Order Conditions, Trees and B-Series

Priestley duality for MV-algebras and beyond

Forum Mathematicum ◽

10.1515/forum-2020-0115 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wesley Fussner ◽

Mai Gehrke ◽

Samuel J. van Gool ◽

Vincenzo Marra

Keyword(s):

Large Class ◽

Order Conditions ◽

Enriched Environment ◽

Priestley Duality ◽

Distributive Lattices ◽

First Order ◽

Dual Spaces ◽

Binary Operations ◽

New Perspective ◽

Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

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Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds

Foundations of Computational Mathematics ◽

10.1007/s10208-021-09495-y ◽

2021 ◽

Author(s):

Adrien Laurent ◽

Gilles Vilmart

Keyword(s):

Invariant Measure ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Linear Group ◽

Langevin Equation ◽

Numerical Experiments ◽

Special Linear Group ◽

Order Conditions ◽

High Order ◽

Differential Equations On Manifolds

AbstractWe derive a new methodology for the construction of high-order integrators for sampling the invariant measure of ergodic stochastic differential equations with dynamics constrained on a manifold. We obtain the order conditions for sampling the invariant measure for a class of Runge–Kutta methods applied to the constrained overdamped Langevin equation. The analysis is valid for arbitrarily high order and relies on an extension of the exotic aromatic Butcher-series formalism. To illustrate the methodology, a method of order two is introduced, and numerical experiments on the sphere, the torus and the special linear group confirm the theoretical findings.

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Constraints in models of production and cost via slack-based measures

Empirical Economics ◽

10.1007/s00181-020-02013-z ◽

2021 ◽

Author(s):

Caroline Khan ◽

Mike G. Tsionas

Keyword(s):

Power Generation ◽

Stochastic Frontier ◽

Inequality Constraints ◽

Order Conditions ◽

Flexible Functional Forms ◽

Cost Share ◽

First Order ◽

Stochastic Frontier Models ◽

Endogenous Variables ◽

Functional Forms

AbstractIn this paper, we propose the use of stochastic frontier models to impose theoretical regularity constraints (like monotonicity and concavity) on flexible functional forms. These constraints take the form of inequalities involving the data and the parameters of the model. We address a major concern when statistically endogenous variables are present in these inequalities. We present results with and without endogeneity in the inequality constraints. In the system case (e.g., cost-share equations) or more generally, in production function-first-order conditions case, we detect an econometric problem which we solve successfully. We provide an empirical application to US electric power generation plants during 1986–1997, previously used by several authors.

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Stratifications of equivariant varieties

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700023315 ◽

1977 ◽

Vol 16 (2) ◽

pp. 279-295 ◽

Cited By ~ 13

Author(s):

M.J. Field

Keyword(s):

Lie Group ◽

General Position ◽

Higher Order ◽

Order Conditions ◽

Compact Lie Group ◽

Algebraic Varieties ◽

Equivariant Maps

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.

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