The Evolution of Stress Intensity Factors and the Propagation of Cracks in Elastic Media

When a crack Γ _s propagates in an elastic medium the stress intensity factors evolve with the tip x(s) of Γ _s . In this paper we derive formulae which describe the evolution of these stress intensity factors for a homogeneous isotropic elastic medium under plane strain conditions. Denoting by ψ=ψ(x,s) the stress potential (ψ is biharmonic and has zero traction along the crack Γ _s ) and by κ(s) the curvature of the crack at the tip x(s), we prove that the stress intensity factors A ₁(s), A ₂(s), as functions of s, satisfy:

A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior

In this paper we study a free boundary problem modeling the growth of radially symmetric tumors with two populations of cells: proliferating cells and quiescent cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations in the tumor, and the tumor's surface is a free boundary . The nutrient concentration satisfies a diffusion equation, and satisfies an integro-differential equation. It is known that this problem has a unique stationary solution with . We prove that (i) if , then , and (ii) the stationary solution is linearly asymptotically stable.

     

Isolation,structural elucidation and cytotoxicity evaluation of a new pentahydroxy-pimarane diterpenoid along with other chemical constituents from Aerva lanata

Aervalanata possesses various useful medicinal and pharmaceutical activities. Phytochemical investigation of the plant has now led to the isolation of a new 2α,3α,15,16,19-pentahydroxy pimar-8(14)-ene diterpenoid (1) together with 12 other known compounds identified as β-sitosterol (2), β-sitosterol-3-O-β-D-glucoside (3), canthin-6-one (4), 10-hydroxycanthin-6-one (aervine, 5), 10-methoxycanthin-6-one (methylaervine, 6), β-carboline-1-propionic acid (7), 1-O-β-D-glucopyranosyl-(2S,3R,8E)-2-[(2′R)-2-hydroxylpalmitoylamino]-8-octadecene-1,3-diol (8), 1-O-(β-D-glucopyranosyl)-(2S,3S,4R,8Z)-2-[(2′R)-2′-hydroxytetracosanoylamino]-8(Z)-octadene-1,3,4-triol (9), (2S,3S,4R,10E)-2-[(2′R)-2′-hydroxytetracosanoylamino]-10-octadecene-1,3,4-triol (10), 6′-O-(4″-hydroxy-trans-cinnamoyl)-kaempferol-3-O-β-D-glucopyranoside (tribuloside, 11), 3-cinnamoyltribuloside (12) and sulfonoquinovosyldiacylglyceride (13). Among these, six compounds (8–13) are reported for the first time from this plant. Cytotoxicity evaluation of the compounds against five cancer cell lines (CHO, HepG2, HeLa, A-431 and MCF-7) shows promising IC₅₀ values for compounds 4, 6 and 12.     

Synthesis and characterization of a new tetradentate ligand for Cu(II) metal ions

The synthesis and characterization of a tailor-made ligand 1 is described. Self-assembly of 1 on a GaAs surface was studied by FT-IR spectroscopy. The IR spectrum of the thin film points to the conclusion that the monolayer adsorbs to the surface via both carboxylates of the malonic acid derivative. The distinction between the possible binding modes is discussed.     

The role of basic amino acids in the molecular recognition of hydroxyapatite by statherin using solid state NMR

Organisms use proteins such as statherin to control the growth of hydroxyapatite (HAP), which is the principal component of teeth and bones. Though much emphasis has been placed on the acidic character of these proteins, the role of their basic amino acids is not well understood. In this work, solid state nuclear magnetic resonance was used to probe the interaction of the basic arginine side chains with the HAP surface. Statherin samples were individually labeled at each arginine site, and the distance to the surface was measured using the Rotational Echo DOuble Resonance (REDOR) technique. The results indicate a strong coupling between the R9 and R10 residues and the phosphorus atoms on the surface, with internuclear distances of 4.62 ± 0.29 Å and 4.53 ± 0.16 Å, respectively. Conversely, results also indicate weak coupling between R13 and the surface, suggesting this residue is more removed from the surface than R9 and R10. Combining these results with previous data, a new model for the molecular recognition of HAP by statherin is constructed.