On aq-gamma and a q-beta matrix functions

2012 ◽  
Vol 60 (6) ◽  
pp. 683-696 ◽  
Author(s):  
Ahmed Salem
Keyword(s):  
Matrix Functions ◽  
Beta Matrix

scholarly journals Some properties of Gamma and Beta matrix functions

1998 ◽  
Vol 11 (1) ◽  
pp. 89-93 ◽  
Author(s):  
L Jódar ◽  
J.C Cortés
Keyword(s):  
Matrix Functions ◽  
Beta Matrix

scholarly journals Some Results on the Extended Hypergeometric Matrix Functions and Related Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Mohamed Abdalla ◽  
Sahar Ahmed Idris ◽  
Ibrahim Mekawy
Keyword(s):  
Recurrence Relations ◽  
Integral Transforms ◽  
Integral Representations ◽  
Transformation Formula ◽  
Matrix Functions ◽  
Generalized Gamma ◽  
Beta Matrix

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.

Decomposition of the metastable beta titanium alloy Ti-15-3

1983 ◽  
Vol 41 ◽  
pp. 264-265
Author(s):  
Y. L. Chen ◽  
S. Fujlshiro
Keyword(s):  
Low Cost ◽  
High Strength ◽  
Alpha Phase ◽  
Thick Sheet ◽  
Omega Phase ◽  
Beta Titanium Alloy ◽  
Beta Titanium ◽  
Beta Matrix ◽  
Metastable Beta ◽  
Very High

Metastable beta titanium alloys have been known to have numerous advantages such as cold formability, high strength, good fracture resistance, deep hardenability, and cost effectiveness. Very high strength is obtainable by precipitation of the hexagonal alpha phase in a bcc beta matrix in these alloys. Precipitation hardening in the metastable beta alloys may also result from the formation of transition phases such as omega phase. Ti-15-3 (Ti-15V- 3Cr-3Al-3Sn) has been developed recently by TIMET and USAF for low cost sheet metal applications. The purpose of the present study was to examine the aging characteristics in this alloy.The composition of the as-received material is: 14.7 V, 3.14 Cr, 3.05 Al, 2.26 Sn, and 0.145 Fe. The beta transus temperature as determined by optical metallographic method was about 770°C. Specimen coupons were prepared from a mill-annealed 1.2 mm thick sheet, and solution treated at 827°C for 2 hr in argon, then water quenched. Aging was also done in argon at temperatures ranging from 316 to 616°C for various times.

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

2018 ◽  
Vol 941 ◽  
pp. 1276-1281
Author(s):  
Anna Terynková ◽  
Jiří Kozlík ◽  
Kristína Bartha ◽  
Tomáš Chráska ◽  
Josef Stráský
Keyword(s):  
Powder Metallurgy ◽  
Bulk Material ◽  
Alpha Phase ◽  
Full Density ◽  
Fine Grained ◽  
Cryogenic Milling ◽  
Aircraft Manufacturing ◽  
Plasma Sintering ◽  
Beta Matrix ◽  
Spark Plasma

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.

scholarly journals Very badly approximable matrix functions

2005 ◽  
Vol 11 (1) ◽  
pp. 127-154 ◽  
Author(s):  
V. V. Peller ◽  
S. R. Treil
Keyword(s):  
Matrix Functions ◽  
Badly Approximable

A New Random Data Description and Its Use in Transferring Road Roughness to Vehicle Response

1974 ◽  
Vol 96 (2) ◽  
pp. 676-679 ◽  
Author(s):  
J. C. Wambold ◽  
W. H. Park ◽  
R. G. Vashlishan
Keyword(s):  
Spectral Density ◽  
Frequency Distribution ◽  
Descriptive Analysis ◽  
Joint Probability ◽  
Amplitude Distribution ◽  
Matrix Functions ◽  
Initial Portion ◽  
Power Spectral ◽  
Road Roughness ◽  
Cross Spectral Density

The initial portion of the paper discusses the more conventional method of obtaining a vehicle transfer function where phase and magnitude are determined by dividing the cross spectral density of the input/output by the power spectral density (PSD) of the input. The authors needed a more descriptive analysis (over PSD) and developed a new signal description called Amplitude Frequency Distribution (AFD); a discrete joint probability of amplitude and frequency with the advantage of retaining amplitude distribution as well as frequency distribution. A better understanding was obtained, and transfer matrix functions were developed using AFD.

Derivatives of Eigenvalues and Eigenvectors of Matrix Functions

1993 ◽  
Vol 14 (4) ◽  
pp. 903-926 ◽  
Author(s):  
Alan L. Andrew ◽  
K.-W. Eric Chu ◽  
Peter Lancaster
Keyword(s):  
Matrix Functions ◽  
Eigenvalues And Eigenvectors ◽  
Derivatives Of
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