The Complex of Solutions of the Nested Bethe Ansatz. The A_2 Spin Chain

The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin chain but their role is similar

Comparison of Bond in Roll-bonded and Adhesively Bonded Aluminums

Lap-shear and peel test measurements of bond strength have been carried out as part of an investigation of roll bonding of 2024 and 7075 aluminum alloys. Shear strengths of the bonded material in the F temper are in the range of 14 to 16 ksi. Corresponding peel strengths are 120 to 130 lb/inch. These values, which are three to five times those reported in the literature for adhesively bonded 2024 and 7075, are a result of the true metallurgical bond achieved. The effects of heat-treating the bonded material are described and the improvements in bond strength discussed relative to the shear strength of the parent material. The significance of the findings for aerospace applications is discussed

Finite-order meromorphic solutions and the discrete Painleve equations

Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z+1)+w(z-1) = R(z,w(z)) (eqn 1) where R(z,w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else equation (1) can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painleve equation of the form (1), together with their autonomous versions. This suggests that the existence of finite-order meromorphic solutions is a good detector of integrable difference equations.Comment: 34 page

Improved electrodes for skin contacts

Design is described of thick, flexible electrodes with appropriate metal surfaces which prevent unnecessary skin motion. Electrodes provide sufficient radial pressure directed toward body surface to depress skin a noticeable portion of its normal resilient thickness

Solid-state time-to-pulse-height converter developed

Solid-state circuit produces an output pulse with an amplitude directly proportional to the time interval between two input pulses. It uses selected circuit options to achieve variable mode operation and a tunnel diode controls the charging time of a capacitor in proportion to the time interval being measured

Erosion, corrosion and erosion-corrosion of EB PVD thermal barrier coatings

Electron beam (EB) physical vapour deposited (PVD) thermal barrier coatings (TBCs) have been used in gas turbine engines for a number of years. The primary mode of failure is attributed to oxidation of the bond coat and growth of the thermally grown oxide (TGO), the alumina scale that forms on the bond coat and to which the ceramic top coat adheres. Once the TGO reaches a critical thickness, the TBC tends to spall and expose the underlying substrate to the hot gases. Erosion is commonly accepted as a secondary failure mechanism, which thins the TBC thus reducing its insulation capability and increasing the TGO growth rate. In severe conditions, erosion can completely remove the TBC over time, again resulting in the exposure of the substrate, typically Ni-based superalloys. Since engine efficiency is related to turbine entry temperature (TET), there is a constant driving force to increase this temperature. With this drive for higher TETs comes corrosion problems for the yttria stabilised zirconia (YSZ) ceramic topcoat. YSZ is susceptible to attack from molten calciumâ  magnesiumâ  aluminaâ  silicates (CMAS) which degrades the YSZ both chemically and micro-structurally. CMAS has a melting point of around 1240 à °C and since it is common in atmospheric dust it is easily deposited onto gas turbine blades. If the CMAS then melts and penetrates into the ceramic, the life of the TBC can be significantly reduced. This paper discusses the various failure mechanisms associated with the erosion, corrosion and erosionâ  corrosion of EB PVD TBCs. The concept of a dimensionless ratio D/d, where D is the contact footprint diameter and d is the column diameter, as a means of determining the erosion mechanism is introduced and discussed for E

Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue of the Clunie Lemma, as well as other results on the value distribution of solutions.Comment: 12 pages. To appear in the Journal of Mathematical Analysis and Application