scholarly journals A GENERAL DUALITY THEORY FOR CLONES

2013 ◽  
Vol 23 (03) ◽  
pp. 457-502 ◽  
Author(s):  
SEBASTIAN KERKHOFF
Keyword(s):  
Duality Theory ◽  
The Relationship ◽  
General Duality ◽  
General Duality Theory

Inspired by work of Mašulović, we outline a general duality theory for clones that will allow us to dualize any given clone, together with its relational counterpart and the relationship between them. Afterwards, we put the approach to work and illustrate it by producing some specific results for concrete examples as well as some general results that come from studying the duals of clones in a rather abstract fashion.

scholarly journals Duality in finite dimensional complex space

1978 ◽  
Vol 18 (1) ◽  
pp. 65-75
Author(s):  
C.H. Scott ◽  
T.R. Jefferson
Keyword(s):  
Quadratic Programming ◽  
Duality Theory ◽  
Complex Space ◽  
Optimization Problems ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Mathematical Programs ◽  
Finite Dimensional ◽  
General Duality ◽  
General Duality Theory

The idea of duality is now a widely accepted and useful idea in the analysis of optimization problems posed in real finite dimensional vector spaces. Although similar ideas have filtered over to the analysis of optimization problems in complex space, these have mainly been concerned with problems of the linear and quadratic programming variety. In this paper we present a general duality theory for convex mathematical programs in finite dimensional complex space, and, by means of an example, show that this formulation captures all previous results in the area.

Near unanimity: an obstacle to general duality theory

1995 ◽  
Vol 33 (3) ◽  
pp. 428-439 ◽  
Author(s):  
B. A. Davey ◽  
L. Heindorf ◽  
R. McKenzie
Keyword(s):  
Duality Theory ◽  
Near Unanimity ◽  
General Duality ◽  
General Duality Theory

scholarly journals Stochastic Separated Continuous Conic Programming: Strong Duality and a Solution Method

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Xiaoqing Wang
Keyword(s):  
Duality Theory ◽  
Solution Method ◽  
Optimization Problems ◽  
Strong Duality ◽  
Conic Programming ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
New Class ◽  
Polynomial Time Approximation Algorithm ◽  
The Relationship

We study a new class of optimization problems calledstochastic separated continuous conic programming(SSCCP). SSCCP is an extension to the optimization model calledseparated continuous conic programming(SCCP) which has applications in robust optimization and sign-constrained linear-quadratic control. Based on the relationship among SSCCP, its dual, and their discretization counterparts, we develop a strong duality theory for the SSCCP. We also suggest a polynomial-time approximation algorithm that solves the SSCCP to any predefined accuracy.

scholarly journals Dual Spaces of Multiparameter Local Hardy Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wei Ding ◽  
Feng Yu
Keyword(s):  
Hardy Spaces ◽  
Duality Theory ◽  
Carleson Measure ◽  
Dual Spaces ◽  
Local Hardy Spaces ◽  
The Relationship

In this paper, we study the duality theory of the multiparameter local Hardy spaces h p ℝ n 1 × ℝ n 2 , and we prove that h p ℝ n 1 × ℝ n 2 ∗ = cm o p ℝ n 1 × ℝ n 2 , where cm o p ℝ n 1 × ℝ n 2 are defined by discrete Carleson measure. Moreover, we discuss the relationship among cm o p ℝ n 1 × ℝ n 2 , Li p p ℝ n 1 × ℝ n 2 , and rectangle cm o rect p ℝ n 1 × ℝ n 2 .

scholarly journals Matrix factorizations via Koszul duality

2014 ◽  
Vol 150 (9) ◽  
pp. 1549-1578 ◽  
Author(s):  
Junwu Tu
Keyword(s):  
Duality Theory ◽  
Hochschild Homology ◽  
Matrix Factorizations ◽  
Koszul Duality ◽  
Technical Tool ◽  
Graded Algebras ◽  
Differential Graded Algebras ◽  
Homological Perturbation ◽  
The Relationship

AbstractIn this paper we prove a version of curved Koszul duality for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{Z}/2\mathbb{Z}$-graded curved coalgebras and their cobar differential graded algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool for studying curved (co)algebras and precomplexes. The results of Koszul duality can be applied to study the category of matrix factorizations $\mathsf{MF}(R,W)$. We show how Dyckerhoff’s generating results fit into the framework of curved Koszul duality theory. This enables us to clarify the relationship between the Borel–Moore Hochschild homology of curved (co)algebras and the ordinary Hochschild homology of the category $\mathsf{MF}(R,W)$. Similar results are also obtained in the orbifold case and in the graded case.

scholarly journals Grothendieck–Neeman duality and the Wirthmüller isomorphism

2016 ◽  
Vol 152 (8) ◽  
pp. 1740-1776 ◽  
Author(s):  
Paul Balmer ◽  
Ivo Dell’Ambrogio ◽  
Beren Sanders
Keyword(s):  
Duality Theory ◽  
Homotopy Theory ◽  
Stable Homotopy ◽  
Adjoint Functors ◽  
Stable Homotopy Theory ◽  
Matlis Duality ◽  
Interesting Pattern ◽  
Tensor Triangulated Categories ◽  
The Relationship ◽  
Compactly Generated

We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk–Hu–May. We exhibit an interesting pattern of symmetry in the existence of adjoint functors between compactly generated tensor-triangulated categories, which leads to a surprising trichotomy: there exist either exactly three adjoints, exactly five, or infinitely many. We highlight the importance of so-called relative dualizing objects and explain how they give rise to dualities on canonical subcategories. This yields a duality theory rich enough to capture the main features of Grothendieck duality in algebraic geometry, of generalized Pontryagin–Matlis duality à la Dwyer–Greenless–Iyengar in the theory of ring spectra, and of Brown–Comenetz duality à la Neeman in stable homotopy theory.

Discrete-time and continuous-time modelling: some bridges and gaps

2007 ◽  
Vol 17 (2) ◽  
pp. 261-276 ◽  
Author(s):  
HUBERT KRIVINE ◽  
ANNICK LESNE ◽  
JACQUES TREINER
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Logistic Equation ◽  
Planetary Motion ◽  
Natural Phenomena ◽  
Predator Prey ◽  
Time Dynamics ◽  
Predator Prey Model ◽  
The Relationship ◽  
General Duality

The relationship between continuous-time dynamics and the corresponding discrete schemes, and its generally limited validity, is an important and widely acknowledged field within numerical analysis. In this paper, we propose another, more physical, viewpoint on this topic in order to understand the possible failure of discretisation procedures and the way to fix it. Three basic examples, the logistic equation, the Lotka–Volterra predator–prey model and Newton's law for planetary motion, are worked out. They illustrate the deep difference between continuous-time evolutions and discrete-time mappings, hence shedding some light on the more general duality between continuous descriptions of natural phenomena and discrete numerical computations.

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