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Biquadratic Exchange and Quadrupolar Ordering

Journal of Applied Physics, 1969
We have studied in the molecular field approximation the statistical mechanical properties of the Hamiltonian H= ∑ mnJ(m−n)Sm·Sn− ∑ mnj(m−n)(Sm·Sn)2,for spin one ions. Other authors have already shown that the biquadratic term can cause the magnetic transition to become first order.1 Closer examination shows that one must consider, in addition to the ...
M. Blume, Y. Y. Hsieh
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On the notion of second-order exchangeability

Erkenntnis, 1996
In this paper we consider the conditions of second-order exchangeability and second-order partially exchangeability together with some applications.
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Second-order eikonal exchange amplitudes

Physical Review A, 1986
The analytic expressions of the second-order eikonal exchange amplitudes are derived for electron-hydrogen scattering in both post and prior forms. In the case of the Glauber exchange amplitude, these expressions are shown to be reducible to closed forms. The results are applied to the calculation of elastic e-H(1s) scattering.
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First-order exchange approximation

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1963
Abstract It is shown that when the Born approximation is applied to rearrangement collisions in the customary way, terms of the first order in the interaction energy between the colliding particles are omitted from the exchange scattering amplitude.
Bell, K. L., Moiseiwitsch, B. L.
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The Exchange Order

2017
This book illuminates a comprehensive social system that comprises explicit markets, tort liability, and criminal liability, and describes each of these three institutions as serving the same function in different social and physical circumstances. It defines exchanges as compensated transfers of rights and objects among individuals, and shows that ...
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Limit order placement across multiple exchanges

2012 IEEE Conference on Computational Intelligence for Financial Engineering & Economics (CIFEr), 2012
The US equity exchange market is organized as a National Market System, enforcing price priority across exchanges, but otherwise allowing competition for order flow among exchanges. This flexibility has naturally evolved to a market where exchanges have varying quality and cost of execution.
Raymond Yim, Andrew Brzezinski
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Exchangeable Random Orders and Almost Uniform Distributions

Journal of Theoretical Probability, 2000
Let \({\mathcal V}\) \([{\mathcal T}]\) denote the set of all partial [total] orders on \(\mathbb{N}\). For \(U,V\in{\mathcal V}\), let \(U\vee V\) be the smallest partial order containing \(U\cup V\), and put \(\langle V\rangle=\{j \in\mathbb{N}\): there is \(k\neq j\) such that either \((j,k)\in V\) or \((k,j)\in V\}\).
Hirth, Ulrich, Ressel, Paul
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Afterword: The Exchange Order

2017
The Afterword illustrates the operation of the exchange order by analogy to Braudel’s division of history into three frames and considers how this order might best be studied. Markets, tort, and criminal liability each operate at three levels of depth: a surface level where individual transactions are carried out and change is rapid, a middle level ...
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Exchange Competition and Order Splitting

SSRN Electronic Journal, 2016
The emergence of new trading platforms has intensified order fragmentation. Yet, little is known on how this phenomenon affects the behavior of profit maximizing exchanges. I show that fragmentation may allow competing exchanges to retain market power. When order splitting is beneficial for traders, competing exchanges are complements.
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Order-order transitions in spin systems with double electron exchange

Journal of Magnetism and Magnetic Materials, 1976
Abstract Spin systems in the presence of isotropic single and double electron exchange are investigated at nonzero temperature. We use a generalized mean field approximation that allows for a variable local axis of quantization. This leads to the introduction of an angular parameter Θ giving the angle between nearest neighbor quantization axes. It is
R.G. Munro, M.D. Girardeau
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