scholarly journals Asymptotic formulas for the distributions of the determinant and the trace of a noncentral beta matrix

1972 ◽  
Vol 2 (2) ◽  
pp. 208-218 ◽  
Author(s):  
Yasunori Fujikoshi
Keyword(s):  
Asymptotic Formulas ◽  
Beta Matrix

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.

Asymptotics for rank moments of overpartitions

2014 ◽  
Vol 10 (08) ◽  
pp. 2011-2036 ◽  
Author(s):  
Renrong Mao
Keyword(s):  
Asymptotic Formulas ◽  
Error Terms ◽  
Cranks Of Partitions

Bringmann, Mahlburg and Rhoades proved asymptotic formulas for all the even moments of the ranks and cranks of partitions with polynomial error terms. In this paper, motivated by their work, we apply the same method and obtain asymptotics for the two rank moments of overpartitions.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

scholarly journals Numerical finite-key analysis of quantum key distribution

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Darius Bunandar ◽  
Luke C. G. Govia ◽  
Hari Krovi ◽  
Dirk Englund
Keyword(s):  
Finite Number ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Numerical Approach ◽  
Asymptotic Formulas ◽  
Quantum Computers ◽  
Secure Communications ◽  
Quantum Relative Entropy ◽  
Asymptotic Equipartition Property ◽  
Optimization Solvers

AbstractQuantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

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