scholarly journals Lagrangian solutions to systems of real principal type

2004 ◽  
Vol 277 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Sönke Hansen ◽  
Daniel Röhrig
Keyword(s):  
Principal Type

Type Inference: Some Results, Some Problems1

1993 ◽  
Vol 19 (1-2) ◽  
pp. 87-125
Author(s):  
Paola Giannini ◽  
Furio Honsell ◽  
Simona Ronchi Della Rocca
Keyword(s):  
Large Class ◽  
Higher Order ◽  
Type Inference ◽  
Principal Type ◽  
Open Problems ◽  
Inference Problem ◽  
Type Assignment ◽  
Unification Problem

In this paper we investigate the type inference problem for a large class of type assignment systems for the λ-calculus. This is the problem of determining if a term has a type in a given system. We discuss, in particular, a collection of type assignment systems which correspond to the typed systems of Barendregt’s “cube”. Type dependencies being shown redundant, we focus on the strongest of all, Fω, the type assignment version of the system Fω of Girard. In order to manipulate uniformly type inferences we give a syntax directed presentation of Fω and introduce the notions of scheme and of principal type scheme. Making essential use of them, we succeed in reducing the type inference problem for Fω to a restriction of the higher order semi-unification problem and in showing that the conditional type inference problem for Fω is undecidable. Throughout the paper we call attention to open problems and formulate some conjectures.

scholarly journals Geometric aspects of self-adjoint Sturm–Liouville problems

2017 ◽  
Vol 147 (6) ◽  
pp. 1279-1295
Author(s):  
Yicao Wang
Keyword(s):  
Boundary Conditions ◽  
Liouville Equation ◽  
Adjoint Action ◽  
Principal Type ◽  
Unitary Matrices ◽  
Adjoint Orbits ◽  
Sturm Liouville ◽  
Refined Classification ◽  
Adjoint Orbit

In this paper we use U(2), the group of 2 × 2 unitary matrices, to parametrize the space of all self-adjoint boundary conditions for a fixed Sturm–Liouville equation on the interval [0, 1]. The adjoint action of U(2) on itself naturally leads to a refined classification of self-adjoint boundary conditions – each adjoint orbit is a subclass of these boundary conditions. We give explicit parametrizations of those adjoint orbits of principal type, i.e. orbits diffeomorphic to the 2-sphere S2, and investigate the behaviour of the nth eigenvalue λnas a function on such orbits.

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