Non-existence of program optimizers in an abstract setting

1974 ◽  
pp. 253-265
Author(s):  
Donald A. Alton ◽  
John L. Lowther
Keyword(s):  
Abstract Setting

scholarly journals Spectral methods for Langevin dynamics and associated error estimates

2018 ◽  
Vol 52 (3) ◽  
pp. 1051-1083 ◽  
Author(s):  
Julien Roussel ◽  
Gabriel Stoltz
Keyword(s):  
Convergence Rates ◽  
Langevin Dynamics ◽  
Galerkin Methods ◽  
Discrete Level ◽  
Rigidity Matrix ◽  
Poisson Equations ◽  
The Poisson Equation ◽  
Convergence Results ◽  
Abstract Setting ◽  
Tensor Basis

We prove the consistency of Galerkin methods to solve Poisson equations where the differential operator under consideration is hypocoercive. We show in particular how the hypocoercive nature of the generator associated with Langevin dynamics can be used at the discrete level to first prove the invertibility of the rigidity matrix, and next provide error bounds on the approximation of the solution of the Poisson equation. We present general convergence results in an abstract setting, as well as explicit convergence rates for a simple example discretized using a tensor basis. Our theoretical findings are illustrated by numerical simulations.

Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)

1995 ◽  
Vol 47 (2) ◽  
pp. 225-245
Author(s):  
Nakhlé Asmar ◽  
Earl Berkson ◽  
T. A. Gillespie
Keyword(s):  
Abelian Group ◽  
Weak Type ◽  
Full Range ◽  
Locally Compact Abelian Group ◽  
Strong Type ◽  
Locally Compact ◽  
Linearization Methods ◽  
Maximal Theorem ◽  
Abstract Setting ◽  
Central Result

AbstractIn the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.

scholarly journals A proof-theoretic study of abstract termination principles

2019 ◽  
Vol 29 (8) ◽  
pp. 1345-1366 ◽  
Author(s):  
Thomas Powell
Keyword(s):  
Complexity Analysis ◽  
Theoretic Analysis ◽  
Rewrite Systems ◽  
Abstract Setting ◽  
Term Rewrite Systems ◽  
Recursive Path

Abstract We carry out a proof-theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of derivation trees that can be defined in Gödel’s system T plus bar recursion. We then carry out a complexity analysis of these terms and demonstrate how this can be applied to bound the derivational height of term rewrite systems.

scholarly journals Super Exponentially Convergent Approximation to the Solution of the Schrödinger Equation in Abstract Setting

2010 ◽  
Vol 10 (4) ◽  
pp. 345-358 ◽  
Author(s):  
I.P. Gavrilyuk
Keyword(s):  
Schrödinger Equation ◽  
Convergence Rate ◽  
Schrodinger Equation ◽  
Exponential Convergence ◽  
Exponential Convergence Rate ◽  
Abstract Setting

AbstractWe have developed an approximation to the solution of the Schrödinger equation in abstract setting. The accuracy of our approximation depends on the smoothness of this solution. We show that for the analytical initial vectors our approximation possesses a super exponential convergence rate.

Homotopical algebra and triangulated categories

1995 ◽  
Vol 118 (2) ◽  
pp. 259-285 ◽  
Author(s):  
Marco Grandis
Keyword(s):  
Triangulated Category ◽  
Triangulated Categories ◽  
Homotopical Algebra ◽  
Abstract Setting

AbstractWe study here the connections between the well known Puppe-Verdier notion of triangulated category and an abstract setting for homotopical algebra, based on homotopy kernels and cokernels, which was expounded by the author in [11, 13[.We show that a right-homotopical category A (having well-behaved homotopy cokernels, i.e. mapping cones) has a sort of weak triangulated structure with regard to the suspension endofunctor σ, called σ-homotopical category. If A is homotopical and h-stable (in a sense related to the suspension-loop adjunction), this structure is also h-stable, i.e. satisfies ‘up to homotopy’ the axioms of Verdier[29[ for a triangulated category, excepting the octahedral one which depends on some further elementary conditions on the cone endofunctor of A. Every σ-homotopical category can be stabilized, by two universal procedures, respectively initial and terminal.

Virtual and Actual Existentials in English, Swedish and Icelandic

2000 ◽  
Vol 23 (2) ◽  
pp. 163-190
Author(s):  
Piotr Twardzisz
Keyword(s):  
Present Article ◽  
Dynamic Process ◽  
Theoretical Background ◽  
Cognitive Grammar ◽  
Abstract Setting ◽  
Virtual Plane ◽  
Existential Construction ◽  
Direct Apprehension

The focus of my analysis is the so-called existential construction. The languages examined are English, Swedish and Icelandic. The present article assumes the perspective of Ronald W. Langacker's cognitive grammar as the theoretical background. First of all, the assumption is that the unstressed, initial pronoun there, or its Scandinavian equivalents, are semantically definable as abstract-setting subjects of their respective sentences, with, possibly, the exception of Icelandic það. Secondly, the conceptualization of the existential scenes in the three languages is a dynamic process in each case. The dynamicity of the semantics of existential scenes is the result of assuming two planes, the actual and a virtual one, and establishing correspondences between them. The actual plane reflects our direct apprehension of reality. A virtual plane consists in the dynamic re-assignment of roles to the actual elements introduced by means of the virtual abstract-setting subject.

scholarly journals MIXED FINITE ELEMENT FORMULATION OF THE BIHARMONIC EQUATION

2005 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
A. D. GARNADI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimate ◽  
Biharmonic Equation ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Element Formulation ◽  
Abstract Setting ◽  
First Time ◽  
Element Method

<p>We will provide an abstract setting for mixed finite element method for biharmonic equation. The abstract setting casts mixed finite element method for first biharmonic equation and sec- ond biharmonic equation into a single framework altogether. We provide error estimates for both type biharmonic equation, and for the first time an error estimate for the second biharmonic equation.</p>

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