Laser Research - Laser side-pumping approach is an extremely attractive configuration for many laser applications. Through this approach, the laser beam can be generated in the...     

Quasistatic Viscoelastic Contact with Normal Compliance and Friction

We prove the existence of a unique weak solution to the quasistatic problem of frictional contact between a deformable body and a rigid foundation. The material is assumed to have nonlinear viscoelastic behavior. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We establish the continuous dependence of the solution on the normal compliance function. Moreover, we prove the existence of a unique solution to the problem of sliding contact with wear. This revised version was published online in August 2006 with corrections to the Cover Date.     

A microconductometric biosensor based on lipase extracted from Candida rugosa for direct and rapid detection of organophosphate pesticides

Organophosphate pesticides (OPs) have been intensively used as insecticides in agriculture; after entering the aquatic environment, they may affect a wide range of organisms. A conductometric enzymatic biosensor based on lipase extracted from Candida rugosa (CRL) has therefore been developed for the direct and rapid quantitative detection of organophosphate pesticides: diazinon, methyl parathion and methyl paraoxon in water. The biosensor signal and response time were obtained under optimum conditions, the enzyme being immobilised in the presence of gold nanoparticles. Under these conditions, the enzymatic biosensor was able to measure concentrations as low as 60 µg/L of diazinon, 26 µg/L of methyl parathion and 25 µg/L of methyl paraoxon very rapidly (response time: 3 min). Moreover, this CRL biosensor was not sensitive to interferences such as carbamates. It presented good storage stability for 21 days when kept at 4°C and it was successfully applied to real samples.     

Cohomology of Some Complex Laminations

In this paper we solve the ${\overline{\partial }}$ -problem along the leaves for two types of laminations: (i) Some open sets Ω of ${{\mathbb C}\times B}$ (where B is any differentiable manifold) endowed with the canonical foliation that is, the foliation whose leaves are the sections ${\Omega ^t=\{ z\in {\mathbb C}:(z,t)\in \Omega \}}$ . We construct a solution to the equation ${\overline{\partial }h=fd\overline z}$ for any function ${f:\Omega\longrightarrow {\mathbb C}}$ of class ${C^{s}\,(s\in \mathbb{N}\cup\{ \infty \}),\,C^\infty}$ along the leaves and satisfies some growth conditions near the singularities. (ii) A complex lamination by Riemann surfaces obtained by suspending a homeomorphism of a closed set of the Euclidean space ${\mathbb{C}\times \mathbb{R}}$ .     

Real quadratic flexible division algebras

In this paper we give a new process called vectorial isotopy, in order to classify the eight-dimensional real quadratic flexible division algebras, and we solve the isomorphism problem.     

On Rate-Type Viscoplastic Problems with Linear Boundary Conditions

In this paper we introduce the abstract concept of “linear boundary conditions” in the study of deformable bodies. We establish two existence and uniqueness results concerning respectively quasistatic and dynamic problems involving such type of boundary conditions. We also apply these existence results in the study of viscoplastic problems involving classical boundary conditions.     

Finite-dimensional absolute-valued algebras

In this paper we provide some new tools for the study of finite-dimensional absolute-valued algebras. We introduce homotopy notions in this field and develop some of their applications. Next, we parametrize these algebras by spin groups and study their isomorphisms. Finally, we introduce a duplication process for the construction of absolute-valued algebras.     

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.