Two high Nb-containing TiAl alloys, Ti46.6Al7.5Nb0.5Si0.2B (Alloy A) and Ti46.1Al7.4Nb5C0.5Si0.2B (Alloy B), were prepared by graphite mold casting. As-cast microstructures of the two alloys were characterized to clarify the effect of carbon addition. The results show that 5 at.% carbon addition can change the primary solidification phase from β phase to α phase. The as-cast microstructure of Alloy A consists of a fully α2 + γ lamellar structure and interdendritic eutectic silicide with a volume fraction of 2.3%. However, in Alloy B, the lamellar structure only forms in the dendritic stem and the massive γ is observed in the interdendritic regions. Two types of carbides, Ti2AlC and TiC, are produced in Alloy B. A large number of randomly distributed primary Ti2AlC particles with volume fraction of 14.9% are observed in both the dendritic and interdendritic regions. Irregularly shaped TiC remains inside of the large Ti2AlC particle, suggesting TiC carbides transformed to Ti2AlC during cooling. The addition of carbon also changes the morphology of the silicides from a eutectic structure to a blocky structure in the massive γ matrix or at the interface of the Ti2AlC and the γ matrix. High level of niobium greatly increases the solid solution limit of carbon, since C content in the matrix is much higher than the solid solubility of that in the TiAl binary system. The hardness of the matrix increases from 325 HV to 917 HV caused by the addition of carbon.
Problem statement: This research provided rigorous proof for the invariant study of the problem in section VI in "matched subspace detectors". About 14 years ago an important research entitled "matched subspace detectors" was published in IEEE transactions on signal processing, Vol. 42, No. 8, August 1994. Since its publication, the study has been widely cited in many areas. The main contribution of the research is to use invariance principle to study the Generalized Likelihood Ratio Test (GLRT) for four kinds of signal detection problems. While the conclusions are all correct, the largest invariant transformation group provided by the geometrical method is questionable. Furthermore the geometrical method in proving the maximal invariants is not helpful. The researchers themselves also frankly acknowledged "a rigorous proof requires an algebraic proof'' (page 2152 in above research). Approach: Hence, this correspondence exactly gave rigorous proof based on algebraic method regarding one problem in the above mentioned research. Results: The algebraic method in this correspondence can be readily applied to other cases in the same research. Conclusion/Recommendations: Through this concrete example, we advocated the algebraic, rigorous method in the invariant study of signal detection problems, while abandoning the geometrical method.
No abstract
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.