Determination of trace elements in the Lavender inflorescence (Lavandula angustifolia Mill.) — Lavender oil system

Bulgaria is a famous world producer of essential oils. Quality control of the lavender oils produced is an important analytical task in view of their wide use in perfumery and cosmetics, the food industry and aromatherapy. The present paper studies the relationship between the trace elements content in lavender inflorescence (Lavandula angustifolia Mill.) and in lavender oil derived from this inflorescence. Three model regions were investigated: two of them are situated far from industrial areas — the village of Zelenikovo and the town of Pavel Banya, and one region is located near the Plovdiv Non-Ferrous Metallurgical Plant. The content of the elements Cd, Cr, Cu, Fe, Mn and Pb in plants was determined after acid digestion by flame and electrothermal atomic absorption spectrometry (ETAAS). Lavender oils were analyzed directly by ETAAS. The results undoubtedly show that there is no strong correlation between the trace elements content in inflorescence and in essential oils. It might be assumed that the trace elements present and accumulated in the inflorescence do not pass in lavender oil during the production by steam distillation.     

Chemical biology of protein lipidation: semi-synthesis and structure elucidation of prenylated RabGTPases

Rab/Ypt guanosine triphosphatases (GTPases) represent a family of key membrane traffic regulators in eukaryotic cells. For their function Rab/Ypt proteins require double modification with two covalently bound geranylgeranyl lipid moieties at the C-terminus. Generally, prenylated proteins are very difficult to obtain by recombinant or enzymatic methods. We generated prenylated RabGTPases using a combination of chemical synthesis and protein engineering. This semi-synthesis depends largely on the availability of functionalized prenylated peptides corresponding to the proteins' native structure or modifications. We developed solution phase and solid phase strategies for the generation of peptides corresponding to the prenylated C-terminus of Rab7 GTPase in preparative amounts enabling us to crystallize the mono-prenylated Ypt1:RabGDI complex. The structure of the complex provides a structural basis for the ability of RabGDI to inhibit the release of nucleotide by Rab proteins and a molecular basis for understanding a RabGDI mutant that causes mental retardation in humans.     

On The Maximum Friction Law for Rigid/Plastic,Hardening Materials

For a rigid/plastic, hardening material model, it is shown that the velocity fields adjacent to surfaces of maximum friction must satisfy the sticking condition. This means that the stress boundary condition, the maximum friction law, may be replaced by the velocity boundary condition. Axisymmetric flows without rotation and planar flows are considered.     

Algebra versus analysis in the theory of flexible polyhedra

Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while Sabitov used algebra, namely, the theory of resultants, to prove that the oriented volume remains constant during the flex. We show that none of these methods can be used to prove both theorems. As a by-product, we prove that the total mean curvature of any polyhedron in the Euclidean 3-space is not an algebraic function of its edge lengths.     

Free-surface roughness of thin-walled tubes in reduction

The problem of the stress-strain state of thin-walled tubes in axisymmetric steady-state deformation is solved using the membrane theory of shells and the model of an ideal rigid-plastic material satisfying the Mises yield condition and the associated flow law. The obtained solution is used together with the empirical relation between the strain state at an arbitrary point of the free surface and the surface roughness parameters at the same point to determine the influence of some tube reduction parameters on the surface roughness parameters in the product. The employed empirical relation is derived assuming that the free surface roughness parameters depend on two independent kinematic variables.     

Stress and strain fields in rotating elastic/plastic annular disks of pressure-dependent material

The Drucker–Prager yield criterion is used in conjunction with its associated flow rule to find the elastic/plastic stress and strain distributions within the rotating annular disks under plane stress conditions. The main distinguished feature of the model, as compared to typical models used for analysis of disks, is that the material is plastically compressible. Using an approach proposed elsewhere, the solution for strain rates is reduced to one nonlinear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one, which significantly simplifies the numerical treatment and increases the accuracy of solution.