Supports of Extremal Doubly Stochastic Measures

2016 ◽  
Vol 59 (2) ◽  
pp. 381-391
Author(s):  
Abbas Moameni
Keyword(s):  
Borel Probability Measure ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Doubly Stochastic ◽  
Extremal Points ◽  
Aperiodic Structure ◽  
Stochastic Measure ◽  
Borel Probability ◽  
Problem Number ◽  
Stochastic Measures

AbstractA doubly stochastic measure on the unit square is a Borel probability measure whose horizontal and vertical marginals both coincide with the Lebesgue measure. The set of doubly stochasticmeasures is convex and compact so its extremal points are of particular interest. The problem number 111 of Birkhoò is to provide a necessary and suõcient condition on the support of a doubly stochastic measure to guarantee extremality. It was proved by Beneš and Štepán that an extremal doubly stochastic measure is concentrated on a set which admits an aperiodic decomposition. Hestir and Williams later found a necessary condition which is nearly sufficient by further refining the aperiodic structure of the support of extremal doubly stochastic measures. Our objective in this work is to provide a more practical necessary and nearly sufficient condition for a set to support an extremal doubly stochastic measure

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

Some remarks on the existence of doubly stochastic measures with latticework hairpin support

1994 ◽  
Vol 47 (2-3) ◽  
pp. 164-174 ◽  
Author(s):  
J. -J. Quesada-Molina ◽  
J. -A. Rodriguez-Lallena
Keyword(s):  
Doubly Stochastic ◽  
Stochastic Measures

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

A minimal distal map on the torus with sub-exponential measure complexity

2018 ◽  
Vol 40 (4) ◽  
pp. 953-974 ◽  
Author(s):  
WEN HUANG ◽  
LEIYE XU ◽  
XIANGDONG YE
Keyword(s):  
Dynamical System ◽  
Probability Measure ◽  
Borel Probability Measure ◽  
Skew Product ◽  
Topological Dynamical System ◽  
Borel Probability ◽  
Product Map

In this paper the notion of sub-exponential measure complexity for an invariant Borel probability measure of a topological dynamical system is introduced. Then a minimal distal skew product map on the torus with sub-exponential measure complexity is constructed.

Rising or Constrained Power?

2010 ◽  
Author(s):  
Eswaran Sridharan
Keyword(s):  
Economic Growth ◽  
High Growth ◽  
The United States ◽  
Asia Pacific ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Economic Weight ◽  
Rising Power ◽  
Global Influence

This chapter analyses India’s prospects as a rising power by asking what kind of power India has the potential to be, given its military, economic, and institutional capacities and the economic and geostrategic constraints it faces. It argues that while sustained high growth is a necessary condition it is not a sufficient condition since economic growth does not necessarily convert smoothly into greater power. Due to such conversion problems India, like some other powers, might not be able to exercise commensurate regional, extra-regional, and global influence as might appear to follow from the revival of sustained high growth and increased economic weight. The more achievable and likely alternative is that of a coalitional or bridging power that can play the role of an effective partner in the security and other spheres to a range of powers, principally to the United States and in the Asia-Pacific and Indian Ocean regions.

scholarly journals Syarat Perlu dan Cukup untuk Keterbatasan Potensial Riesz di Ruang Morrey Klasik

2013 ◽  
Vol 14 (3) ◽  
pp. 227
Author(s):  
Mohammad Imam Utoyo ◽  
Basuki Widodo ◽  
Toto Nusantara ◽  
Suhariningsih Suhariningsih
Keyword(s):  
Characteristic Function ◽  
Morrey Space ◽  
Necessary Conditions ◽  
Riesz Potential ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Research Results ◽  
Necessary And Sufficient

This script was aimed to determine the necessary conditions for boundedness of Riesz potential in the classical Morrey space. If these results are combined with previous research results will be obtained the necessary and sufficient condition for boundedness of Riesz potential. This necessary condition is obtained through the use of characteristic function as one member of the classical Morrey space.

scholarly journals Spatio-temporal Dynamics of the Patterning of Arabidopsis Flower Meristem

2020 ◽  
Author(s):  
José Díaz ◽  
Elena R. Álvarez-Buylla
Keyword(s):  
Flower Development ◽  
Apical Meristem ◽  
Temporal Dynamics ◽  
Positional Information ◽  
Floral Organ ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Abc Model ◽  
Flower Meristem ◽  
Spatio Temporal

AbstractThe qualitative model presented in this work recovers the onset of the four fields that correspond to those of each floral organ whorl of Arabidopsis flower, suggesting a mechanism for the generation of the positional information required for the differential expression of the A, B and C identity genes according to the ABC model for organ determination during early stages of flower development. Our model integrates a previous model for the emergence of WUS pattern in the apical meristem, and shows that this pre-pattern is a necessary but not sufficient condition for the posterior information of the four fields predicted by the ABC model. Furthermore, our model predicts that LFY diffusion along the L1 layer of cells is not a necessary condition for the patterning of the floral meristem.

scholarly journals Generalized approximate boundary synchronization for a coupled system of wave equations

2020 ◽  
Author(s):  
Yanyan Wang
Keyword(s):  
Wave Equations ◽  
Dirichlet Boundary ◽  
Coupled System ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Exact Boundary ◽  
Boundary Controls ◽  
The Relationship ◽  
Exact Boundary Synchronization ◽  
Dirichlet Boundary Controls

In this paper, we consider the generalized approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls. We analyse the relationship between the generalized approximate boundary synchronization and the generalized exact boundary synchronization, give a sufficient condition to realize the generalized approximate boundary synchronization and a necessary condition in terms of Kalman’s matrix, and show the meaning of the number of total controls. Besides, by the generalized synchronization decomposition, we define the generalized approximately synchronizable state, and obtain its properties and a sufficient condition for it to be independent of applied boundary controls.

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

scholarly journals On extreme doubly stochastic measures.

1970 ◽  
Vol 17 (3) ◽  
pp. 249-254 ◽  
Author(s):  
James R. Brown ◽  
Ray C. Shiflett
Keyword(s):  
Doubly Stochastic ◽  
Stochastic Measures
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