A note on the Gauss-Jacobi quadrature formulae for singular integral equations of the second kind

A fast and efficient numerical method based on the Gauss-Jacobi quadrature is described that is suitable for solving Fredholm singular integral equations of the second kind that are frequently encountered in fracture and contact mechanics. Here we concentrate on the case when the unknown function is singular at both ends of the interval. Quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. Finally, an application of the method to a plane problem involving complete contact is presented.     

Light-induced electron spin polarization in the ground state of water-soluble copper porphyrins

Light-induced spin-polarized transient EPR spectra are reported for several water-soluble copper porphyrins. The spectra are assigned to the doublet ground state, with emissive spin polarization resulting from photoexcitation and subsequent electronic relaxation. In contrast to other systems for which polarization of a doublet ground state has been observed, the exchange interactions in the copper porphyrins are strong and the geometry is fixed. It is proposed that intersystem crossing from the photoexcited trip-doublet to the trip-quartet state can lead to net polarization of the spin system and that this polarization is maintained during electronic decay, possibly via charge-transfer and exciplex states. The intensity of the observed spin polarization is essentially independent of the molecular orientation in the external field, but is strongly dependent on the nature of the charged peripheral groups. Possible reasons for this behavior are discussed.     

Hopping and optical absorption of electrons in nano-porous crystal 12CaO·7Al2O3

Recently it has been discovered that a nano-porous main group oxide 12CaO·7Al₂O₃ (C12A7) can be converted from a wide-gap insulator to a good transparent conductor. Using ab initio modelling we explain good conductivity of this material by very small barriers for hopping of localised electrons between neighbouring positive cages. We show that optical absorption of C12A7 in infrared region and at energies higher than 2.7 eV is due to inter-cage and intra-cage electron transitions, respectively. The proposed mechanisms can be useful in further search for conducting transparent media.     

Experimental evidence of a relationship between monomer plasma residence time and carboxyl group retention in acrylic acid plasma polymers

Decreasing carboxyl retention in deposits from the glow region of an acrylic acid plasma was measured by X-ray photoelectron spectroscopy and chemical derivatisation as the collection distance from the monomer vapour inlet was increased. Volatilisation of plasma polymerised acrylic acid was detected after trifluoroethanol derivatisation; this is correlated with evaporation of low molecular weight components observed previously.     

On a large-gain theorem

The aim of this paper is to give a general quantitative requirement which the loop gain must satisfy in order to stabilize a given unstable (possibly nonlinear and time-varying) plant, namely that the gain must exceed one.     

EVALUATING SOFTWARE OUTSOURCING OPTIONS Do Your Software Operations Add Value ?

If you don't know the current productivity rates, usage volumes, and other quantitative baseline data for your software operations, then software might not be a key component of the company's core business. The evaluation criteria in this article can help the IS executive determine the outsourcing options for software operations.     

The rationale for cementless total hip replacement

Current cementing techniques of distal plugging, pulsatile water cleaning of the canal, and retrograde filling with PMMA in a low-viscous state prepared using porosity reduction techniques and then pressurized have been shown to give excellent results at 10 or more years after operation. However, physical and aging characteristics of PMMA do not guarantee that those results will hold up in the 20- to 30-year time frame. Fifteen-year experience with bony ingrowth systems indicate the development of a durable interface without PMMA, although the interface does appear more vulnerable to attack by the biologic reaction to HMWPE debris. Bone remodeling appears more favorable around proximally fixed bone ingrowth prostheses than around distally fixed prostheses. Softening of the physical characteristics of the stem tip may reduce the incidence of thigh pain. Patients with high activity potential and a life expectancy of greater than 25 years should be strongly considered for a proximally fixed bone ingrowth or ongrowth prosthesis.