Annular and circular rigid inclusions planted into a penny-shaped crack and factorization of triangular matrices.

Analytical solutions to two axisymmetric problems of a penny-shaped crack when an annulus-shaped (model 1) or a disc-shaped (model 2) rigid inclusion of arbitrary profile are embedded into the crack are derived. The problems are governed by integral equations with the Weber-Sonine kernel on two segments. By the Mellin convolution theorem, the integral equations associated with models 1 and 2 reduce to vector Riemann-Hilbert problems with 3 × 3 and 2 × 2 triangular matrix coefficients whose entries consist of meromorphic and plus or minus infinite indices exponential functions. Canonical matrices of factorization are derived and the partial indices are computed. Exact representation formulae for the normal stress, the stress intensity factors (SIFs) at the crack and inclusion edges, and the normal displacement are obtained and the results of numerical tests are reported. In addition, simple asymptotic formulae for the SIFs are derived.

Nonlinear bending models for beams and plates.

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler-Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition.

The tetrapeptide AcSDKP, a negative regulator of cell cycle entry, inhibits the proliferation of human and chicken lymphocytes.

The tetrapeptide AcSer-Asp-Lys-Pro (AcSDKP) is a physiological negative regulator of hematopoiesis in mammals. It acts by blocking the cell cycle entry of quiescent stem cells and progenitors. In the present study we report that AcSDKP blocks the proliferation of human as well as chicken lymphocytes. It inhibits by 25 to 40% the polyclonal mitogen- (phytohemagglutinin (PHA), pokeweed mitogen (PWM), or concanavalin A) or mixed lymphocyte reaction-induced proliferation of chicken lymphocytes. A comparable degree of inhibition was observed in human whole blood cultures stimulated by "T" (PHA) or "T and B" (PWM) mitogens. Our results obtained on two phylogenetically distant species show that AcSDKP reduces the lymphocyte proliferation probably by blocking or retarding entry into the cell cycle as previously demonstrated for hematopoietic progenitors and hepatocytes. Therefore, this endogenous, non-species-specific tetrapeptide may be involved in the regulation of immune response.