scholarly journals A complex ray method using asymptotic expansions applied to the penetrable wedge

1991 ◽  
Vol 89 (4B) ◽  
pp. 1895-1895
Author(s):  
Grant B. Deane
Keyword(s):  
Asymptotic Expansions ◽  
Ray Method ◽  
Complex Ray ◽  
Complex Ray Method

Eulerian number asymptotics

1994 ◽  
Vol 445 (1924) ◽  
pp. 291-303 ◽  
Keyword(s):  
Formal Methods ◽  
Asymptotic Expansions ◽  
Recursion Relation ◽  
Matched Asymptotic Expansions ◽  
Ray Method ◽  
Eulerian Numbers ◽  
Eulerian Number ◽  
Asymptotic Formulae

Asymptotic formulae for the eulerian numbers A(n, k) for n ≫ 1 are obtained directly from their recursion relation by the ray method and the method of matched asymptotic expansions. These are formal methods, so they do not prove that the formulae are asymptotic, although they suggest it. The formulae agree with the previously known results where those results are valid. They also agree very well with the exact values of A(n, k) for 1 ≼ n ≼ 170, and the agreement improves as n increases.

Phase Transformations in Ti-7w/oMo-3w/oMe Alloy

1974 ◽  
Vol 32 ◽  
pp. 514-515
Author(s):  
S. Fujishiro
Keyword(s):  
Electron Microscopy ◽  
Mechanical Properties ◽  
Transmission Electron Microscopy ◽  
Tensile Strength ◽  
Mechanical Processing ◽  
Ray Method ◽  
X Ray ◽  
Transmission Electron ◽  
Water Quench ◽  
Alpha Beta

The mechanical properties of three titanium alloys (Ti-7Mo-3Al, Ti-7Mo- 3Cu and Ti-7Mo-3Ta) were evaluated as function of: 1) Solutionizing in the beta field and aging, 2) Thermal Mechanical Processing in the beta field and aging, 3) Solutionizing in the alpha + beta field and aging. The samples were isothermally aged in the temperature range 300° to 700*C for 4 to 24 hours, followed by a water quench. Transmission electron microscopy and X-ray method were used to identify the phase formed. All three alloys solutionized at 1050°C (beta field) transformed to martensitic alpha (alpha prime) upon being water quenched. Despite this heavily strained alpha prime, which is characterized by microtwins the tensile strength of the as-quenched alloys is relatively low and the elongation is as high as 30%.

scholarly journals Asymptotic Expansions and Strategies in the Online Increasing Subsequence Problem

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
Amirlan Seksenbayev
Keyword(s):  
Dynamic Programming ◽  
Asymptotic Expansions ◽  
Dual Problem ◽  
Infinite Length ◽  
Expected Time ◽  
Selection Strategies ◽  
Dynamic Programming Equation ◽  
Optimal Values ◽  
Design Selection ◽  
Selection Of

AbstractWe study two closely related problems in the online selection of increasing subsequence. In the first problem, introduced by Samuels and Steele (Ann. Probab. 9(6):937–947, 1981), the objective is to maximise the length of a subsequence selected by a nonanticipating strategy from a random sample of given size $n$ n . In the dual problem, recently studied by Arlotto et al. (Random Struct. Algorithms 49:235–252, 2016), the objective is to minimise the expected time needed to choose an increasing subsequence of given length $k$ k from a sequence of infinite length. Developing a method based on the monotonicity of the dynamic programming equation, we derive the two-term asymptotic expansions for the optimal values, with $O(1)$ O ( 1 ) remainder in the first problem and $O(k)$ O ( k ) in the second. Settling a conjecture in Arlotto et al. (Random Struct. Algorithms 52:41–53, 2018), we also design selection strategies to achieve optimality within these bounds, that are, in a sense, best possible.

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