Search results for "Duality"
showing 10 items of 226 documents
An optimal bound for embedding linear spaces into projective planes
1988
Abstract Linear spaces with υ >n 2 − 1 2 n + 1 points, b⩽n2 + n + 1 lines and not constant point degree are classified. It turns out that there is essentially one class of such linear spaces which are not near pencils and which can not be embedded into any projective plane of order n.
Zur Hyperebenenalgebraisierung in desargues-Schen projektiven Verbandsgeometrien
1991
As a completion and extension of a result of A. Day and D. Pickering [5] we obtain the following structure theorem in the conceptual frame of projective lattice geometries: In a Desarguesian projective geometry the subgeometry of every at least one-dimensional hyperplane is module induced.
On the duality between mechanistic learners and what it is they learn
1993
All previous work in inductive inference and theoretical machine learning has taken the perspective of looking for a learning algorithm that successfully learns a collection of functions. In this work, we consider the perspective of starting with a set of functions, and considering the collection of learning algorithms that are successful at learning the given functions. Some strong dualities are revealed.
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
2021
This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular…
New expressions for string loop amplitudes leading to an ultrasimple conception of string dynamics
1991
New expressions are derived for string loop amplitudes as overlap integrals of string wave functionals. They are shown to take the form of exchange terms coming from the Bose-Einstein symmetrization between string segments. One is thus led to the ultrasimple conception that string theory is basically free, and that ``string interactions'' are merely due to the fact that strings are composite objects with Bose-Einstein segments as constituents.
Beyond the eidetics of living beings: contingency, plasticity, individuality
2021
Saving living phenomena means saving their contingency, their plasticity, their individuality. A fruitful dialogue between metaphysics, phenomenology and morphology can be of help to investigate the ontological question of form, giving us the possibility to investigate the question of form and its epistemological significance providing a revision of that eidetic approach which instead is in danger of losing the sense of the continuous plastic morphogenesis of living beings.
Convex Duality in Stochastic Optimization and Mathematical Finance
2011
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension of some useful techniques from these two fields to a much wider class of problems. In particular, combining certain finite-dimensional techniques from convex analysis with measure theoretic techniques from mathematical finance, we are able to close the duality gap in some situations where traditional topological arguments fail.
Nodes of entangledN-particle wave functions
2006
In a recent paper [Bressanini et al. Phys. Rev. Lett. 95, 110201 (2005)] it was pointed out that ``the nodes of even simple wave functions are largely unexplored.'' Here we show that for $N$-particle wave functions nodal surfaces arise from the spin and orbital entanglement of constituent two-particle wave functions and derive, for two-electron atoms, 11 exact nodal rules applicable in $LS$ coupling. In addition, the ``higher symmetry'' identified numerically in the above paper is shown to be an approximate dynamical symmetry described by a molecular model or a classical unstable periodic orbit. We show that the analysis is readily extended to four-particle wave functions and consider the c…
Darcy–Forchheimer Magnetized Nanofluid flow along with Heating and Dissipation Effects over a Shrinking Exponential Sheet with Stability Analysis
2022
Nanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydrodynamic (MHD) Darcy–Forchheimer nanofluid flow across an exponentially contracting sheet is presented. In this mathematical model, the effects of viscous dissipation, joule heating, first-order velocity, and thermal slip conditions are also examined. Using similarity transformations, a system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs). The problem is …
Euro Area Structural Convergence? A Multi-Criterion Cluster Analysis
2015
Abstract This paper proposes a classification of the old member countries of the euro area in a structural data rich environment and run a convergence analysis using the same framework. First, we use a clustering approach and identify two structurally distinct clusters of countries that are not modified between 1999 and 2012: the South Countries Group (SCG) – composed of Greece, Italy, Portugal and Spain – and the Other Countries Group (OCG). Second, we propose a convergence metrics and reach three key findings: (i) increase over time of the between-clusters׳ dispersion; (ii) diverging demographics and innovation performance into the OCG, and (iii) an unfortunate convergence towards high la…