Some Results on the Extended Hypergeometric Matrix Functions and Related Functions

In this article, we discuss certain properties for generalized gamma and Euler’s beta matrix functions and the generalized hypergeometric matrix functions. The current results for these functions include integral representations, transformation formula, recurrence relations, and integral transforms.

PRELIMINARY INVESTIGATION OF BILLET PROCESSING ROUTE ON MICROSTRUCTURE, TEXTURE AND FATIGUE RESPONSE OF Ti834 FORGED DISC PRODUCTS

Non-standard processing routes for the manufacture of industrial scale Ti834 billet have been undertaken to investigate their effect on macrozones in final forged product. Microstructure, texture and dwell fatigue fracture surfaces were characterised from forged disc samples fabricated from these new billets. All processing routes showed a bimodal microstructure consisting of 25pct of primary alpha grains in a transformed beta matrix. Texture analysis has revealed variations in the presence and size of macrozones with relatively weak textures. Quasi-cleavage facets were present in all dwell fatigue samples although the fatigue life was doubled for the sample whose thermomechanical processing has the highest imposed strain.

Ultra-Fine Grained Ti-15Mo Alloy Prepared by Powder Metallurgy

Ti-15Mo alloy belongs to metastable β-Ti alloys that are currently used in aircraft manufacturing and Ti15Mo alloy is a perspective candidate for the use in medicine thanks to its biotolerant composition. In this study, Ti15Mo alloy was prepared by advanced techniques of powder metallurgy. The powder of gas atomized Ti-15Mo alloy was subjected to cryogenic milling to achieve ultra-fine grained microstructure within the powder particles. Powder was subsequently compacted using spark plasma sintering (SPS). The effect of cryogenic milling on the microstructure and phase composition of final bulk material after SPS was studied by scanning electron microscopy. Sintering at 750°C was not sufficient for achieving full density in gas atomized powder, while milled material could be successfully sintered at this temperature. Alpha phase particles precipitated during sintering and their size, as well as the size of beta matrix grains, was strongly affected by the sintering temperature.

Beta Matrix and Common Factors in Stock Returns

We consider the estimation methods for the rank of a beta matrix corresponding to a multifactor model and study which method would be appropriate for data with a large number of assets. Our simulation results indicate that a restricted version of Cragg and Donald’s (1997) Bayesian information criterion estimator is quite reliable for such data. We use this estimator to analyze some selected asset pricing models with U.S. stock returns. Our results indicate that the beta matrix from many models fails to have full column rank, suggesting that risk premiums in these models are underidentified.

Effect of TiB on the Nucleation and Growth of α Phase in Ti-6Al-4V-0.1B Alloy

The effect of TiB on the nucleation and growth of α phase both in as-casted and as-annealed Ti-6Al-4V-0.1B alloy by optical microscopy and EBSD technique. The results show that during the solidification α phases nucleate and grow up in the β phase matrix and the interface between beta matrix and TiB phase. TiB phase acts as a nucleation site for α phase and promotes the nucleation and growth, resulting in refined α colonies in as-cast microstructure. During the furnace cooling process from above β transus temperature, α precipitates is a consequence of its orientation relationship with TiB, which restraints the lath growth. Equiaxed α phase precipitates during the furnace cooling from the above β transus temperature.