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On Second-Order Subdifferentials and Their Applications
SIAM Journal on Optimization, 2001The authors study second-order subdifferentials of extended-real-valued functions. The starting point is the second-order subdifferential introduced by the first author as the coderivative of the first-order subdifferentiable mapping. Beside this, a semiconvex version is introduced as the coderivative of the convexified first-order subdifferential ...
Boris S. Mordukhovich, Jirí V. Outrata
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Second-order micromotives and macrobehaviour
Journal of Computational Social Science, 2020This paper deals with the gap between the preferences of individual agents and collective outcomes. The typical example of this topic is the Schelling–Sakoda segregation model where a first-order discrimination criterion is used to decide whether or not a person will leave his place.
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2004
Der Titel bezieht sich auf eine zweite Art von Theoremen, auf algebraische Theoreme. Die algebraischen Theoreme explizieren die Einsicht, dass in bestimmten algebraischen Gefugen bestimmte Teilausdrucke unbegrenzt erweiterbar bzw. Variablen und Operatoren auf hochstens zwei reduzierbar sind.
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Der Titel bezieht sich auf eine zweite Art von Theoremen, auf algebraische Theoreme. Die algebraischen Theoreme explizieren die Einsicht, dass in bestimmten algebraischen Gefugen bestimmte Teilausdrucke unbegrenzt erweiterbar bzw. Variablen und Operatoren auf hochstens zwei reduzierbar sind.
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1984
In what follows we discuss second order spectra, in particular complete second order spectra. To start with, we briefly sumarize known facts about first order spectra. Let F be sentence of first order predicate calculus with equality. The spectrum Sp ( F ) is the set of natural numbers n such that F has model of cardinality n . H.
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In what follows we discuss second order spectra, in particular complete second order spectra. To start with, we briefly sumarize known facts about first order spectra. Let F be sentence of first order predicate calculus with equality. The spectrum Sp ( F ) is the set of natural numbers n such that F has model of cardinality n . H.
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Second-Order Structured Deformations
Archive for Rational Mechanics and Analysis, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Owen, David R., Paroni, Roberto
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Mathematical Logic Quarterly, 1984
A sentence F from second order predicate calculus with equality has standard form if \(F=(Q_ 0)...(Q_ k)(I)F'\) where: (1) \(Q_ j\) is a string \(E^*\) or a string \(\forall^*\) of second order quantifiers, (2) if \(Q_ j\) is \(E^*\) (or \(\forall^*)\) then \(Q_{j+1}\) is \(\forall^*\) or \(E^*\), respectively, (3) I is a string of individual ...
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A sentence F from second order predicate calculus with equality has standard form if \(F=(Q_ 0)...(Q_ k)(I)F'\) where: (1) \(Q_ j\) is a string \(E^*\) or a string \(\forall^*\) of second order quantifiers, (2) if \(Q_ j\) is \(E^*\) (or \(\forall^*)\) then \(Q_{j+1}\) is \(\forall^*\) or \(E^*\), respectively, (3) I is a string of individual ...
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1980
Plain predicate logic is called “first-order logic”, as it allows us to handle objects of structure, and to quantify over them. One might just as well allow quantification over subsets of structures. In that case we speak of a “second-order logic”, which is a logic with two kinds of quantifiers: ∀x and ∀X.
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Plain predicate logic is called “first-order logic”, as it allows us to handle objects of structure, and to quantify over them. One might just as well allow quantification over subsets of structures. In that case we speak of a “second-order logic”, which is a logic with two kinds of quantifiers: ∀x and ∀X.
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On Second-Order Generalized Convexity
Journal of Optimization Theory and Applications, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Second-order equations from a second-order formalism
Journal of Mathematical Physics, 1989It is often assumed that Lagrangians of gravitation that are quadratic in the curvature tensor produce field equations of fourth differential order in the metric tensor from a Hilbert variational principle. It is shown here, for the Lagrangian given by R+RμνRμν, that independent variations of the metric tensor and the torsion tensor produce ...
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ON SECOND ORDER DIFFERENTIAL OPERATORS
The Annals of Mathematics, 1955Nevertheless, (1.2) is meaningful only under differentiability conditions which are unnatural for (1.1). An adjoint to (1.1) exists always, but it cannot be written in terms of derivatives with respect to x. The characteristic property of A appears to be (1) that it is of local character, (2) that whenever f has a local minimum at xo and f(xo) = 0 ...
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