Semi-Fredholm solvability and asymptotic expansions of singular solutions for Protter problems

2013 ◽  
Author(s):  
Nedyu Popivanov ◽  
Todor Popov ◽  
Allen Tesdall
Keyword(s):  
Asymptotic Expansions ◽  
Singular Solutions ◽  
Fredholm Solvability

scholarly journals Asymptotic expansions of singular solutions for (3+1)-D Protter problems

2007 ◽  
Vol 331 (2) ◽  
pp. 1093-1112 ◽  
Author(s):  
Nedyu Popivanov ◽  
Todor Popov ◽  
Rudolf Scherer
Keyword(s):  
Asymptotic Expansions ◽  
Singular Solutions

Finite Element Method for Solving Problems with Singular Solutions.

1995 ◽  
Author(s):  
I. Babuska ◽  
B. Andersson ◽  
B. Guo ◽  
H. S. Oh ◽  
J. M. Melenk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singular Solutions ◽  
Element Method

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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