Quadratic orbits: a dual problem

2000 ◽  
pp. 231-246
Author(s):  
André Unterberger
Keyword(s):  
Dual Problem

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.

scholarly journals On the Classical Capacity of General Quantum Gaussian Measurement

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 377
Author(s):  
Alexander Holevo
Keyword(s):  
Dual Problem ◽  
Measurement Channel ◽  
Gaussian Channel ◽  
Quantum Communications ◽  
Classical Capacity ◽  
Optimal Ensemble ◽  
Accessible Information ◽  
Measurement Channels ◽  
Gaussian Ensemble ◽  
Average State

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble. Our findings are relevant to practical situations in quantum communications where the receiver is Gaussian (say, a general-dyne detection) and concatenation of the Gaussian channel and the receiver can be considered as one Gaussian measurement channel. Our efforts in this and preceding papers are then aimed at establishing full Gaussianity of the optimal ensemble (usually taken as an assumption) in such schemes.

scholarly journals The Hausdorff dual problem for connected groups

1981 ◽  
Vol 43 (1) ◽  
pp. 60-68 ◽  
Author(s):  
Larry Baggett ◽  
Terje Sund
Keyword(s):  
Dual Problem

GCSE science – a dual problem

Physics World ◽  
2008 ◽  
Vol 21 (05) ◽  
pp. 22-22
Author(s):  
Michael Huber ◽  
Trevor Hill
Keyword(s):  
Dual Problem

scholarly journals Numerical Approximation of a Compressible Multiphase System

2014 ◽  
Vol 15 (5) ◽  
pp. 1237-1265 ◽  
Author(s):  
Remi Abgrall ◽  
Harish Kumar
Keyword(s):  
Dual Problem ◽  
Conservative System ◽  
Model Description ◽  
Multiphase System ◽  
Discontinuous Solutions ◽  
Glimm Scheme ◽  
Conservation Principles ◽  
Difficult Challenge ◽  
Limit Solutions ◽  
Mesh Convergence

AbstractThe numerical simulation of non conservative system is a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly from conservation principles, so that in general, if the model description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [1]. In this paper we are interested in the “dual” problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme.

scholarly journals Mixed E-duality for E-differentiable Vector Optimization Problems Under (Generalized) V-E-invexity

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Najeeb Abdulaleem
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Duality Theorems ◽  
Differentiable Vector

AbstractIn this paper, a class of E-differentiable vector optimization problems with both inequality and equality constraints is considered. The so-called vector mixed E-dual problem is defined for the considered E-differentiable vector optimization problem with both inequality and equality constraints. Then, several mixed E-duality theorems are established under (generalized) V-E-invexity hypotheses.

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